Knot Atlas - User contributions [en]

Data:10 132/ThurstonBennequinNumber

2007-10-10T15:02:36Z

Lng:

Notes for 10 132's three dimensional invariants

2007-10-10T15:01:32Z

Lng:

10<sub>132</sub> is a very interesting knot from the point of view of contact geometry. In particular, it is a transversely nonsimple knot, and it was the last knot with at most 10 crossings for which the maximal Thurston-Bennequin number was calculated.

Who Am I

2007-06-22T14:08:24Z

Lng:

--[[User:Lng|Lng]]

K11n141 Quick Notes

2006-12-02T13:06:34Z

Lng:

Also known as the pretzel knot P(5,-3,-3).

K11n139 Quick Notes

2006-12-02T13:03:12Z

Lng:

Also known as the pretzel knot P(5,3,-3).

K11a362 Quick Notes

2006-12-02T13:02:00Z

Lng:

Also known as the pretzel knot P(5,3,3).

To Do

2006-12-02T12:59:13Z

Lng: /* Papers to consider extracting data from */

* Update this To Do list.
* Make sure all KnotAtlas associated software is in either the KnotTheory or KnotAtlas svn repositories, and document how to get programs from svn. See [[:Category:Software]].
* Remove all the splicing programs.

== Knot Atlas issues ==
* Link to us from relevant pages on wikipedia and elsewhere.
* Add "comment" hooks near each of the sections on the knot pages.
* The right floating tables of contents in the manual don't layout properly in safari. I don't have access to safari, so can't do any testing. --[[User:Scott|Scott]] 05:08, 25 Sep 2005 (EDT)
**You seem to forget that both your officemates have iBooks they bring to school regularly. (as a Safari user, I can attest that this is still a problem a lot of places). [[User:Ben|Ben]] 17:47, 21 Nov 2005 (EST)

=== Pages to write ===
# Further edit [[How you can contribute]].
# Finish [[Extending/Modifying KnotTheory`]].
# Prepare [[List of Modules in KnotTheory`]].
# Document "The A2 invariant", "The G2 invariant" and "other quantum invariants".

=== More complicated projects ===
# Identify torus knots.
## should we have an 'identify this knot' function in [[KnotTheory`]]? How to implement it?
# Clarify orientation issues, especially for links.
# Extend tables beyond 11 crossings.
# Add pages on rational knots and other classes of "special" knots.
# Add a page for "sporadic" special knots.

=== Data to include ===
# Add Tristram-Levine signatures.
# Chiral? Invertible?
# Indicate which knots are the components of given links.
# Add something about hyperbolic invariants.
# "Similar Links" using [[The Multivariable Alexander Polynomial]]; add the The Multivariable Alexander Polynomial to the simulated Mathematica sessions.

==Things to calculate==
# Compute ''HOMFLYPT'' for torus knots -- this has been added to the [[Upload_Queues]].
# compute Reshetikhin-Turaev invariants for everything in sight.

==KnotTheory`==
# Put the MIT license notice in all the source files. (You can consider this note as MIT licensing for now. If you're one of the contributors, and you didn't complain when we proposed MIT licensing for everything, you can still complain now!)
# Write some functions to generate knot families, taking advantage of ConwayNotation. Pretzel knots, etc.
# Unite <code>DrawPD</code> and <code>BraidPlot</code> under Draw.
# Remove <code>Simplify</code> from ColouredJones.
# Custom knot drawings! Output in ps, TeX, etc.
# Browsable source code for <code>KnotTheory`</code>.
# Fix the <tt>In</tt>/<tt>Out</tt> numbering in [[Graphical Input]].

==katlas software==
* Find out if it's possible to eliminate the need for &action=purge when transcluded pages change?
* Tell people about the modifications to [[ImagePage.php]]
* Fix/improve the "disappearing transclusion" tag <nowiki><ifpageexists></nowiki>.
* Replace the "bracket" splicing model by a "templated" one.

==texvc==
# can texvc use dvi2bitmap instead of convert? might be much faster? [http://heim.ifi.uio.no/~simek/document/document.ps]
## alternatively see [http://meta.wikimedia.org/wiki/Problems_with_texvc]
## what about a cron job to randomly delete entries from mw_math, and the corresponding png's?
# Apply patches to texvc, for making transparent, font-sizes png in math mode. [http://meta.wikimedia.org/wiki/Help_talk:Formula]

==Other things==
# Add the Universal Vassiliev Invariant.
# Something about knot colouring.
# Add Ozsvath-Szabo stuff.
# Make all sources public.
# Add Dowker codes for links.
# Identify the knot at http://commons.wikimedia.org/wiki/Image:Gateknot.jpg (see also [[User talk:Drorbn]]).

==Papers to consider extracting data from==
# Extract data from Stanford's paper [http://www.maths.warwick.ac.uk/gt/GTMon4/paper23.abs.html].
# Extract data from Livingston's paper [http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-1.abs.html].
# Extract data from Rasmussen's paper, {{arXiv|math.GT/0402131}}. (I think this has been done - I imported s-invariant data from KnotInfo. --[[User:Scott|Scott]] 02:06, 26 May 2006 (EDT))
# Extract data from Hikami's paper, {{arXiv|math.GT/0403224}}.
# Extract data from Stoimenow's paper, {{arXiv|math.GT/0405076}}.
# Extract data from De Wit and Links, {{arXiv|math.GT/0501224}}, and from De Wit, Ishii and Links, {{arXiv|math.GT/0405403}}.
# Extract data from Cha-Livingston's paper, {{arXiv|math.GT/0503125}}.
# Extract data from Hirasawa-Teragaito's paper, {{arXiv|math.GT/0504446}}.
# Extract data from Cimasoni-Florens' paper, {{arXiv|math.GT/0505185}}.
# Extract data from Ashton-Cantarella-Piatek-Rawdon's paper, {{arXiv|math.DG/0508248}}.
# Boundary slope data. There's Dunfield's paper, and associated program, {{arXiv|math.GT/9901120}}, and also a paper by Hoste and Shanahan {{arXiv|math.GT/0505442}}, which contains data for many two component links.
# Extract data from Baldwin-Gillam's paper, {{arXiv|math.GT/0610167}}.

[[Special:Whatlinkshere&target=Template:Todo-later|Pages with the 'todo-later' template]]
[[Special:Whatlinkshere&target=Template:Todo|Pages with the 'todo' template]]

5 1 Further Notes and Views

2006-08-22T14:08:55Z

Lng:

{|
|- valign=top
{{Knot View Template|
image = 5_1Interlink_160.gif |
text = The VISA Interlink Logo [http://www.cardweb.com/cardtrak/news/2001/september/18a.html]}}
|
{{Knot View Template|
image = ShirtInLisboa_160.jpg |
text = The [http://en.wikipedia.org/wiki/United_States_Bicentennial US bicentennial] logo on a shirt seen in Lisboa [http://www.math.toronto.edu/~drorbn/Talks/Oporto-0407/KnotsInLisboa.html]}}
|
{{Knot View Template|
image = PentagonalTable_120.jpg |
text = A pentagonal table by Bob Mackay [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/PentagonalTable.html]}}
|
{{Knot View Template|
image = UtahSPlogo.jpg |
text = The Utah State Parks logo}}
|}


<font size=-2 color=orange>This sentence was last edited by Dror.</font>
<font size=-2 color=green>Sometime later, Scott added this sentence.</font>

File:UtahSPlogo.jpg

2006-08-22T14:03:30Z

Lng: 5_1 logo for the Utah State Parks system, photo taken at Escalante State Park.

[[5_1]] logo for the Utah State Parks system, photo taken at Escalante State Park.

A Khovanov homology bibliography

2005-12-13T21:00:10Z

Lng:

This is the very beginning of a bibliography for work on Khovanov homology. Anyone should feel free to update, modify, or comment, as they wish.

*D. Bar-Natan, [http://www.math.toronto.edu/~drorbn/papers/Categorification/ ''On Khovanov's categorification of the Jones polynomial''], Algebraic and Geometric Topology 2-16 (2002) 337-370, {{arXiv|math.GT/0201043}}.
*D. Bar-Natan, [http://www.math.toronto.edu/~drorbn/papers/Cobordism/ ''Khovanov's Homology for Tangles and Cobordisms''], Geometry and Topology 9-33 (2005) 1443-1499, {{arXiv|math.GT/0410495}}.
*D. Bar-Natan, [http://www.math.toronto.edu/~drorbn/Talks/GWU-050213/index.html ''I've Computed Kh(T(9,5)) and I'm Happy''], talk given at Knots in Washington XX, George Washington University, February 2005.
*M. Khovanov, ''A categorification of the Jones polynomial'', {{arXiv|math.QA/9908171}}.
*M. Khovanov, ''An invariant of tangle cobordisms'', {{arXiv|math.QA/0207264}}.
*Paul Turner, ''Calculating Bar-Natan's characteristic two Khovanov homology'', {{arXiv|math.GT/0411225}}.
*Jozef H. Przytycki, ''When the theories meet: Khovanov homology as Hochschild homology of links'', {{arXiv|math.GT/0509334}}.
*E. S. Lee, ''An endomorphism of the Khovanov invariant'', Advances in Mathematics 197 (2005) 554-586, {{arXiv|math.GT/0210213}}.
*J. Rasmussen, ''Khovanov homology and the slice genus'', {{arXiv|math.GT/0402131}}.
*P. Seidel and I. Smith, ''A link invariant from the symplectic geometry of nilpotent slices'', {{arXiv|math.SG/0405089}}.
*C. Manolescu, ''Nilpotent slices, Hilbert schemes, and the Jones polynomial'', {{arXiv|math.SG/0411015}}.
*O. Plamenevskaya, ''Transverse knots and Khovanov homology'', {{arXiv|math.GT/0412184}}.
*L. Ng, ''A Legendrian Thurston-Bennequin bound from Khovanov homology'', Algebraic and Geometric Topology 5-66 (2005) 1637-1653, {{arXiv|math.GT/0508649}}.
*{{bibitem|author=|title=|arXiv=math.QA/0409414}}
*http://arxiv.org/abs/math/0509692
*{{bibitem|author=Mikhail Khovanov|title=Triply-graded link homology and Hochschild homology of Soergel bimodules|arXiv=math.GT/0510265}}
*{{arXiv|math/0510382}}
*{{arXiv|math.CO/0412264}}
*http://front.math.ucdavis.edu/math.QA/0304375
*{{arXiv|math.CO/0511557}}
*{{arXiv|math.GT/0511532}}
*{{arXiv|math.QA/0511529}}
*{{arXiv|math.GT/0508064}}

==Todo==
Scott is planning on one day writing some scripts to automate the boring work in making this page work. Ideally, anyone should be able to just enter minimal information for an article (e.g., just math.CO/0412264, or even just a title!) on a line, and have a robot come through later and fill things in.

Such a robot should be able to construct the appropriate link to the arXiv (easy -- use the arXiv template), fill in or correct the author and title, and possibly even send a [[Wikipedia:TrackBack|TrackBack]] ping to the [http://arxiv.org/help/trackback/ arXiv].

A Khovanov homology bibliography

2005-12-13T20:49:54Z

Lng:

This is the very beginning of a bibliography for work on Khovanov homology. Anyone should feel free to update, modify, or comment, as they wish.

*D. Bar-Natan, [http://www.math.toronto.edu/~drorbn/papers/Categorification/ ''On Khovanov's categorification of the Jones polynomial''], Algebraic and Geometric Topology 2-16 (2002) 337-370, {{arXiv|math.GT/0201043}}.
*D. Bar-Natan, [http://www.math.toronto.edu/~drorbn/papers/Cobordism/ ''Khovanov's Homology for Tangles and Cobordisms''], Geometry and Topology 9-33 (2005) 1443-1499, {{arXiv|math.GT/0410495}}.
*D. Bar-Natan, [http://www.math.toronto.edu/~drorbn/Talks/GWU-050213/index.html ''I've Computed Kh(T(9,5)) and I'm Happy''], talk given at Knots in Washington XX, George Washington University, February 2005.
*M. Khovanov, ''A categorification of the Jones polynomial'', {{arXiv|math.QA/9908171}}.
*M. Khovanov, ''An invariant of tangle cobordisms'', {{arXiv|math.QA/0207264}}.
*Paul Turner, ''Calculating Bar-Natan's characteristic two Khovanov homology'', {{arXiv|math.GT/0411225}}.
*Jozef H. Przytycki, ''When the theories meet: Khovanov homology as Hochschild homology of links'', {{arXiv|math.GT/0509334}}.
*Lenhard Ng, ''A Legendrian Thurston-Bennequin bound from Khovanov homology'', Algebraic and Geometric Topology 5 (2005) 1637-1653,{{arXiv|math.GT/0508649}}.
*{{bibitem|author=|title=|arXiv=math.QA/0409414}}
*http://arxiv.org/abs/math/0509692
*{{bibitem|author=Mikhail Khovanov|title=Triply-graded link homology and Hochschild homology of Soergel bimodules|arXiv=math.GT/0510265}}
*{{arXiv|math/0510382}}
*{{arXiv|math.CO/0412264}}
*http://front.math.ucdavis.edu/math.QA/0304375
*{{arXiv|math.CO/0511557}}
*{{arXiv|math.GT/0511532}}
*{{arXiv|math.QA/0511529}}
*{{arXiv|math.GT/0508064}}

==Todo==
Scott is planning on one day writing some scripts to automate the boring work in making this page work. Ideally, anyone should be able to just enter minimal information for an article (e.g., just math.CO/0412264, or even just a title!) on a line, and have a robot come through later and fill things in.

Such a robot should be able to construct the appropriate link to the arXiv (easy -- use the arXiv template), fill in or correct the author and title, and possibly even send a [[Wikipedia:TrackBack|TrackBack]] ping to the [http://arxiv.org/help/trackback/ arXiv].

10 142 Quick Notes

2005-11-07T01:55:19Z

Lng:

Also known as the pretzel knot P(-4,3,3).

10 140 Quick Notes

2005-11-07T01:54:56Z

Lng:

Also known as the pretzel knot P(4,3,-3).

10 126 Quick Notes

2005-11-07T01:54:26Z

Lng:

Also known as the pretzel knot P(-5,3,2).

10 125 Quick Notes

2005-11-07T01:54:02Z

Lng:

Also known as the pretzel knot P(5,-3,2).

10 124 Quick Notes

2005-11-07T01:53:34Z

Lng:

Also known as the torus knot [[T(5,3)]] or the pretzel knot P(5,3,-2). It is one of two knots which are both torus knots and pretzel knots, the other being [[8_19]] = [[T(4,3)]] = P(3,3,-2).

10 61 Quick Notes

2005-11-07T01:50:52Z

Lng:

Also known as the pretzel knot P(4,3,3).

10 46 Quick Notes

2005-11-07T01:50:21Z

Lng:

Also known as the pretzel knot P(5,3,2).

9 46 Quick Notes

2005-11-07T01:49:51Z

Lng:

Also known as the pretzel knot P(3,3,-3).

9 35 Quick Notes

2005-11-07T01:49:21Z

Lng:

Also known as the pretzel knot P(3,3,3).

8 20 Quick Notes

2005-11-07T01:48:44Z

Lng:

Also known as the pretzel knot P(3,-3,2).

8 19 Quick Notes

2005-11-07T01:48:20Z

Lng:

This is the first non-obvious torus knot in the table - it is in fact [[T(4,3)]]. It is also the pretzel knot P(3,3,-2).

8 5 Quick Notes

2005-11-07T01:46:53Z

Lng:

Also known as the pretzel knot P(3,3,2).

File:RHtrefoil-rectilinear.gif

2005-11-03T06:44:21Z

Lng: Rectilinear front diagram for a right-handed trefoil.

Rectilinear front diagram for a right-handed trefoil.

Maximal Thurston-Bennequin number

2005-11-02T21:43:33Z

Lng:

{{Manual TOC Sidebar}}

The Thurston-Bennequin number, usually denoted <math>tb</math>, is an invariant of nullhomologous Legendrian knots in contact manifolds, and in particular Legendrian knots in <math>{\mathbf R}^3</math> with the standard contact structure. It is a classical result of {{ref|Bennequin}} that <math>tb</math> is bounded above for Legendrian knots in any given topological knot type in <math>{\mathbf R}^3</math>. The maximal Thurston-Bennequin number of a smooth knot is the largest value of <math>tb</math> among all Legendrian representatives of the knot.

Here is a quick combinatorial definition of maximal Thurston-Bennequin number. Define a <i>rectilinear front diagram</i> to be a knot diagram composed of only horizontal and vertical line segments, such that at any crossing, the horizontal segment lies over the vertical segment. To any rectilinear front diagram <math>F</math>, one can associate two integers: the writhe <math>w(F)</math>, defined as for any diagram by counting the number of crossings with signs (<math>+1</math> for <math>(\overcrossing)</math> and <math>-1</math> for <math>(\undercrossing)</math>), and the cusp number <math>c(F)</math>, defined to be the number of locally upper-right corners of <math>F</math>. Next define the Thurston-Bennequin number <math>tb(F)</math> to be <math>w(F)-c(F)</math>. Finally, the maximal Thurston-Bennequin number of a knot is the maximal value of <math>tb(F)</math> over all rectilinear front diagrams <math>F</math> in the knot type.

[[Image:RHtrefoil-rectilinear.gif]]

For example, the rectilinear front diagram in the figure, which is a right-handed trefoil, has <math>w=3</math>, <math>c=2</math>, and <math>tb=1</math>. In fact, the maximal Thurston-Bennequin number of the right-handed trefoil is <math>1</math>.

In the Knot Atlas, maximal Thurston-Bennequin number is given as <math>[a][b]</math>, where <math>a</math> and <math>b</math> are the maximal Thurston-Bennequin numbers of the knot and its mirror, respectively.

{{note|Bennequin}} D. Bennequin, ''Entrelacements et équations de Pfaff'', Astérisque '''107-108''' (1983) 87-161.

Template:3D Invariants

2005-11-02T20:57:29Z

Lng: /* Three dimensional invariants */

<div style="border: solid pink 1px">
===[[Three Dimensional Invariants|Three dimensional invariants]]===
<table width=98%>
<tr>

<td>
<table>
<tr style="background: rgb(240,240,240);">
<td>Symmetry type</td>
<td>{{Data:{{PAGENAME}}/Symmetry Type}}</td>
</tr><tr style="background: rgb(240,240,240);">
<td>Unknotting number</td>
<td align=center>{{Data:{{PAGENAME}}/Unknotting Number}}</td>
</tr><tr style="background: rgb(240,240,240);">
<td>3-genus</td>
<td align=center>{{Data:{{PAGENAME}}/3-Genus}}</td>
</tr><ifpageexists><tr style="background: rgb(240,240,240);">
<td>Bridge index</td>
<td align=center>{{Data:{{PAGENAME}}/Bridge Index}}</td>
</tr></ifpageexists>
<ifpageexists><tr style="background: rgb(240,240,240);">
<td>Super bridge index</td>
<td align=center>{{Data:{{PAGENAME}}/Super Bridge Index}}</td>
</tr></ifpageexists>
<ifpageexists><tr style="background: rgb(240,240,240);">
<td>Nakanishi index</td>
<td align=center>{{Data:{{PAGENAME}}/Nakanishi Index}}</td>
</tr></ifpageexists>
<tr style="background: rgb(240,240,240);">
<td>[[Maximal Thurston-Bennequin number]]</td>
<td align=center>{{Data:{{PAGENAME}}/ThurstonBennequinNumber}}</td>
</tr>
</table>
</td><td valign=top>

{{edit link|Notes for {{PAGENAME}}'s three dimensional invariants}}

<ifpageexists>{{:Notes for {{PAGENAME}}'s three dimensional invariants}}</ifpageexists>
</td>
</tr></table>
</div>

Data:0 1/ThurstonBennequinNumber

2005-11-02T20:54:03Z

Lng:

Notes for 10 132's three dimensional invariants

2005-11-02T18:46:54Z

Lng:

It is currently unknown whether the maximal Thurston-Bennequin number for the mirror 10<sub>132</sub> knot is -1 or 0. This is the only knot with at most 10 crossings for which this invariant is unknown.

Template:3D Invariants

2005-11-02T18:35:00Z

Lng: /* Three dimensional invariants */

<div style="border: solid pink 1px">
===[[Three Dimensional Invariants|Three dimensional invariants]]===
<table width=98%>
<tr>

<td>
<table>
<tr style="background: rgb(240,240,240);">
<td>Symmetry type</td>
<td>{{Data:{{PAGENAME}}/Symmetry Type}}</td>
</tr><tr style="background: rgb(240,240,240);">
<td>Unknotting number</td>
<td align=center>{{Data:{{PAGENAME}}/Unknotting Number}}</td>
</tr><tr style="background: rgb(240,240,240);">
<td>3-genus</td>
<td align=center>{{Data:{{PAGENAME}}/3-Genus}}</td>
</tr><ifpageexists><tr style="background: rgb(240,240,240);">
<td>Bridge index</td>
<td align=center>{{Data:{{PAGENAME}}/Bridge Index}}</td>
</tr></ifpageexists>
<ifpageexists><tr style="background: rgb(240,240,240);">
<td>Super bridge index</td>
<td align=center>{{Data:{{PAGENAME}}/Super Bridge Index}}</td>
</tr></ifpageexists>
<ifpageexists><tr style="background: rgb(240,240,240);">
<td>Nakanishi index</td>
<td align=center>{{Data:{{PAGENAME}}/Nakanishi Index}}</td>
</tr></ifpageexists>
<ifpageexists><tr style="background: rgb(240,240,240);">
<td>Maximal Thurston-Bennequin number</td>
<td align=center>{{Data:{{PAGENAME}}/ThurstonBennequinNumber}}</td>
</tr></ifpageexists>
</table>
</td><td valign=top>

{{edit link|Notes for {{PAGENAME}}'s three dimensional invariants}}

<ifpageexists>{{:Notes for {{PAGENAME}}'s three dimensional invariants}}</ifpageexists>
</td>
</tr></table>
</div>

Template:3D Invariants

2005-11-02T18:32:18Z

Lng: /* Three dimensional invariants */

<div style="border: solid pink 1px">
===[[Three Dimensional Invariants|Three dimensional invariants]]===
<table width=98%>
<tr>

<td>
<table>
<tr style="background: rgb(240,240,240);">
<td>Symmetry type</td>
<td>{{Data:{{PAGENAME}}/Symmetry Type}}</td>
</tr><tr style="background: rgb(240,240,240);">
<td>Unknotting number</td>
<td align=center>{{Data:{{PAGENAME}}/Unknotting Number}}</td>
</tr><tr style="background: rgb(240,240,240);">
<td>3-genus</td>
<td align=center>{{Data:{{PAGENAME}}/3-Genus}}</td>
</tr><ifpageexists><tr style="background: rgb(240,240,240);">
<td>Bridge index</td>
<td align=center>{{Data:{{PAGENAME}}/Bridge Index}}</td>
</tr></ifpageexists>
<ifpageexists><tr style="background: rgb(240,240,240);">
<td>Super bridge index</td>
<td align=center>{{Data:{{PAGENAME}}/Super Bridge Index}}</td>
</tr></ifpageexists>
<ifpageexists><tr style="background: rgb(240,240,240);">
<td>Nakanishi index</td>
<td align=center>{{Data:{{PAGENAME}}/Nakanishi Index}}</td>
</tr></ifpageexists>
<tr style="background: rgb(240,240,240);">
<td>[[Maximal Thurston-Bennequin number]]'''</td>
<td align=center>{{Data:{{PAGENAME}}/ThurstonBennequinNumber}}</td>
</tr>
</table>
</td><td valign=top>

{{edit link|Notes for {{PAGENAME}}'s three dimensional invariants}}

<ifpageexists>{{:Notes for {{PAGENAME}}'s three dimensional invariants}}</ifpageexists>
</td>
</tr></table>
</div>

Template:3D Invariants

2005-11-02T18:18:29Z

Lng: /* Three dimensional invariants */

<div style="border: solid pink 1px">
===[[Three Dimensional Invariants|Three dimensional invariants]]===
<table width=98%>
<tr>

<td>
<table>
<tr style="background: rgb(240,240,240);">
<td>Symmetry type</td>
<td>{{Data:{{PAGENAME}}/Symmetry Type}}</td>
</tr><tr style="background: rgb(240,240,240);">
<td>Unknotting number</td>
<td align=center>{{Data:{{PAGENAME}}/Unknotting Number}}</td>
</tr><tr style="background: rgb(240,240,240);">
<td>3-genus</td>
<td align=center>{{Data:{{PAGENAME}}/3-Genus}}</td>
</tr><ifpageexists><tr style="background: rgb(240,240,240);">
<td>Bridge index</td>
<td align=center>{{Data:{{PAGENAME}}/Bridge Index}}</td>
</tr></ifpageexists>
<ifpageexists><tr style="background: rgb(240,240,240);">
<td>Super bridge index</td>
<td align=center>{{Data:{{PAGENAME}}/Super Bridge Index}}</td>
</tr></ifpageexists>
<ifpageexists><tr style="background: rgb(240,240,240);">
<td>Nakanishi index</td>
<td align=center>{{Data:{{PAGENAME}}/Nakanishi Index}}</td>
</tr></ifpageexists>
<ifpageexists><tr style="background: rgb(240,240,240);">
<td>[[Maximal Thurston-Bennequin number]]</td>
<td align=center>{{Data:{{PAGENAME}}/ThurstonBennequinNumber}}</td>
</tr></ifpageexists>
</table>
</td><td valign=top>

{{edit link|Notes for {{PAGENAME}}'s three dimensional invariants}}

<ifpageexists>{{:Notes for {{PAGENAME}}'s three dimensional invariants}}</ifpageexists>
</td>
</tr></table>
</div>

Who Am I

2005-11-02T00:22:38Z

Lng:

--[[User:Lng|Lng]]

To Do

2005-11-01T21:04:26Z

Lng: /* Other things */

* Update this To Do list.

* Set up a backup routine.
** Make sure we're backing up all the right things. In particular, httpd.conf should probably be backed up.
* Systematic updates of the executable programs (KnotTheory`, WikiLink.m, splicers). See [[:Category:Software]].

== Knot Atlas issues ==
* Link to us from relevant pages on wikipedia and elsewhere.
* Add "comment" hooks near each of the sections on the knot pages.
** Eliminate the need for "&action=purge" after editing a comments section.
* Learn some MySQL and figure how to do "bulk additions from a file" to the database. This is a 'Dror and Scott only' technique, because it requires direct database access, and in most cases we'd be better off thinking in terms of uploading via WikiLink; either command line java, or a mathematica notebook. But direct SQL may be the only way to go for loading data for, say, all 16 crossing knots.
* The right floating tables of contents in the manual don't layout properly in safari. I don't have access to safari, so can't do any testing. --[[User:Scott|Scott]] 05:08, 25 Sep 2005 (EDT)
* The "Quantum Invariants" pages have no link back to the "parent" knot page". What's worse, they are not generated in a way that allows to add such "link back" in an easy way! See e.g. [[3_1_Quantum_Invariants]].

=== Pages to write ===
# Further edit [[How you can contribute]].
# Finish [[Extending/Modifying KnotTheory`]].
# Prepare [[List of Modules in KnotTheory`]].
# Document "The A2 invariant", "The G2 invariant" and "other quantum invariants".

=== More complicated projects ===
# Identify torus knots.
## should we have an 'identify this knot' function in [[KnotTheory`]]? How to implement it?
# Clarify orientation issues, especially for links.
# Extend tables beyond 11 crossings.
# work out a sensible way to show quantum knot invariants.
# Add pages on rational knots and other classes of "special" knots.
# Add a page for "sporadic" special knots.

=== Data to include ===
# Add Tristram-Levine signatures.
# Chiral? Invertible?
# Indicate which knots are the components of given links.
# Add something about hyperbolic invariants.
# "Similar Links" using [[The Multivariable Alexander Polynomial]]; add the The Multivariable Alexander Polynomial to the simulated Mathematica sessions.

==Things to calculate==
# Compute ''HOMFLYPT'' for torus knots.
# compute Reshetikhin-Turaev invariants for everything in sight.

==KnotTheory`==
# Unite <code>DrawPD</code> and <code>BraidPlot</code> under Draw.
# Remove <code>Simplify</code> from ColouredJones.
# Custom knot drawings! Output in ps, TeX, etc.
# Browsable source code for <code>KnotTheory`</code>.

==katlas software==
* Find out if it's possible to eliminate the need for &action=purge when transcluded pages change?
* Tell people about the modifications to [[ImagePage.php]]
* Fix/improve the "disappearing transclusion" tag <nowiki><ifpageexists></nowiki>.
* Replace the "bracket" splicing model by a "templated" one.

===texvc===
# can texvc use dvi2bitmap instead of convert? might be much faster? [http://heim.ifi.uio.no/~simek/document/document.ps]
## alternatively see [http://meta.wikimedia.org/wiki/Problems_with_texvc]
## what about a cron job to randomly delete entries from mw_math, and the corresponding png's?
# Apply patches to texvc, for making transparent, font-sizes png in math mode. [http://meta.wikimedia.org/wiki/Help_talk:Formula]

==Other things==
# Add the Universal Vassiliev Invariant.
# Something about knot colouring.
# Add Ozsvath-Szabo stuff.
# Make all sources public.
# Add Dowker codes for links.

==Papers to consider extracting data from==
# Extract data from Stanford's paper [http://www.maths.warwick.ac.uk/gt/GTMon4/paper23.abs.html].
# Extract data from Livingston's paper [http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-1.abs.html].
# Extract data from Rasmussen's paper, {{arXiv|math.GT/0402131}}.
# Extract data from Hikami's paper, {{arXiv|math.GT/0403224}}.
# Extract data from Stoimenow's paper, {{arXiv|math.GT/0405076}}.
# Extract data from De Wit and Links, {{arXiv|math.GT/0501224}}, and from De Wit, Ishii and Links, {{arXiv|math.GT/0405403}}.
# Extract data from Cha-Livingston's paper, {{arXiv|math.GT/0503125}}.
# Extract data from Hirasawa-Teragaito's paper, {{arXiv|math.GT/0504446}}.
# Extract data from Cimasoni-Florens' paper, {{arXiv|math.GT/0505185}}.
# Extract data from Hoste-Shanahan's paper, {{arXiv|math.GT/0505442}}.
# Extract data from Ashton-Cantarella-Piatek-Rawdon's paper, {{arXiv|math.DG/0508248}}.
# Extract A-polynomial data from Cooper-Culler-Gillet-Long-Shalen.

[[Special:Whatlinkshere&target=Template:Todo-later|Pages with the 'todo-later' template]]
[[Special:Whatlinkshere&target=Template:Todo|Pages with the 'todo' template]]