Link Splice Base: Difference between revisions

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<!-- <*K=Knot[ThisKnot];{n,k}=List@@K;*> -->
<!-- <* (* -->{{Splice Base Notice}}<!-- *) *> -->
<!-- <* (* --><!-- You can ignore this warning; it's for people trying to edit individual knot pages--><!-- *) *> -->

<!-- WARNING! WARNING! WARNING!
<!-- provide an anchor so we can return to the top of the page -->
<!-- This page was generated from the splice template [[Link Splice Template]]. Please do not edit!
<span id="top"></span>
<!-- Almost certainly, you want to edit [[Template:Link Page]], which actually produces this page.

<!-- The text below simply calls [[Template:Link Page]] setting the values of all the parameters appropriately.
<!-- this relies on transclusion for next and previous links -->
<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Link Splice Template]]. -->
{{Knot Navigation Links|ext=gif}}
<!-- <*{n,k}=Drop[List@@K,{2}];*> -->

{{Link Page|
{| align=left
n = <*n*> |
|- valign=top
t = <*If[AlternatingQ[K],"a","n"]*> |
|[[Image:{{PAGENAME}}.gif]]
k = <*k*> |
|{{Link Knot Site Links |n=<*n*>|t=<*If[AlternatingQ[K],"a","n"]*>|k=<*k*>|KnotilusURL=<*KnotilusURL[K]*>}}
KnotilusURL = <*KnotilusURL[K]*> |
|{{:{{PAGENAME}} Quick Notes}}
braid_table = <* BraidPlot[CollapseBraid[BR[K]], Mode -> "Wiki",
⚫
|}
Images -> {"BraidPart0.gif", "BraidPart1.gif",

"BraidPart2.gif", "BraidPart3.gif", "BraidPart4.gif"}] *> |
<br style="clear:both" />
⚫
khovanov_table = <*TabularKh[Kh[K][q, t], KnotSignature[K]+{1,-1}]*>

⚫
}}
{{:{{PAGENAME}} Further Notes and Views}}

{{Link Presentations}}
{{Link Polynomial Invariants}}
{{Vassiliev Invariants}}

===[[Khovanov Homology]]===

The coefficients of the monomials <math>t^rq^j</math> are shown, along with their alternating sums <math>\chi</math> (fixed <math>j</math>, alternation over <math>r</math>). The squares with <font class=HLYellow>yellow</font> highlighting are those on the "critical diagonals", where <math>j-2r=s+1</math> or <math>j-2r=s+1</math>, where <math>s=</math>{{Data:{{PAGENAME}}/Signature}} is the signature of {{PAGENAME}}. Nonzero entries off the critical diagonals (if any exist) are highlighted in <font class=HLRed>red</font>.

⚫
<center><*TabularKh[Kh[K][q, t], KnotSignature[K]+{1,-1}]*></center>

{{Computer Talk Header}}

<table>
<tr valign=top>
<td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=&nbsp;&nbsp;&nbsp;&nbsp;</pre></td>
<td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td>
</tr>
<tr valign=top><td colspan=2><pre style="border: 0px; padding: 0em"><*InOut[1]; KnotTheoryWelcomeMessage[]*></pre></td></tr>
<*InOut["Crossings[``]", K]*>
<*InOut["PD[``]", K]*>
<*InOut["GaussCode[``]", K]*>
<*InOut["BR[``]", K]*>
<*InOut["alex = Alexander[``][t]", K]*>
<*InOut["Conway[``][z]", K]*>
<*InOut["Select[AllKnots[], (alex === Alexander[#][t])&]"]*>
<*InOut["{KnotDet[`1`], KnotSignature[`1`]}", K]*>
<*InOut["J=Jones[``][q]", K]*>
<*InOut[
"Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]"
]*>
<* If[Crossings[K]<=18, Include["ColouredJonesM.mhtml"] ,""] *>
<*InOut["A2Invariant[``][q]", K]*>
<*InOut["Kauffman[``][a, z]", K]*>
<*InOut["{Vassiliev[2][`1`], Vassiliev[3][`1`]}", K ]*>
<*InOut["Kh[``][q, t]", K]*>
</table>

<* (* <!-- *) *> {{Category:Knot Page}} <* (* --> *) *>
<* (* {{Category:Splice Template}} *) *>

Latest revision as of 16:11, 18 September 2005

Stop hand.png This page is a 'splice base'.
It is used to generate knot pages for each knot in a certain knot table. Be careful editting! Changes will not be reflected on individual knot pages until the 'splicer' is run again.

[[Image:Data:Link Splice Base/Previous Knot.gif|80px|link=Data:Link Splice Base/Previous Knot]]

[[Data:Link Splice Base/Previous Knot]]

[[Image:Data:Link Splice Base/Next Knot.gif|80px|link=Data:Link Splice Base/Next Knot]]

[[Data:Link Splice Base/Next Knot]]

File:Link Splice Base.gif
(Knotscape image) 		See the full Thistlethwaite Link Table (up to 11 crossings).

Visit Data:Link Splice Base/KnotilusGaussCode Link Splice Base at Knotilus!

[edit Link Splice Base Quick Notes]
[edit Link Splice Base Further Notes and Views]


Link Presentations

[edit Notes on Link Splice Base's Link Presentations]

Planar diagram presentation Data:Link Splice Base/PD Presentation
Gauss code Data:Link Splice Base/Gauss Code
A Braid Representative <* BraidPlot[CollapseBraid[BR[K]], Mode -> "Wiki", 
                     Images -> {"BraidPart0.gif", "BraidPart1.gif",
                    "BraidPart2.gif", "BraidPart3.gif", "BraidPart4.gif"}] *>
A Morse Link Presentation File:Link Splice Base ML.gif

Khovanov Homology

The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ).    Data:Link Splice Base/KhovanovTable
Integral Khovanov Homology

(db, data source)

   Data:Link Splice Base/Integral Khovanov Homology

Computer Talk

Much of the above data can be recomputed by Mathematica using the package KnotTheory`. See A Sample KnotTheory` Session.

Modifying This Page

Read me first: Modifying Knot Pages

See/edit the Link Page master template (intermediate).

See/edit the Link_Splice_Base (expert).

Back to the top.

[[Image:Data:Link Splice Base/Previous Knot.gif|80px|link=Data:Link Splice Base/Previous Knot]]

[[Data:Link Splice Base/Previous Knot]]

[[Image:Data:Link Splice Base/Next Knot.gif|80px|link=Data:Link Splice Base/Next Knot]]

[[Data:Link Splice Base/Next Knot]]

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