Template:Hoste-Thistlethwaite Knot Page
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| File:Hoste-Thistlethwaite Knot Page.gif (Knotscape image) |
Visit [{{{KnotilusURL}}} Hoste-Thistlethwaite Knot Page's page] at Knotilus!
Visit Hoste-Thistlethwaite Knot Page's page at the original Knot Atlas! |
| Edit Hoste-Thistlethwaite Knot Page Quick Notes
<ifpageexists>Hoste-Thistlethwaite Knot Page Quick Notes</ifpageexists> |
Edit Hoste-Thistlethwaite Knot Page Further Notes and Views <ifpageexists>Hoste-Thistlethwaite Knot Page Further Notes and Views</ifpageexists>
Knot presentations
| Planar diagram presentation | Data:Hoste-Thistlethwaite Knot Page/PD Presentation |
| Gauss code | Data:Hoste-Thistlethwaite Knot Page/Gauss Code |
| Dowker-Thistlethwaite code | Data:Hoste-Thistlethwaite Knot Page/DT Code |
| A Braid Representative
(for some knots you may need a wide browser window!) |
{{{braid_table}}} |
| A Morse Link Presentation | File:Hoste-Thistlethwaite Knot Page ML.gif |
Three dimensional invariants
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[edit Notes for Hoste-Thistlethwaite Knot Page's three dimensional invariants] |
Four dimensional invariants
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[edit Notes for Hoste-Thistlethwaite Knot Page's four dimensional invariants] |
Polynomial invariants
KnotTheory`, as shown in the (simulated) Mathematica session below. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting. This Mathematica session is also available (albeit only for the knot 5_2) as the notebook PolynomialInvariantsSession.nb.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
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AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.
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In[3]:=
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K = Knot["Hoste-Thistlethwaite Knot Page"];
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In[4]:=
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Alexander[K][t]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
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Data:Hoste-Thistlethwaite Knot Page/Alexander Polynomial |
In[5]:=
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Conway[K][z]
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Out[5]=
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Data:Hoste-Thistlethwaite Knot Page/Conway Polynomial |
In[6]:=
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Alexander[K, 2][t]
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KnotTheory::credits: The program Alexander[K, r] to compute Alexander ideals was written by Jana Archibald at the University of Toronto in the summer of 2005.
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Out[6]=
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Data:Hoste-Thistlethwaite Knot Page/2nd AlexanderIdeal |
In[7]:=
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{KnotDet[K], KnotSignature[K]}
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Out[7]=
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{ Data:Hoste-Thistlethwaite Knot Page/Determinant, Data:Hoste-Thistlethwaite Knot Page/Signature } |
In[8]:=
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Jones[K][q]
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KnotTheory::loading: Loading precomputed data in Jones4Knots`.
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Out[8]=
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Data:Hoste-Thistlethwaite Knot Page/Jones Polynomial |
In[9]:=
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HOMFLYPT[K][a, z]
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KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
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Out[9]=
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Data:Hoste-Thistlethwaite Knot Page/HOMFLYPT Polynomial |
In[10]:=
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Kauffman[K][a, z]
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KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
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Out[10]=
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Data:Hoste-Thistlethwaite Knot Page/Kauffman Polynomial |
"Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {{{{same_alexander}}}}
Same Jones Polynomial (up to mirroring, ): {{{{same_jones}}}}
KnotTheory`. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
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AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
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In[3]:=
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K = Knot["Hoste-Thistlethwaite Knot Page"];
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In[4]:=
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{A = Alexander[K][t], J = Jones[K][q]}
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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KnotTheory::loading: Loading precomputed data in Jones4Knots`.
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Out[4]=
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{ Data:Hoste-Thistlethwaite Knot Page/Alexander Polynomial, Data:Hoste-Thistlethwaite Knot Page/Jones Polynomial } |
In[5]:=
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DeleteCases[Select[AllKnots[], (A === Alexander[#][t]) &], K]
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KnotTheory::loading: Loading precomputed data in DTCode4KnotsTo11`.
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KnotTheory::credits: The GaussCode to PD conversion was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.
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Out[5]=
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{{{{same_alexander}}}} |
In[6]:=
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DeleteCases[
Select[
AllKnots[],
(J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) &
],
K
]
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KnotTheory::loading: Loading precomputed data in Jones4Knots11`.
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Out[6]=
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{{{{same_jones}}}} |
Vassiliev invariants
| V2 and V3: | (Data:Hoste-Thistlethwaite Knot Page/V 2, Data:Hoste-Thistlethwaite Knot Page/V 3) |
V2,1 through V6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V2 and V3.
Khovanov Homology
| The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ). The squares with yellow highlighting are those on the "critical diagonals", where or , where Data:Hoste-Thistlethwaite Knot Page/Signature is the signature of Hoste-Thistlethwaite Knot Page. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. | Data:Hoste-Thistlethwaite Knot Page/KhovanovTable |
| Integral Khovanov Homology
(db, data source) |
Data:Hoste-Thistlethwaite Knot Page/Integral Khovanov Homology |
Computer Talk
Much of the above data can be recomputed by Mathematica using the package KnotTheory`. See A Sample KnotTheory` Session.
{{{computer_talk}}}
Modifying This Page
| Read me first: Modifying Knot Pages.
See/edit the Hoste-Thistlethwaite Knot Page master template (intermediate). See/edit the Hoste-Thistlethwaite_Splice_Base (expert). Back to the top. |
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