L11a94

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L11a93.gif

L11a93

L11a95.gif

L11a95

Contents

L11a94.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11a94 at Knotilus!


Link Presentations

[edit Notes on L11a94's Link Presentations]

Planar diagram presentation X6172 X12,4,13,3 X20,8,21,7 X22,17,5,18 X18,21,19,22 X16,10,17,9 X14,12,15,11 X10,16,11,15 X8,20,9,19 X2536 X4,14,1,13
Gauss code {1, -10, 2, -11}, {10, -1, 3, -9, 6, -8, 7, -2, 11, -7, 8, -6, 4, -5, 9, -3, 5, -4}
A Braid Representative
BraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart2.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart1.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gif
BraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart1.gifBraidPart2.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart2.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart1.gifBraidPart4.gif
BraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart1.gifBraidPart2.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart2.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart1.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart0.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart1.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart3.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
A Morse Link Presentation L11a94 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) \frac{(u-1) (v-1) \left(2 v^2-7 v+2\right)}{\sqrt{u} v^{3/2}} (db)
Jones polynomial q^{15/2}-3 q^{13/2}+6 q^{11/2}-10 q^{9/2}+12 q^{7/2}-14 q^{5/2}+14 q^{3/2}-12 \sqrt{q}+\frac{8}{\sqrt{q}}-\frac{5}{q^{3/2}}+\frac{2}{q^{5/2}}-\frac{1}{q^{7/2}} (db)
Signature 1 (db)
HOMFLY-PT polynomial z a^{-7} -2 z^3 a^{-5} -z a^{-5} +z^5 a^{-3} +a^3 z-z a^{-3} +a^3 z^{-1} - a^{-3} z^{-1} +z^5 a^{-1} -2 a z^3+z^3 a^{-1} -3 a z+3 z a^{-1} -2 a z^{-1} +2 a^{-1} z^{-1} (db)
Kauffman polynomial z^6 a^{-8} -3 z^4 a^{-8} +2 z^2 a^{-8} +3 z^7 a^{-7} -9 z^5 a^{-7} +7 z^3 a^{-7} -2 z a^{-7} +4 z^8 a^{-6} -10 z^6 a^{-6} +5 z^4 a^{-6} -z^2 a^{-6} +3 z^9 a^{-5} -4 z^7 a^{-5} -4 z^5 a^{-5} +5 z^3 a^{-5} -2 z a^{-5} +z^{10} a^{-4} +4 z^8 a^{-4} -13 z^6 a^{-4} +10 z^4 a^{-4} -2 z^2 a^{-4} +5 z^9 a^{-3} -10 z^7 a^{-3} +a^3 z^5+10 z^5 a^{-3} -3 a^3 z^3-6 z^3 a^{-3} +3 a^3 z+3 z a^{-3} -a^3 z^{-1} - a^{-3} z^{-1} +z^{10} a^{-2} +2 z^8 a^{-2} +2 a^2 z^6-2 z^6 a^{-2} -4 a^2 z^4-z^4 a^{-2} +2 a^2 z^2+3 z^2 a^{-2} +2 z^9 a^{-1} +2 a z^7-z^7 a^{-1} +a z^5+5 z^5 a^{-1} -9 a z^3-10 z^3 a^{-1} +8 a z+8 z a^{-1} -2 a z^{-1} -2 a^{-1} z^{-1} +2 z^8+2 z^6-7 z^4+4 z^2-1 (db)

Khovanov Homology

The coefficients of the monomials t^rq^j are shown, along with their alternating sums \chi (fixed j, alternation over r).   
\ r
  \  
j \
-4-3-2-101234567χ
16           1-1
14          2 2
12         41 -3
10        62  4
8       64   -2
6      86    2
4     66     0
2    68      -2
0   48       4
-2  14        -3
-4 14         3
-6 1          -1
-81           1
Integral Khovanov Homology

(db, data source)

  
\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z} i=0 i=2
r=-4 {\mathbb Z}
r=-3 {\mathbb Z}\oplus{\mathbb Z}_2 {\mathbb Z}
r=-2 {\mathbb Z}^{4}\oplus{\mathbb Z}_2 {\mathbb Z}
r=-1 {\mathbb Z}^{4}\oplus{\mathbb Z}_2^{4} {\mathbb Z}^{4}
r=0 {\mathbb Z}^{8}\oplus{\mathbb Z}_2^{4} {\mathbb Z}^{6}
r=1 {\mathbb Z}^{8}\oplus{\mathbb Z}_2^{6} {\mathbb Z}^{6}
r=2 {\mathbb Z}^{6}\oplus{\mathbb Z}_2^{8} {\mathbb Z}^{8}
r=3 {\mathbb Z}^{6}\oplus{\mathbb Z}_2^{6} {\mathbb Z}^{6}
r=4 {\mathbb Z}^{4}\oplus{\mathbb Z}_2^{6} {\mathbb Z}^{6}
r=5 {\mathbb Z}^{2}\oplus{\mathbb Z}_2^{4} {\mathbb Z}^{4}
r=6 {\mathbb Z}\oplus{\mathbb Z}_2^{2} {\mathbb Z}^{2}
r=7 {\mathbb Z}_2 {\mathbb Z}

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).

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L11a93.gif

L11a93

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L11a95