L11n133

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L11n132.gif

L11n132

L11n134.gif

L11n134

Contents

L11n133.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11n133 at Knotilus!


Link Presentations

[edit Notes on L11n133's Link Presentations]

Planar diagram presentation X8192 X18,11,19,12 X3,10,4,11 X2,17,3,18 X12,5,13,6 X6718 X9,16,10,17 X13,20,14,21 X15,22,16,7 X19,4,20,5 X21,14,22,15
Gauss code {1, -4, -3, 10, 5, -6}, {6, -1, -7, 3, 2, -5, -8, 11, -9, 7, 4, -2, -10, 8, -11, 9}
A Braid Representative
BraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gif
BraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart3.gifBraidPart3.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart3.gif
BraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gif
A Morse Link Presentation L11n133 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) -\frac{u^2 v^6+u v^4-u v^3+u v^2+1}{u v^3} (db)
Jones polynomial -\frac{1}{q^{9/2}}+\frac{1}{q^{25/2}}-\frac{1}{q^{23/2}}+\frac{1}{q^{21/2}}-\frac{1}{q^{19/2}}-\frac{1}{q^{13/2}} (db)
Signature -7 (db)
HOMFLY-PT polynomial -z^3 a^{13}-3 z a^{13}-2 a^{13} z^{-1} +z^7 a^{11}+8 z^5 a^{11}+20 z^3 a^{11}+18 z a^{11}+5 a^{11} z^{-1} -z^9 a^9-9 z^7 a^9-28 z^5 a^9-36 z^3 a^9-18 z a^9-3 a^9 z^{-1} (db)
Kauffman polynomial a^{16} z^2-a^{16}+a^{15} z^3-a^{15} z+a^{14} z^2-a^{13} z^3+4 a^{13} z-2 a^{13} z^{-1} +a^{12} z^8-8 a^{12} z^6+20 a^{12} z^4-18 a^{12} z^2+5 a^{12}+a^{11} z^9-9 a^{11} z^7+28 a^{11} z^5-38 a^{11} z^3+23 a^{11} z-5 a^{11} z^{-1} +a^{10} z^8-8 a^{10} z^6+20 a^{10} z^4-18 a^{10} z^2+5 a^{10}+a^9 z^9-9 a^9 z^7+28 a^9 z^5-36 a^9 z^3+18 a^9 z-3 a^9 z^{-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 \
-9-8-7-6-5-4-3-2-10χ
-8         11
-10         11
-12       1  1
-14     1    1
-16     11   0
-18   21     1
-20   11     0
-22 11       0
-24          0
-261         -1
Integral Khovanov Homology

(db, data source)

  
\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z} i=-10 i=-8 i=-6
r=-9 {\mathbb Z}
r=-8 {\mathbb Z}_2 {\mathbb Z}
r=-7 {\mathbb Z}
r=-6 {\mathbb Z}\oplus{\mathbb Z}_2 {\mathbb Z}^{2}
r=-5 {\mathbb Z} {\mathbb Z}
r=-4 {\mathbb Z} {\mathbb Z}
r=-3 {\mathbb Z}
r=-2 {\mathbb Z}_2 {\mathbb Z}
r=-1
r=0 {\mathbb Z} {\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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L11n132

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L11n134