L10a100

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L10a99.gif

L10a99

L10a101.gif

L10a101

Contents

L10a100.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L10a100 at Knotilus!


Link Presentations

[edit Notes on L10a100's Link Presentations]

Planar diagram presentation X10,1,11,2 X12,3,13,4 X14,19,15,20 X18,7,19,8 X16,5,17,6 X4,15,5,16 X6,17,7,18 X20,13,9,14 X2,9,3,10 X8,11,1,12
Gauss code {1, -9, 2, -6, 5, -7, 4, -10}, {9, -1, 10, -2, 8, -3, 6, -5, 7, -4, 3, -8}
A Braid Representative
BraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart2.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart1.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart0.gifBraidPart3.gif
BraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart4.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
A Morse Link Presentation L10a100 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) -\frac{2 u^3 v^2-u^3 v+2 u^2 v^3-3 u^2 v^2+3 u^2 v-u^2-u v^3+3 u v^2-3 u v+2 u-v^2+2 v}{u^{3/2} v^{3/2}} (db)
Jones polynomial -\frac{4}{q^{9/2}}+\frac{2}{q^{7/2}}-\frac{1}{q^{5/2}}-\frac{1}{q^{25/2}}+\frac{2}{q^{23/2}}-\frac{4}{q^{21/2}}+\frac{6}{q^{19/2}}-\frac{7}{q^{17/2}}+\frac{8}{q^{15/2}}-\frac{8}{q^{13/2}}+\frac{5}{q^{11/2}} (db)
Signature -5 (db)
HOMFLY-PT polynomial z^3 a^{11}+2 z a^{11}-z^5 a^9-2 z^3 a^9+z a^9+a^9 z^{-1} -2 z^5 a^7-7 z^3 a^7-6 z a^7-a^7 z^{-1} -z^5 a^5-3 z^3 a^5-z a^5 (db)
Kauffman polynomial -z^5 a^{15}+3 z^3 a^{15}-2 z a^{15}-2 z^6 a^{14}+5 z^4 a^{14}-2 z^2 a^{14}-2 z^7 a^{13}+3 z^5 a^{13}+z^3 a^{13}-2 z^8 a^{12}+5 z^6 a^{12}-8 z^4 a^{12}+7 z^2 a^{12}-z^9 a^{11}+z^7 a^{11}-z^5 a^{11}-z a^{11}-4 z^8 a^{10}+13 z^6 a^{10}-19 z^4 a^{10}+7 z^2 a^{10}-z^9 a^9+6 z^5 a^9-13 z^3 a^9+5 z a^9-a^9 z^{-1} -2 z^8 a^8+4 z^6 a^8-z^4 a^8-3 z^2 a^8+a^8-3 z^7 a^7+10 z^5 a^7-12 z^3 a^7+7 z a^7-a^7 z^{-1} -2 z^6 a^6+5 z^4 a^6-z^2 a^6-z^5 a^5+3 z^3 a^5-z a^5 (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 \
-10-9-8-7-6-5-4-3-2-10χ
-4          11
-6         21-1
-8        2  2
-10       32  -1
-12      52   3
-14     33    0
-16    45     -1
-18   23      1
-20  24       -2
-22 13        2
-24 1         -1
-261          1
Integral Khovanov Homology

(db, data source)

  
\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z} i=-6 i=-4
r=-10 {\mathbb Z}
r=-9 {\mathbb Z}\oplus{\mathbb Z}_2 {\mathbb Z}
r=-8 {\mathbb Z}^{3}\oplus{\mathbb Z}_2 {\mathbb Z}^{2}
r=-7 {\mathbb Z}^{4}\oplus{\mathbb Z}_2^{2} {\mathbb Z}^{2}
r=-6 {\mathbb Z}^{3}\oplus{\mathbb Z}_2^{4} {\mathbb Z}^{4}
r=-5 {\mathbb Z}^{5}\oplus{\mathbb Z}_2^{3} {\mathbb Z}^{3}
r=-4 {\mathbb Z}^{3}\oplus{\mathbb Z}_2^{5} {\mathbb Z}^{5}
r=-3 {\mathbb Z}^{2}\oplus{\mathbb Z}_2^{3} {\mathbb Z}^{3}
r=-2 {\mathbb Z}^{2}\oplus{\mathbb Z}_2^{2} {\mathbb Z}^{2}
r=-1 {\mathbb Z}_2^{2} {\mathbb Z}^{2}
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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L10a99.gif

L10a99

L10a101.gif

L10a101