L11n199

From Knot Atlas
Jump to: navigation, search

L11n198.gif

L11n198

L11n200.gif

L11n200

Contents

L11n199.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11n199 at Knotilus!


Link Presentations

[edit Notes on L11n199's Link Presentations]

Planar diagram presentation X10,1,11,2 X12,3,13,4 X5,14,6,15 X16,7,17,8 X20,15,21,16 X13,18,14,19 X21,6,22,7 X17,22,18,9 X4,19,5,20 X2,9,3,10 X8,11,1,12
Gauss code {1, -10, 2, -9, -3, 7, 4, -11}, {10, -1, 11, -2, -6, 3, 5, -4, -8, 6, 9, -5, -7, 8}
A Braid Representative
BraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart2.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart1.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gif
BraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart3.gif
BraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gif
A Morse Link Presentation L11n199 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) -\frac{u^3 v^4+u^2 v^5-u^2 v^4+u^2 v^2+u v^3-u v+u+v}{u^{3/2} v^{5/2}} (db)
Jones polynomial -\frac{1}{q^{7/2}}+\frac{1}{q^{9/2}}-\frac{2}{q^{11/2}}+\frac{1}{q^{13/2}}-\frac{1}{q^{15/2}}+\frac{1}{q^{17/2}}-\frac{1}{q^{19/2}} (db)
Signature -7 (db)
HOMFLY-PT polynomial -z a^{13}-a^{13} z^{-1} +z^5 a^{11}+6 z^3 a^{11}+8 z a^{11}+3 a^{11} z^{-1} -z^7 a^9-6 z^5 a^9-10 z^3 a^9-6 z a^9-2 a^9 z^{-1} -z^7 a^7-6 z^5 a^7-10 z^3 a^7-5 z a^7 (db)
Kauffman polynomial z^2 a^{14}-a^{14}+z^3 a^{13}-z a^{13}+a^{13} z^{-1} -z^8 a^{12}+7 z^6 a^{12}-15 z^4 a^{12}+13 z^2 a^{12}-3 a^{12}-z^9 a^{11}+7 z^7 a^{11}-17 z^5 a^{11}+22 z^3 a^{11}-14 z a^{11}+3 a^{11} z^{-1} -2 z^8 a^{10}+12 z^6 a^{10}-20 z^4 a^{10}+12 z^2 a^{10}-3 a^{10}-z^9 a^9+6 z^7 a^9-11 z^5 a^9+11 z^3 a^9-8 z a^9+2 a^9 z^{-1} -z^8 a^8+5 z^6 a^8-5 z^4 a^8-z^7 a^7+6 z^5 a^7-10 z^3 a^7+5 z a^7 (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 \
-8-7-6-5-4-3-2-10χ
-6        11
-8       110
-10      1  1
-12    111  1
-14   121   0
-16   11    0
-18  22     0
-201        1
-2211       0
Integral Khovanov Homology

(db, data source)

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

Back to the top.

L11n198.gif

L11n198

L11n200.gif

L11n200