L11n381

From Knot Atlas
Jump to: navigation, search

L11n380.gif

L11n380

L11n382.gif

L11n382

Contents

L11n381.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11n381 at Knotilus!


Link Presentations

[edit Notes on L11n381's Link Presentations]

Planar diagram presentation X6172 X14,7,15,8 X4,15,1,16 X5,10,6,11 X8493 X22,18,19,17 X11,20,12,21 X19,12,20,13 X18,22,5,21 X9,16,10,17 X2,14,3,13
Gauss code {1, -11, 5, -3}, {-8, 7, 9, -6}, {-4, -1, 2, -5, -10, 4, -7, 8, 11, -2, 3, 10, 6, -9}
A Braid Representative
BraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart2.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gif
BraidPart0.gifBraidPart2.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart2.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart4.gifBraidPart3.gif
BraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart3.gifBraidPart2.gifBraidPart1.gifBraidPart0.gifBraidPart1.gifBraidPart4.gifBraidPart3.gifBraidPart4.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart0.gifBraidPart4.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
A Morse Link Presentation L11n381 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) 0 (db)
Jones polynomial - q^{-7} + q^{-6} - q^{-5} + q^{-3} + q^{-2} +q+2 q^{-1} (db)
Signature -1 (db)
HOMFLY-PT polynomial a^6 \left(-z^2\right)-a^6 z^{-2} -2 a^6+a^4 z^4+5 a^4 z^2+4 a^4 z^{-2} +7 a^4-a^2 z^4-5 a^2 z^2-5 a^2 z^{-2} -8 a^2+z^2+2 z^{-2} +3 (db)
Kauffman polynomial a^6 z^8+a^4 z^8+a^7 z^7+2 a^5 z^7+a^3 z^7-6 a^6 z^6-7 a^4 z^6-a^2 z^6-6 a^7 z^5-14 a^5 z^5-8 a^3 z^5+9 a^6 z^4+15 a^4 z^4+7 a^2 z^4+z^4+10 a^7 z^3+28 a^5 z^3+20 a^3 z^3+2 a z^3-4 a^6 z^2-15 a^4 z^2-15 a^2 z^2-4 z^2-6 a^7 z-19 a^5 z-21 a^3 z-8 a z+3 a^6+10 a^4+11 a^2+5+a^7 z^{-1} +5 a^5 z^{-1} +9 a^3 z^{-1} +5 a z^{-1} -a^6 z^{-2} -4 a^4 z^{-2} -5 a^2 z^{-2} -2 z^{-2} (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 \
-7-6-5-4-3-2-1012χ
3         11
1       1  1
-1      141 2
-3     113  3
-5    13    2
-7   111    1
-9   12     -1
-11 11       0
-13          0
-151         -1
Integral Khovanov Homology

(db, data source)

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

Back to the top.

L11n380.gif

L11n380

L11n382.gif

L11n382