L11n383

From Knot Atlas
Jump to: navigation, search

L11n382.gif

L11n382

L11n384.gif

L11n384

Contents

L11n383.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11n383 at Knotilus!


Link Presentations

[edit Notes on L11n383's Link Presentations]

Planar diagram presentation X6172 X14,7,15,8 X4,15,1,16 X10,6,11,5 X8493 X17,22,18,19 X11,20,12,21 X19,12,20,13 X21,18,22,5 X16,10,17,9 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.gifBraidPart1.gifBraidPart2.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart4.gifBraidPart1.gifBraidPart4.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart0.gifBraidPart2.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 L11n383 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) -\frac{(t(1)-1) (t(3)-1)^2 \left(t(3)^3+t(2)\right)}{\sqrt{t(1)} \sqrt{t(2)} t(3)^{5/2}} (db)
Jones polynomial - q^{-7} +3 q^{-6} -3 q^{-5} +5 q^{-4} -4 q^{-3} +q^2+6 q^{-2} -2 q-4 q^{-1} +3 (db)
Signature 0 (db)
HOMFLY-PT polynomial -z^2 a^6+a^6 z^{-2} -a^6+2 z^4 a^4+6 z^2 a^4-2 a^4 z^{-2} +2 a^4-z^6 a^2-5 z^4 a^2-8 z^2 a^2+a^2 z^{-2} -3 a^2+z^4+3 z^2+2 (db)
Kauffman polynomial 2 a^5 z^9+2 a^3 z^9+3 a^6 z^8+7 a^4 z^8+4 a^2 z^8+a^7 z^7-7 a^5 z^7-6 a^3 z^7+2 a z^7-15 a^6 z^6-36 a^4 z^6-21 a^2 z^6-4 a^7 z^5-a^5 z^5-5 a^3 z^5-8 a z^5+20 a^6 z^4+53 a^4 z^4+36 a^2 z^4+3 z^4+3 a^7 z^3+11 a^5 z^3+17 a^3 z^3+11 a z^3+2 z^3 a^{-1} -8 a^6 z^2-27 a^4 z^2-26 a^2 z^2+z^2 a^{-2} -6 z^2-a^7 z-a^5 z-5 a^3 z-7 a z-2 z a^{-1} -a^6+2 a^4+5 a^2+3-2 a^5 z^{-1} -2 a^3 z^{-1} +a^6 z^{-2} +2 a^4 z^{-2} +a^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
5         11
3        21-1
1       21 1
-1      441 -1
-3     332  2
-5    35    2
-7   331    1
-9  251     2
-11 11       0
-13 2        2
-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}\oplus{\mathbb Z}_2 {\mathbb Z}
r=-5 {\mathbb Z}\oplus{\mathbb Z}_2^{2} {\mathbb Z}^{2}
r=-4 {\mathbb Z}^{5}\oplus{\mathbb Z}_2 {\mathbb Z}^{3}
r=-3 {\mathbb Z} {\mathbb Z}^{3}\oplus{\mathbb Z}_2^{3} {\mathbb Z}^{3}
r=-2 {\mathbb Z}\oplus{\mathbb Z}_2 {\mathbb Z}^{5}\oplus{\mathbb Z}_2^{3} {\mathbb Z}^{3}
r=-1 {\mathbb Z}_2 {\mathbb Z}^{3}\oplus{\mathbb Z}_2^{4} {\mathbb Z}^{4}
r=0 {\mathbb Z}^{2} {\mathbb Z}^{4}\oplus{\mathbb Z}_2^{2} {\mathbb Z}^{2}
r=1 {\mathbb Z} {\mathbb Z}\oplus{\mathbb Z}_2^{2} {\mathbb Z}^{2}
r=2 {\mathbb Z}_2 {\mathbb Z}\oplus{\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.

L11n382.gif

L11n382

L11n384.gif

L11n384