L11n205

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L11n204.gif

L11n204

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L11n206

Contents

L11n205.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11n205 at Knotilus!


Link Presentations

[edit Notes on L11n205's Link Presentations]

Planar diagram presentation X10,1,11,2 X7,16,8,17 X18,12,19,11 X2,19,3,20 X3,12,4,13 X13,21,14,20 X14,5,15,6 X6,9,7,10 X22,16,9,15 X17,8,18,1 X21,4,22,5
Gauss code {1, -4, -5, 11, 7, -8, -2, 10}, {8, -1, 3, 5, -6, -7, 9, 2, -10, -3, 4, 6, -11, -9}
A Braid Representative
BraidPart3.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart3.gifBraidPart0.gif
BraidPart4.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart4.gifBraidPart4.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart4.gifBraidPart1.gif
BraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart2.gif
A Morse Link Presentation L11n205 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) -\frac{\left(u v^2+1\right) \left(u^2+v^3\right)}{u^{3/2} v^{5/2}} (db)
Jones polynomial -\frac{1}{q^{7/2}}-\frac{1}{q^{17/2}} (db)
Signature -2 (db)
HOMFLY-PT polynomial z^3 a^7+4 z a^7+2 a^7 z^{-1} -z^5 a^5-6 z^3 a^5-9 z a^5-3 a^5 z^{-1} +z a^3+a^3 z^{-1} (db)
Kauffman polynomial a^9 z^7-7 a^9 z^5+14 a^9 z^3-7 a^9 z-a^7 z^3+4 a^7 z-2 a^7 z^{-1} -a^6 z^6+6 a^6 z^4-9 a^6 z^2+3 a^6-a^5 z^7+7 a^5 z^5-15 a^5 z^3+12 a^5 z-3 a^5 z^{-1} -a^4 z^6+6 a^4 z^4-9 a^4 z^2+3 a^4+a^3 z-a^3 z^{-1} +a^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 \
-8-7-6-5-4-3-2-10χ
-2       110
-4       110
-6     12  1
-8      1  1
-10   121   0
-12         0
-14  11     0
-161        1
-181        1
Integral Khovanov Homology

(db, data source)

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

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L11n204

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L11n206