L9n14

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L9n13.gif

L9n13

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L9n15

Contents

L9n14.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L9n14 at Knotilus!

L9n14 is 9^2_{50} in the Rolfsen table of links.


Link Presentations

[edit Notes on L9n14's Link Presentations]

Planar diagram presentation X8192 X11,17,12,16 X3,10,4,11 X15,3,16,2 X5,13,6,12 X6718 X14,10,15,9 X18,14,7,13 X17,4,18,5
Gauss code {1, 4, -3, 9, -5, -6}, {6, -1, 7, 3, -2, 5, 8, -7, -4, 2, -9, -8}
A Braid Representative
BraidPart3.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart3.gifBraidPart0.gif
BraidPart4.gifBraidPart1.gifBraidPart2.gifBraidPart3.gifBraidPart3.gifBraidPart2.gifBraidPart1.gifBraidPart4.gifBraidPart1.gif
BraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart4.gifBraidPart4.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gif
A Morse Link Presentation L9n14 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) -\frac{u^2 v^2-u^2 v+u v-v+1}{u v} (db)
Jones polynomial q^{9/2}-q^{7/2}+q^{5/2}-\frac{1}{q^{5/2}}-2 q^{3/2}+\frac{1}{q^{3/2}}+\sqrt{q}-\frac{2}{\sqrt{q}} (db)
Signature -1 (db)
HOMFLY-PT polynomial z^3 a^{-3} +3 z a^{-3} + a^{-3} z^{-1} -z^5 a^{-1} +a z^3-5 z^3 a^{-1} +3 a z-7 z a^{-1} +2 a z^{-1} -3 a^{-1} z^{-1} (db)
Kauffman polynomial -z^7 a^{-1} -z^7 a^{-3} -2 z^6 a^{-2} -z^6 a^{-4} -z^6+5 z^5 a^{-1} +5 z^5 a^{-3} +9 z^4 a^{-2} +5 z^4 a^{-4} +4 z^4-2 a z^3-9 z^3 a^{-1} -7 z^3 a^{-3} -a^2 z^2-10 z^2 a^{-2} -6 z^2 a^{-4} -5 z^2-a^3 z+4 a z+9 z a^{-1} +4 z a^{-3} +3 a^{-2} + a^{-4} +3-2 a z^{-1} -3 a^{-1} z^{-1} - a^{-3} z^{-1} (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 \
-2-1012345χ
10       1-1
8        0
6     11 0
4    1   1
2    1   1
0  21    1
-2  1     1
-411      0
-61       1
Integral Khovanov Homology

(db, data source)

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

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L9n13

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L9n15