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

Visit L9a44 at Knotilus!

L9a44 is 9^3_{3} in the Rolfsen table of links.

Link Presentations

[edit Notes on L9a44's Link Presentations]

Planar diagram presentation X6172 X10,3,11,4 X18,14,9,13 X16,12,17,11 X12,18,13,17 X8,16,5,15 X14,8,15,7 X2536 X4,9,1,10
Gauss code {1, -8, 2, -9}, {8, -1, 7, -6}, {9, -2, 4, -5, 3, -7, 6, -4, 5, -3}
A Braid Representative
A Morse Link Presentation L9a44 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) \frac{-t(1) t(3)^3+t(1) t(2) t(3)^3-2 t(2) t(3)^3+t(3)^3+2 t(1) t(3)^2-t(1) t(2) t(3)^2+2 t(2) t(3)^2-t(3)^2-2 t(1) t(3)+t(1) t(2) t(3)-2 t(2) t(3)+t(3)+2 t(1)-t(1) t(2)+t(2)-1}{\sqrt{t(1)} \sqrt{t(2)} t(3)^{3/2}} (db)
Jones polynomial -q^6+3 q^5-6 q^4+7 q^3-7 q^2+8 q-5+5 q^{-1} - q^{-2} + q^{-3} (db)
Signature 2 (db)
HOMFLY-PT polynomial z^6 a^{-2} +4 z^4 a^{-2} -z^4 a^{-4} -2 z^4+a^2 z^2+7 z^2 a^{-2} -2 z^2 a^{-4} -7 z^2+3 a^2+8 a^{-2} -2 a^{-4} -9+2 a^2 z^{-2} +4 a^{-2} z^{-2} - a^{-4} z^{-2} -5 z^{-2} (db)
Kauffman polynomial z^3 a^{-7} +3 z^4 a^{-6} +6 z^5 a^{-5} -6 z^3 a^{-5} +3 z a^{-5} - a^{-5} z^{-1} +7 z^6 a^{-4} -11 z^4 a^{-4} +6 z^2 a^{-4} + a^{-4} z^{-2} -2 a^{-4} +4 z^7 a^{-3} -z^5 a^{-3} -12 z^3 a^{-3} +13 z a^{-3} -5 a^{-3} z^{-1} +z^8 a^{-2} +a^2 z^6+7 z^6 a^{-2} -5 a^2 z^4-21 z^4 a^{-2} +9 a^2 z^2+16 z^2 a^{-2} +2 a^2 z^{-2} +4 a^{-2} z^{-2} -7 a^2-10 a^{-2} +a z^7+5 z^7 a^{-1} -a z^5-8 z^5 a^{-1} -6 a z^3-11 z^3 a^{-1} +11 a z+21 z a^{-1} -5 a z^{-1} -9 a^{-1} z^{-1} +z^8+z^6-12 z^4+19 z^2+5 z^{-2} -14 (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 \
13         1-1
11        2 2
9       41 -3
7      32  1
5     44   0
3    43    1
1   47     3
-1  11      0
-3  4       4
-511        0
-71         1
Integral Khovanov Homology

(db, data source)

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

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