L9a26

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	[edit L9a26 Quick Notes] L9a26 is $9_{11}^{2}$ in the Rolfsen table of links.

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Link Presentations

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Planar diagram presentation	X₈₁₉₂ X_10,4,11,3 X_18,10,7,9 X_14,6,15,5 X_16,14,17,13 X_12,18,13,17 X₂₇₃₈ X_4,12,5,11 X_6,16,1,15
Gauss code	{1, -7, 2, -8, 4, -9}, {7, -1, 3, -2, 8, -6, 5, -4, 9, -5, 6, -3}

A Braid Representative

A Morse Link Presentation

Polynomial invariants

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	$-{\frac {2u^{2}v^{2}-3u^{2}v+u^{2}-3uv^{2}+5uv-3u+v^{2}-3v+2}{uv}}$ (db)
Jones polynomial	$8q^{9/2}-8q^{7/2}+6q^{5/2}-5q^{3/2}+q^{17/2}-3q^{15/2}+5q^{13/2}-7q^{11/2}+2{\sqrt {q}}-{\frac {1}{\sqrt {q}}}$ (db)
Signature	3 (db)
HOMFLY-PT polynomial	$z^{3}a^{-7}+za^{-7}-z^{5}a^{-5}-2z^{3}a^{-5}-za^{-5}-z^{5}a^{-3}-2z^{3}a^{-3}-za^{-3}-a^{-3}z^{-1}+z^{3}a^{-1}+2za^{-1}+a^{-1}z^{-1}$ (db)
Kauffman polynomial	$z^{4}a^{-10}-z^{2}a^{-10}+3z^{5}a^{-9}-4z^{3}a^{-9}+za^{-9}+4z^{6}a^{-8}-5z^{4}a^{-8}+2z^{2}a^{-8}+3z^{7}a^{-7}-z^{5}a^{-7}-2z^{3}a^{-7}+za^{-7}+z^{8}a^{-6}+5z^{6}a^{-6}-9z^{4}a^{-6}+4z^{2}a^{-6}+5z^{7}a^{-5}-6z^{5}a^{-5}+za^{-5}+z^{8}a^{-4}+3z^{6}a^{-4}-7z^{4}a^{-4}+2z^{2}a^{-4}+2z^{7}a^{-3}-z^{5}a^{-3}-5z^{3}a^{-3}+4za^{-3}-a^{-3}z^{-1}+2z^{6}a^{-2}-4z^{4}a^{-2}+z^{2}a^{-2}+a^{-2}+z^{5}a^{-1}-3z^{3}a^{-1}+3za^{-1}-a^{-1}z^{-1}$ (db)

Khovanov Homology

The coefficients of the monomials

t^{r}q^{j}

are shown, along with their alternating sums

\chi

(fixed

j

, alternation over

r

).

\		r
	\
j		\

-2

-1

0

1

2

3

4

5

6

7

χ

18

1

-1

16

2

14

3

1

-2

12

4

2

10

4

3

-1

8

4

0

6

3

5

2

4

2

3

-1

2

1

4

3

0

1

-1

-2

1

Integral Khovanov Homology

(db, data source)

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