L9a35

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	[edit L9a35 Quick Notes] L9a35 is $9_{9}^{2}$ in the Rolfsen table of links.

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More symmetric depiction

Link Presentations

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Planar diagram presentation	X_10,1,11,2 X_12,3,13,4 X_16,8,17,7 X_14,6,15,5 X_18,13,9,14 X_6,16,7,15 X_4,18,5,17 X_2,9,3,10 X_8,11,1,12
Gauss code	{1, -8, 2, -7, 4, -6, 3, -9}, {8, -1, 9, -2, 5, -4, 6, -3, 7, -5}

A Braid Representative	{{{braid_table}}}
A Morse Link Presentation

Polynomial invariants

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	${\frac {(t(1)-1)(t(2)-1)\left(t(2)t(1)^{2}+t(2)^{2}t(1)-t(2)t(1)+t(1)+t(2)\right)}{t(1)^{3/2}t(2)^{3/2}}}$ (db)
Jones polynomial	$-q^{9/2}+{\frac {1}{q^{9/2}}}+3q^{7/2}-{\frac {2}{q^{7/2}}}-5q^{5/2}+{\frac {3}{q^{5/2}}}+6q^{3/2}-{\frac {6}{q^{3/2}}}-7{\sqrt {q}}+{\frac {6}{\sqrt {q}}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$az^{5}+z^{5}a^{-1}-a^{3}z^{3}+3az^{3}+2z^{3}a^{-1}-z^{3}a^{-3}-2a^{3}z+3az-za^{-3}+az^{-1}-a^{-1}z^{-1}$ (db)
Kauffman polynomial	$-a^{2}z^{8}-z^{8}-2a^{3}z^{7}-5az^{7}-3z^{7}a^{-1}-a^{4}z^{6}-5z^{6}a^{-2}-4z^{6}+8a^{3}z^{5}+14az^{5}+z^{5}a^{-1}-5z^{5}a^{-3}+4a^{4}z^{4}+7a^{2}z^{4}+6z^{4}a^{-2}-3z^{4}a^{-4}+12z^{4}-10a^{3}z^{3}-12az^{3}+4z^{3}a^{-1}+5z^{3}a^{-3}-z^{3}a^{-5}-4a^{4}z^{2}-6a^{2}z^{2}-2z^{2}a^{-2}+z^{2}a^{-4}-5z^{2}+4a^{3}z+6az-2za^{-3}+1-az^{-1}-a^{-1}z^{-1}$ (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		\

-5

-4

-3

-2

-1

0

1

2

3

4

χ

10

1

8

2

-2

6

3

1

2

4

3

2

-1

2

4

3

1

0

4

5

1

-2

2

0

-4

1

4

3

-6

1

2

-1

-8

1

-10

1

-1

Integral Khovanov Homology

(db, data source)

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