L11a26

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Link Presentations

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Planar diagram presentation	X₆₁₇₂ X_10,3,11,4 X_14,8,15,7 X_20,18,21,17 X_18,12,19,11 X_12,20,13,19 X_22,16,5,15 X_16,22,17,21 X_8,14,9,13 X₂₅₃₆ X_4,9,1,10
Gauss code	{1, -10, 2, -11}, {10, -1, 3, -9, 11, -2, 5, -6, 9, -3, 7, -8, 4, -5, 6, -4, 8, -7}

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

Polynomial invariants

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	${\frac {2t(1)t(2)^{3}-5t(2)^{3}-8t(1)t(2)^{2}+10t(2)^{2}+10t(1)t(2)-8t(2)-5t(1)+2}{{\sqrt {t(1)}}t(2)^{3/2}}}$ (db)
Jones polynomial	$-11q^{9/2}+14q^{7/2}-{\frac {1}{q^{7/2}}}-16q^{5/2}+{\frac {2}{q^{5/2}}}+16q^{3/2}-{\frac {6}{q^{3/2}}}+q^{15/2}-3q^{13/2}+7q^{11/2}-14{\sqrt {q}}+{\frac {9}{\sqrt {q}}}$ (db)
Signature	1 (db)
HOMFLY-PT polynomial	$za^{-7}-2z^{3}a^{-5}+a^{-5}z^{-1}+z^{5}a^{-3}-z^{3}a^{-3}+a^{3}z-3za^{-3}+a^{3}z^{-1}-2a^{-3}z^{-1}+z^{5}a^{-1}-2az^{3}-2az+za^{-1}-az^{-1}+a^{-1}z^{-1}$ (db)
Kauffman polynomial	$z^{6}a^{-8}-3z^{4}a^{-8}+2z^{2}a^{-8}+3z^{7}a^{-7}-8z^{5}a^{-7}+5z^{3}a^{-7}-za^{-7}+5z^{8}a^{-6}-14z^{6}a^{-6}+13z^{4}a^{-6}-9z^{2}a^{-6}+3a^{-6}+4z^{9}a^{-5}-7z^{7}a^{-5}+z^{5}a^{-5}-z^{3}a^{-5}+2za^{-5}-a^{-5}z^{-1}+z^{10}a^{-4}+9z^{8}a^{-4}-34z^{6}a^{-4}+46z^{4}a^{-4}-30z^{2}a^{-4}+7a^{-4}+7z^{9}a^{-3}-16z^{7}a^{-3}+a^{3}z^{5}+20z^{5}a^{-3}-3a^{3}z^{3}-18z^{3}a^{-3}+3a^{3}z+10za^{-3}-a^{3}z^{-1}-2a^{-3}z^{-1}+z^{10}a^{-2}+7z^{8}a^{-2}+2a^{2}z^{6}-21z^{6}a^{-2}-3a^{2}z^{4}+28z^{4}a^{-2}-16z^{2}a^{-2}+a^{2}+4a^{-2}+3z^{9}a^{-1}+3az^{7}-3z^{7}a^{-1}-3az^{5}+7z^{5}a^{-1}-az^{3}-10z^{3}a^{-1}+2az+6za^{-1}-az^{-1}-a^{-1}z^{-1}+3z^{8}-5z^{4}+3z^{2}$ (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		\

-4

-3

-2

-1

0

1

2

3

4

5

6

7

χ

16

1

-1

14

2

12

5

1

-4

10

6

2

4

8

5

-3

6

8

6

2

4

8

0

2

6

8

-2

0

4

9

5

-2

2

5

-3

-4

4

-6

1

2

-1

-8

1

Integral Khovanov Homology

(db, data source)

$\dim {\mathcal {G}}_{2r+i}\operatorname {KH} _{\mathbb {Z} }^{r}$	$i=0$	$i=2$
$r=-4$	${\mathbb {Z} }$	${\mathbb {Z} }$
$r=-3$	${\mathbb {Z} }^{2}$
$r=-2$	${\mathbb {Z} }^{4}\oplus {\mathbb {Z} }_{2}^{2}$	${\mathbb {Z} }^{2}$
$r=-1$	${\mathbb {Z} }^{5}\oplus {\mathbb {Z} }_{2}^{4}$	${\mathbb {Z} }^{4}$
$r=0$	${\mathbb {Z} }^{9}\oplus {\mathbb {Z} }_{2}^{5}$	${\mathbb {Z} }^{6}$
$r=1$	${\mathbb {Z} }^{8}\oplus {\mathbb {Z} }_{2}^{8}$	${\mathbb {Z} }^{8}$
$r=2$	${\mathbb {Z} }^{8}\oplus {\mathbb {Z} }_{2}^{8}$	${\mathbb {Z} }^{8}$
$r=3$	${\mathbb {Z} }^{6}\oplus {\mathbb {Z} }_{2}^{8}$	${\mathbb {Z} }^{8}$
$r=4$	${\mathbb {Z} }^{5}\oplus {\mathbb {Z} }_{2}^{6}$	${\mathbb {Z} }^{6}$
$r=5$	${\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}^{5}$	${\mathbb {Z} }^{5}$
$r=6$	${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}^{2}$	${\mathbb {Z} }^{2}$
$r=7$	${\mathbb {Z} }_{2}$	${\mathbb {Z} }$