L9a6

(Knotscape image)	See the full Thistlethwaite Link Table (up to 11 crossings). Visit L9a6 at Knotilus!
	[edit L9a6 Quick Notes] L9a6 is $9_{29}^{2}$ in the Rolfsen table of links.

[edit L9a6 Further Notes and Views]

Link Presentations

[edit Notes on L9a6's Link Presentations]

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

A Braid Representative

A Morse Link Presentation

Polynomial invariants

Multivariable Alexander Polynomial (in $u$ , $v$ , $w$ , ...)	${\frac {-2uv^{4}+3uv^{3}-3uv^{2}+2uv-u-v^{5}+2v^{4}-3v^{3}+3v^{2}-2v}{{\sqrt {u}}v^{5/2}}}$ (db)
Jones polynomial	$-{\frac {5}{q^{9/2}}}+{\frac {2}{q^{7/2}}}-{\frac {1}{q^{5/2}}}+{\frac {1}{q^{23/2}}}-{\frac {2}{q^{21/2}}}+{\frac {5}{q^{19/2}}}-{\frac {7}{q^{17/2}}}+{\frac {7}{q^{15/2}}}-{\frac {8}{q^{13/2}}}+{\frac {6}{q^{11/2}}}$ (db)
Signature	-5 (db)
HOMFLY-PT polynomial	$a^{11}(-z)-2a^{11}z^{-1}+3a^{9}z^{3}+8a^{9}z+5a^{9}z^{-1}-2a^{7}z^{5}-7a^{7}z^{3}-7a^{7}z-3a^{7}z^{-1}-a^{5}z^{5}-3a^{5}z^{3}-2a^{5}z$ (db)
Kauffman polynomial	$-z^{4}a^{14}+2z^{2}a^{14}-a^{14}-2z^{5}a^{13}+2z^{3}a^{13}-3z^{6}a^{12}+3z^{4}a^{12}-z^{2}a^{12}-3z^{7}a^{11}+4z^{5}a^{11}-6z^{3}a^{11}+6za^{11}-2a^{11}z^{-1}-z^{8}a^{10}-5z^{6}a^{10}+14z^{4}a^{10}-15z^{2}a^{10}+5a^{10}-6z^{7}a^{9}+15z^{5}a^{9}-21z^{3}a^{9}+17za^{9}-5a^{9}z^{-1}-z^{8}a^{8}-4z^{6}a^{8}+14z^{4}a^{8}-13z^{2}a^{8}+5a^{8}-3z^{7}a^{7}+8z^{5}a^{7}-10z^{3}a^{7}+9za^{7}-3a^{7}z^{-1}-2z^{6}a^{6}+4z^{4}a^{6}-z^{2}a^{6}-z^{5}a^{5}+3z^{3}a^{5}-2za^{5}$ (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		\

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

χ

-4

1

-6

2

1

-1

-8

3

-10

3

2

-1

-12

5

3

2

-14

3

4

1

-16

4

0

-18

1

3

2

-20

1

4

-3

-22

1

-24

1

-1

Integral Khovanov Homology

(db, data source)

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