11n
92
(K11n
92
)
A knot diagram
1
Linearized knot diagam
6 1 11 9 2 3 10 4 1 3 8
Solving Sequence
3,11 4,8
1 2 10 7 6 5 9
c
3
c
11
c
2
c
10
c
7
c
6
c
5
c
9
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−74u
9
+ 28u
8
+ 589u
7
− 208u
6
− 1099u
5
+ 580u
4
− 535u
3
− 218u
2
+ 439b − 447u + 41,
− 90u
9
− 49u
8
+ 835u
7
+ 364u
6
− 2357u
5
− 576u
4
+ 1485u
3
− 277u
2
+ 439a + 453u + 38,
u
10
+ u
9
− 8u
8
− 8u
7
+ 16u
6
+ 16u
5
+ 3u
4
− 2u
3
+ 2u + 1i
I
u
2
= h−u
6
+ u
5
+ 3u
4
− 2u
3
− 2u
2
+ b + u, u
4
− u
3
− 3u
2
+ a + 2u + 2, u
7
− u
6
− 4u
5
+ 3u
4
+ 5u
3
− 2u
2
− 2u − 1i
I
u
3
= h−2u
3
+ 5u
2
+ b + 2u − 12, 4u
3
− 11u
2
+ 7a − 2u + 23, u
4
− u
3
− 4u
2
+ 4u + 7i
* 3 irreducible components of dim
C
= 0, with total 21 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−74u
9
+ 28u
8
+ · · · + 439b + 41, −90u
9
− 49u
8
+ · · · + 439a +
38, u
10
+ u
9
+ · · · + 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
0.205011u
9
+ 0.111617u
8
+ ··· − 1.03189u − 0.0865604
0.168565u
9
− 0.0637813u
8
+ ··· + 1.01822u − 0.0933941
a
1
=
−0.931663u
9
− 0.296128u
8
+ ··· − 1.34396u − 0.362187
0.558087u
9
+ 0.248292u
8
+ ··· + 1.35763u + 0.542141
a
2
=
−1.39180u
9
− 0.635535u
8
+ ··· − 1.96128u − 1.32346
1.29841u
9
+ 0.373576u
8
+ ··· + 1.46469u + 2.11845
a
10
=
−u
u
a
7
=
0.275626u
9
+ 0.138952u
8
+ ··· − 0.753986u + 0.239180
0.0979499u
9
− 0.0911162u
8
+ ··· + 0.740319u − 0.419134
a
6
=
0.373576u
9
+ 0.0478360u
8
+ ··· − 0.0136674u − 0.179954
0.0979499u
9
− 0.0911162u
8
+ ··· + 0.740319u − 0.419134
a
5
=
−0.0933941u
9
− 0.261959u
8
+ ··· − 0.496583u − 1.20501
−0.232346u
9
+ 0.00683371u
8
+ ··· − 0.430524u − 0.168565
a
9
=
0.205011u
9
+ 0.111617u
8
+ ··· − 0.0318907u − 0.0865604
0.168565u
9
− 0.0637813u
8
+ ··· + 1.01822u − 0.0933941
a
9
=
0.205011u
9
+ 0.111617u
8
+ ··· − 0.0318907u − 0.0865604
0.168565u
9
− 0.0637813u
8
+ ··· + 1.01822u − 0.0933941
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
1240
439
u
9
−
480
439
u
8
+
9846
439
u
7
+
3503
439
u
6
−
18914
439
u
5
−
5302
439
u
4
−
7197
439
u
3
+
1354
439
u
2
−
490
439
u −
452
439
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
10
− 6u
9
+ ··· − 10u + 4
c
2
u
10
+ 2u
9
+ ··· + 20u + 16
c
3
, c
4
, c
8
c
10
u
10
+ u
9
− 8u
8
− 8u
7
+ 16u
6
+ 16u
5
+ 3u
4
− 2u
3
+ 2u + 1
c
6
u
10
+ 12u
9
+ ··· + 1072u + 712
c
7
, c
9
u
10
+ 2u
9
+ ··· − 12u + 1
c
11
u
10
+ 5u
9
+ 12u
8
+ 15u
7
+ 10u
6
+ 4u
5
+ 6u
4
+ 8u
3
+ 5u
2
+ 3u + 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
10
+ 2y
9
+ ··· + 20y + 16
c
2
y
10
+ 38y
9
+ ··· + 3216y + 256
c
3
, c
4
, c
8
c
10
y
10
− 17y
9
+ ··· − 4y + 1
c
6
y
10
+ 68y
9
+ ··· + 2222848y + 506944
c
7
, c
9
y
10
+ 46y
9
+ ··· − 38y + 1
c
11
y
10
− y
9
+ 14y
8
− 13y
7
+ 54y
6
− 42y
5
+ 30y
4
+ 12y
3
+ y
2
+ 11y + 4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.303786 + 0.554609I
a = −1.19659 − 1.04112I
b = −0.210597 − 0.072758I
−1.58196 + 1.29510I −1.93721 + 1.18186I
u = −0.303786 − 0.554609I
a = −1.19659 + 1.04112I
b = −0.210597 + 0.072758I
−1.58196 − 1.29510I −1.93721 − 1.18186I
u = −0.595593 + 0.161209I
a = 1.251620 − 0.570638I
b = −0.897475 + 0.589151I
−0.62036 + 3.20996I 3.63110 − 5.43743I
u = −0.595593 − 0.161209I
a = 1.251620 + 0.570638I
b = −0.897475 − 0.589151I
−0.62036 − 3.20996I 3.63110 + 5.43743I
u = 0.470796 + 0.374659I
a = −0.742938 − 0.762785I
b = 0.262089 + 0.698748I
1.01700 + 1.01665I 4.69191 − 3.41900I
u = 0.470796 − 0.374659I
a = −0.742938 + 0.762785I
b = 0.262089 − 0.698748I
1.01700 − 1.01665I 4.69191 + 3.41900I
u = 2.01532 + 0.15224I
a = 0.624248 + 0.501185I
b = −0.19806 − 2.25477I
−19.7069 + 0.3487I 4.25811 + 0.03534I
u = 2.01532 − 0.15224I
a = 0.624248 − 0.501185I
b = −0.19806 + 2.25477I
−19.7069 − 0.3487I 4.25811 − 0.03534I
u = −2.08674 + 0.29586I
a = −0.436339 − 0.622756I
b = 0.54405 + 2.41435I
−19.4087 − 8.7708I 4.35608 + 3.79545I
u = −2.08674 − 0.29586I
a = −0.436339 + 0.622756I
b = 0.54405 − 2.41435I
−19.4087 + 8.7708I 4.35608 − 3.79545I
5
II. I
u
2
= h−u
6
+ u
5
+ 3u
4
− 2u
3
− 2u
2
+ b + u, u
4
− u
3
− 3u
2
+ a + 2u +
2, u
7
− u
6
− 4u
5
+ 3u
4
+ 5u
3
− 2u
2
− 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
−u
4
+ u
3
+ 3u
2
− 2u − 2
u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
− u
a
1
=
−u
6
+ u
5
+ 3u
4
− 2u
3
− 3u
2
+ u + 2
u
4
− u
3
− 2u
2
+ 2u
a
2
=
−u
4
+ 2u
3
+ u
2
− 3u + 2
−u
5
+ 2u
4
+ u
3
− 4u
2
+ u + 1
a
10
=
−u
u
a
7
=
−u
4
+ 3u
2
− u − 2
u
6
− u
5
− 3u
4
+ 3u
3
+ 2u
2
− 2u
a
6
=
u
6
− u
5
− 4u
4
+ 3u
3
+ 5u
2
− 3u − 2
u
6
− u
5
− 3u
4
+ 3u
3
+ 2u
2
− 2u
a
5
=
−u
5
+ u
4
+ 3u
3
− 3u
2
− 2u + 1
u
5
− 3u
3
+ 2u + 1
a
9
=
−u
4
+ u
3
+ 3u
2
− 3u − 2
u
6
− u
5
− 3u
4
+ 3u
3
+ 2u
2
− u
a
9
=
−u
4
+ u
3
+ 3u
2
− 3u − 2
u
6
− u
5
− 3u
4
+ 3u
3
+ 2u
2
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
6
+ 2u
5
− 8u
4
− 3u
3
+ 12u
2
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
7
− u
6
+ 2u
5
− 2u
4
+ 2u
3
− 3u
2
+ u − 1
c
2
u
7
+ 3u
6
+ 4u
5
− 6u
3
− 9u
2
− 5u − 1
c
3
, c
8
u
7
− u
6
− 4u
5
+ 3u
4
+ 5u
3
− 2u
2
− 2u − 1
c
4
, c
10
u
7
+ u
6
− 4u
5
− 3u
4
+ 5u
3
+ 2u
2
− 2u + 1
c
5
u
7
+ u
6
+ 2u
5
+ 2u
4
+ 2u
3
+ 3u
2
+ u + 1
c
6
u
7
+ 2u
6
− 2u
5
− 3u
4
− 3u
3
+ 6u
2
− u + 1
c
7
, c
9
u
7
+ 2u
6
− u
5
− 3u
4
− 2u
3
+ u
2
+ 2u + 1
c
11
u
7
− 2u
6
+ u
5
+ 2u
4
− 3u
3
+ u
2
+ 2u − 1
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
7
+ 3y
6
+ 4y
5
− 6y
3
− 9y
2
− 5y −1
c
2
y
7
− y
6
+ 4y
5
− 4y
4
+ 2y
3
− 21y
2
+ 7y −1
c
3
, c
4
, c
8
c
10
y
7
− 9y
6
+ 32y
5
− 57y
4
+ 51y
3
− 18y
2
− 1
c
6
y
7
− 8y
6
+ 10y
5
− 23y
4
+ 45y
3
− 24y
2
− 11y −1
c
7
, c
9
y
7
− 6y
6
+ 9y
5
− 5y
4
+ 2y
3
− 3y
2
+ 2y −1
c
11
y
7
− 2y
6
+ 3y
5
− 2y
4
+ 5y
3
− 9y
2
+ 6y −1
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.212610 + 0.314318I
a = −0.186986 + 0.922572I
b = −0.25287 − 1.43719I
4.41567 + 1.74618I 3.81474 − 1.89982I
u = 1.212610 − 0.314318I
a = −0.186986 − 0.922572I
b = −0.25287 + 1.43719I
4.41567 − 1.74618I 3.81474 + 1.89982I
u = −1.303070 + 0.139348I
a = 0.819449 + 0.558129I
b = −0.275124 − 0.778615I
2.10492 − 4.17967I 2.47305 + 4.17814I
u = −1.303070 − 0.139348I
a = 0.819449 − 0.558129I
b = −0.275124 + 0.778615I
2.10492 + 4.17967I 2.47305 − 4.17814I
u = −0.278087 + 0.369158I
a = −1.48979 − 1.34313I
b = 0.466038 − 0.754209I
−1.45284 + 2.44043I −0.66357 − 2.79895I
u = −0.278087 − 0.369158I
a = −1.48979 + 1.34313I
b = 0.466038 + 0.754209I
−1.45284 − 2.44043I −0.66357 + 2.79895I
u = 1.73710
a = −0.285336
b = −0.876095
6.31383 6.75150
9
III.
I
u
3
= h−2u
3
+5u
2
+b+2u−12, 4u
3
−11u
2
+7a−2u+23, u
4
−u
3
−4u
2
+4u+7i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
8
=
−
4
7
u
3
+
11
7
u
2
+
2
7
u −
23
7
2u
3
− 5u
2
− 2u + 12
a
1
=
−
5
7
u
3
+
12
7
u
2
+
6
7
u −
27
7
1
a
2
=
5
7
u
3
−
12
7
u
2
−
6
7
u +
34
7
−1
a
10
=
−u
u
a
7
=
10
7
u
3
−
24
7
u
2
−
12
7
u +
75
7
−2
a
6
=
10
7
u
3
−
24
7
u
2
−
12
7
u +
61
7
−2
a
5
=
15
7
u
3
−
36
7
u
2
−
18
7
u +
95
7
−3
a
9
=
3
7
u
3
−
3
7
u
2
−
12
7
u +
12
7
u
3
− 2u
2
+ u + 5
a
9
=
3
7
u
3
−
3
7
u
2
−
12
7
u +
12
7
u
3
− 2u
2
+ u + 5
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
+ 8u
2
+ 4u − 10
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u + 1)
4
c
2
(u − 1)
4
c
3
, c
4
, c
8
c
10
u
4
− u
3
− 4u
2
+ 4u + 7
c
6
(u + 2)
4
c
7
, c
9
u
4
− 3u
3
+ 2u
2
+ 6u + 13
c
11
(u
2
− u + 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
4
, c
8
c
10
y
4
− 9y
3
+ 38y
2
− 72y + 49
c
6
(y −4)
4
c
7
, c
9
y
4
− 5y
3
+ 66y
2
+ 16y + 169
c
11
(y
2
+ y + 1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.328780 + 0.090174I
a = 0.418587 − 0.623340I
b = 1.24248 + 1.97169I
6.57974 + 2.02988I 8.00000 − 3.46410I
u = −1.328780 − 0.090174I
a = 0.418587 + 0.623340I
b = 1.24248 − 1.97169I
6.57974 − 2.02988I 8.00000 + 3.46410I
u = 1.82878 + 0.77585I
a = −0.061444 + 0.499622I
b = 0.257518 − 1.105670I
6.57974 + 2.02988I 8.00000 − 3.46410I
u = 1.82878 − 0.77585I
a = −0.061444 − 0.499622I
b = 0.257518 + 1.105670I
6.57974 − 2.02988I 8.00000 + 3.46410I
13
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u + 1)
4
(u
7
− u
6
+ 2u
5
− 2u
4
+ 2u
3
− 3u
2
+ u − 1)
· (u
10
− 6u
9
+ ··· − 10u + 4)
c
2
(u − 1)
4
(u
7
+ 3u
6
+ 4u
5
− 6u
3
− 9u
2
− 5u − 1)
· (u
10
+ 2u
9
+ ··· + 20u + 16)
c
3
, c
8
(u
4
− u
3
− 4u
2
+ 4u + 7)(u
7
− u
6
− 4u
5
+ 3u
4
+ 5u
3
− 2u
2
− 2u − 1)
· (u
10
+ u
9
− 8u
8
− 8u
7
+ 16u
6
+ 16u
5
+ 3u
4
− 2u
3
+ 2u + 1)
c
4
, c
10
(u
4
− u
3
− 4u
2
+ 4u + 7)(u
7
+ u
6
− 4u
5
− 3u
4
+ 5u
3
+ 2u
2
− 2u + 1)
· (u
10
+ u
9
− 8u
8
− 8u
7
+ 16u
6
+ 16u
5
+ 3u
4
− 2u
3
+ 2u + 1)
c
5
(u + 1)
4
(u
7
+ u
6
+ 2u
5
+ 2u
4
+ 2u
3
+ 3u
2
+ u + 1)
· (u
10
− 6u
9
+ ··· − 10u + 4)
c
6
(u + 2)
4
(u
7
+ 2u
6
− 2u
5
− 3u
4
− 3u
3
+ 6u
2
− u + 1)
· (u
10
+ 12u
9
+ ··· + 1072u + 712)
c
7
, c
9
(u
4
− 3u
3
+ 2u
2
+ 6u + 13)(u
7
+ 2u
6
+ ··· + 2u + 1)
· (u
10
+ 2u
9
+ ··· − 12u + 1)
c
11
(u
2
− u + 1)
2
(u
7
− 2u
6
+ u
5
+ 2u
4
− 3u
3
+ u
2
+ 2u − 1)
· (u
10
+ 5u
9
+ 12u
8
+ 15u
7
+ 10u
6
+ 4u
5
+ 6u
4
+ 8u
3
+ 5u
2
+ 3u + 2)
14
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y −1)
4
(y
7
+ 3y
6
+ 4y
5
− 6y
3
− 9y
2
− 5y −1)
· (y
10
+ 2y
9
+ ··· + 20y + 16)
c
2
(y −1)
4
(y
7
− y
6
+ 4y
5
− 4y
4
+ 2y
3
− 21y
2
+ 7y −1)
· (y
10
+ 38y
9
+ ··· + 3216y + 256)
c
3
, c
4
, c
8
c
10
(y
4
− 9y
3
+ 38y
2
− 72y + 49)(y
7
− 9y
6
+ ··· − 18y
2
− 1)
· (y
10
− 17y
9
+ ··· − 4y + 1)
c
6
(y −4)
4
(y
7
− 8y
6
+ 10y
5
− 23y
4
+ 45y
3
− 24y
2
− 11y −1)
· (y
10
+ 68y
9
+ ··· + 2222848y + 506944)
c
7
, c
9
(y
4
− 5y
3
+ 66y
2
+ 16y + 169)
· (y
7
− 6y
6
+ ··· + 2y −1)(y
10
+ 46y
9
+ ··· − 38y + 1)
c
11
(y
2
+ y + 1)
2
(y
7
− 2y
6
+ 3y
5
− 2y
4
+ 5y
3
− 9y
2
+ 6y −1)
· (y
10
− y
9
+ 14y
8
− 13y
7
+ 54y
6
− 42y
5
+ 30y
4
+ 12y
3
+ y
2
+ 11y + 4)
15
