11a
340
(K11a
340
)
A knot diagram
1
Linearized knot diagam
8 7 1 11 9 10 2 3 6 4 5
Solving Sequence
3,7
2 8 9 1
4,10
6 5 11
c
2
c
7
c
8
c
1
c
3
c
6
c
5
c
11
c
4
, c
9
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
16
+ 2u
15
+ ··· + b − 1, u
17
− u
16
+ ··· + 2a + 6u, u
18
− 3u
17
+ ··· − 4u + 2i
I
u
2
= hu
12
a + u
11
a + ··· + b + a, u
12
+ u
11
+ ··· + a
2
− a,
u
14
+ u
13
+ 7u
12
+ 6u
11
+ 18u
10
+ 13u
9
+ 19u
8
+ 10u
7
+ 4u
6
− 2u
5
− 4u
4
− 4u
3
+ u + 1i
I
u
3
= hb − 1, 2a + u, u
2
+ 2i
I
v
1
= ha, b + 1, v + 1i
* 4 irreducible components of dim
C
= 0, with total 49 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−u
16
+2u
15
+· · ·+b−1, u
17
−u
16
+· · ·+2a+6u, u
18
−3u
17
+· · ·−4u+2i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
8
=
−u
u
3
+ u
a
9
=
−u
3
− 2u
u
3
+ u
a
1
=
u
2
+ 1
−u
4
− 2u
2
a
4
=
−u
6
− 3u
4
− 2u
2
+ 1
u
8
+ 4u
6
+ 4u
4
a
10
=
−
1
2
u
17
+
1
2
u
16
+ ··· + u
2
− 3u
u
16
− 2u
15
+ ··· − 3u
2
+ 1
a
6
=
1
2
u
17
−
3
2
u
16
+ ··· + 2u − 2
u
14
− u
13
+ ··· + u + 1
a
5
=
3
2
u
17
−
9
2
u
16
+ ··· + 6u − 6
−u
15
+ 3u
14
+ ··· − 12u
2
+ 3
a
11
=
−
1
2
u
17
+
1
2
u
16
+ ··· − u + 1
u
17
− 2u
16
+ ··· + 2u − 1
a
11
=
−
1
2
u
17
+
1
2
u
16
+ ··· − u + 1
u
17
− 2u
16
+ ··· + 2u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
17
− 6u
16
+ 26u
15
− 50u
14
+ 118u
13
− 156u
12
+ 242u
11
−
212u
10
+ 202u
9
− 66u
8
− 28u
7
+ 128u
6
− 124u
5
+ 98u
4
− 14u
3
− 16u
2
+ 22u − 12
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
18
− 3u
17
+ ··· − 4u + 2
c
3
u
18
− 3u
17
+ ··· − 144u
2
+ 16
c
4
, c
5
, c
6
c
9
, c
10
, c
11
u
18
+ u
17
+ ··· − u − 1
c
8
u
18
+ 3u
17
+ ··· + 24u + 34
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y
18
+ 17y
17
+ ··· − 32y + 4
c
3
y
18
+ 5y
17
+ ··· − 4608y + 256
c
4
, c
5
, c
6
c
9
, c
10
, c
11
y
18
− 19y
17
+ ··· − 13y + 1
c
8
y
18
+ 5y
17
+ ··· − 4384y + 1156
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.536324 + 0.718976I
a = −0.69596 + 1.40617I
b = 0.807347 + 0.538462I
−6.73513 + 4.54783I −15.8301 − 1.8142I
u = 0.536324 − 0.718976I
a = −0.69596 − 1.40617I
b = 0.807347 − 0.538462I
−6.73513 − 4.54783I −15.8301 + 1.8142I
u = 0.775406 + 0.334408I
a = 1.67997 − 0.31282I
b = −2.01461 + 0.21828I
−8.01786 − 9.07750I −17.1458 + 6.7523I
u = 0.775406 − 0.334408I
a = 1.67997 + 0.31282I
b = −2.01461 − 0.21828I
−8.01786 + 9.07750I −17.1458 − 6.7523I
u = −0.809273
a = −1.82368
b = 2.15054
−12.4435 −20.5970
u = −0.363479 + 1.186890I
a = 0.413807 + 1.111040I
b = −1.61785 + 1.19506I
−8.78390 + 4.21996I −16.6895 − 3.5646I
u = −0.363479 − 1.186890I
a = 0.413807 − 1.111040I
b = −1.61785 − 1.19506I
−8.78390 − 4.21996I −16.6895 + 3.5646I
u = −0.042738 + 1.319350I
a = −0.240648 − 0.315054I
b = 0.458014 − 0.563844I
3.51645 + 1.27379I −7.18490 − 5.17198I
u = −0.042738 − 1.319350I
a = −0.240648 + 0.315054I
b = 0.458014 + 0.563844I
3.51645 − 1.27379I −7.18490 + 5.17198I
u = 0.550592 + 0.360230I
a = −0.671067 − 0.760810I
b = 0.463787 + 0.211202I
1.75017 − 1.69601I −7.17935 + 4.88688I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.550592 − 0.360230I
a = −0.671067 + 0.760810I
b = 0.463787 − 0.211202I
1.75017 + 1.69601I −7.17935 − 4.88688I
u = 0.21362 + 1.42778I
a = 0.548707 − 0.014230I
b = −1.26192 − 0.75164I
7.46429 − 4.53021I −4.17935 + 4.22610I
u = 0.21362 − 1.42778I
a = 0.548707 + 0.014230I
b = −1.26192 + 0.75164I
7.46429 + 4.53021I −4.17935 − 4.22610I
u = 0.30373 + 1.44463I
a = −0.438796 + 0.877410I
b = 2.64593 + 0.70371I
−2.32354 − 12.99620I −12.9688 + 7.3705I
u = 0.30373 − 1.44463I
a = −0.438796 − 0.877410I
b = 2.64593 − 0.70371I
−2.32354 + 12.99620I −12.9688 − 7.3705I
u = 0.10546 + 1.52636I
a = −0.085263 − 0.844947I
b = 0.103194 + 0.177421I
0.70132 + 2.48793I −13.16040 − 3.49031I
u = 0.10546 − 1.52636I
a = −0.085263 + 0.844947I
b = 0.103194 − 0.177421I
0.70132 − 2.48793I −13.16040 + 3.49031I
u = −0.348560
a = 0.802182
b = −0.318335
−0.533570 −18.7260
6
II.
I
u
2
= hu
12
a + u
11
a + · · · + b + a, u
12
+ u
11
+ · · · + a
2
− a, u
14
+ u
13
+ · · · + u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
8
=
−u
u
3
+ u
a
9
=
−u
3
− 2u
u
3
+ u
a
1
=
u
2
+ 1
−u
4
− 2u
2
a
4
=
−u
6
− 3u
4
− 2u
2
+ 1
u
8
+ 4u
6
+ 4u
4
a
10
=
a
−u
12
a − u
11
a + ··· − au − a
a
6
=
−u
13
− u
12
+ ··· + au + 2u
2
u
12
a + u
13
+ ··· − 2u
3
− u
2
a
5
=
−u
13
− u
12
+ ··· + au + 2u
2
u
12
a + u
13
+ ··· + u
2
a − u
2
a
11
=
u
10
+ 5u
8
+ ··· + a + 1
−u
12
a − u
11
a + ··· − a + u
a
11
=
u
10
+ 5u
8
+ ··· + a + 1
−u
12
a − u
11
a + ··· − a + u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
12
+ 4u
11
+ 24u
10
+ 20u
9
+ 52u
8
+ 32u
7
+ 44u
6
+ 8u
5
+ 4u
4
−16u
3
−8u
2
−4u −10
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
(u
14
+ u
13
+ ··· + u + 1)
2
c
3
(u
14
− 3u
13
+ ··· − 7u + 3)
2
c
4
, c
5
, c
6
c
9
, c
10
, c
11
u
28
+ u
27
+ ··· − 4u + 3
c
8
(u
14
− u
13
+ ··· + 3u + 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
(y
14
+ 13y
13
+ ··· − y + 1)
2
c
3
(y
14
+ 5y
13
+ ··· + 23y + 9)
2
c
4
, c
5
, c
6
c
9
, c
10
, c
11
y
28
− 21y
27
+ ··· + 32y + 9
c
8
(y
14
+ y
13
+ ··· − y + 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.135360 + 1.128160I
a = −0.171103 + 1.160650I
b = 0.93567 + 2.14908I
−1.84948 − 2.19128I −13.23919 + 3.85718I
u = 0.135360 + 1.128160I
a = 0.584560 − 0.465439I
b = −0.888411 − 0.124832I
−1.84948 − 2.19128I −13.23919 + 3.85718I
u = 0.135360 − 1.128160I
a = −0.171103 − 1.160650I
b = 0.93567 − 2.14908I
−1.84948 + 2.19128I −13.23919 − 3.85718I
u = 0.135360 − 1.128160I
a = 0.584560 + 0.465439I
b = −0.888411 + 0.124832I
−1.84948 + 2.19128I −13.23919 − 3.85718I
u = −0.681829 + 0.299736I
a = 0.743891 − 0.831039I
b = −0.514590 + 0.182971I
−2.72606 + 5.07185I −13.6715 − 6.3313I
u = −0.681829 + 0.299736I
a = −1.77480 − 0.38840I
b = 2.07865 + 0.29445I
−2.72606 + 5.07185I −13.6715 − 6.3313I
u = −0.681829 − 0.299736I
a = 0.743891 + 0.831039I
b = −0.514590 − 0.182971I
−2.72606 − 5.07185I −13.6715 + 6.3313I
u = −0.681829 − 0.299736I
a = −1.77480 + 0.38840I
b = 2.07865 − 0.29445I
−2.72606 − 5.07185I −13.6715 + 6.3313I
u = −0.373222 + 0.543854I
a = 0.528563 − 0.787767I
b = −0.451286 + 0.309528I
−1.59516 − 1.40484I −10.49073 + 0.52948I
u = −0.373222 + 0.543854I
a = 0.79795 + 1.69739I
b = −0.503932 + 0.498617I
−1.59516 − 1.40484I −10.49073 + 0.52948I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.373222 − 0.543854I
a = 0.528563 + 0.787767I
b = −0.451286 − 0.309528I
−1.59516 + 1.40484I −10.49073 − 0.52948I
u = −0.373222 − 0.543854I
a = 0.79795 − 1.69739I
b = −0.503932 − 0.498617I
−1.59516 + 1.40484I −10.49073 − 0.52948I
u = 0.600586 + 0.155632I
a = −1.18251 + 1.06646I
b = 0.532477 + 0.072927I
−4.65252 − 0.62859I −18.3165 + 1.4225I
u = 0.600586 + 0.155632I
a = 2.04796 − 0.31700I
b = −2.31445 + 0.26373I
−4.65252 − 0.62859I −18.3165 + 1.4225I
u = 0.600586 − 0.155632I
a = −1.18251 − 1.06646I
b = 0.532477 − 0.072927I
−4.65252 + 0.62859I −18.3165 − 1.4225I
u = 0.600586 − 0.155632I
a = 2.04796 + 0.31700I
b = −2.31445 − 0.26373I
−4.65252 + 0.62859I −18.3165 − 1.4225I
u = 0.228017 + 1.369790I
a = −0.332944 + 0.904226I
b = 2.89859 + 1.41256I
0.22261 − 3.62879I −12.33383 + 2.63226I
u = 0.228017 + 1.369790I
a = −0.237127 − 0.803442I
b = 0.288686 + 0.146900I
0.22261 − 3.62879I −12.33383 + 2.63226I
u = 0.228017 − 1.369790I
a = −0.332944 − 0.904226I
b = 2.89859 − 1.41256I
0.22261 + 3.62879I −12.33383 − 2.63226I
u = 0.228017 − 1.369790I
a = −0.237127 + 0.803442I
b = 0.288686 − 0.146900I
0.22261 + 3.62879I −12.33383 − 2.63226I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.14277 + 1.43183I
a = 0.150261 − 0.788188I
b = −0.187283 + 0.114420I
4.53640 + 0.47055I −6.67171 + 0.18349I
u = −0.14277 + 1.43183I
a = −0.428432 + 0.007713I
b = 1.12407 − 0.96410I
4.53640 + 0.47055I −6.67171 + 0.18349I
u = −0.14277 − 1.43183I
a = 0.150261 + 0.788188I
b = −0.187283 − 0.114420I
4.53640 − 0.47055I −6.67171 − 0.18349I
u = −0.14277 − 1.43183I
a = −0.428432 − 0.007713I
b = 1.12407 + 0.96410I
4.53640 − 0.47055I −6.67171 − 0.18349I
u = −0.26614 + 1.42034I
a = 0.395255 + 0.876622I
b = −2.82299 + 0.90423I
2.77434 + 8.53123I −9.27652 − 6.18031I
u = −0.26614 + 1.42034I
a = −0.621525 − 0.029773I
b = 1.32479 − 0.63685I
2.77434 + 8.53123I −9.27652 − 6.18031I
u = −0.26614 − 1.42034I
a = 0.395255 − 0.876622I
b = −2.82299 − 0.90423I
2.77434 − 8.53123I −9.27652 + 6.18031I
u = −0.26614 − 1.42034I
a = −0.621525 + 0.029773I
b = 1.32479 + 0.63685I
2.77434 − 8.53123I −9.27652 + 6.18031I
12
III. I
u
3
= hb − 1, 2a + u, u
2
+ 2i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
2
a
8
=
−u
−u
a
9
=
0
−u
a
1
=
−1
0
a
4
=
1
0
a
10
=
−
1
2
u
1
a
6
=
−
1
2
u
u + 1
a
5
=
−
1
2
u
1
a
11
=
−
1
2
u − 1
1
a
11
=
−
1
2
u − 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u
2
+ 2
c
3
u
2
c
4
, c
9
(u − 1)
2
c
5
, c
6
, c
10
c
11
(u + 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
(y + 2)
2
c
3
y
2
c
4
, c
5
, c
6
c
9
, c
10
, c
11
(y −1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = − 0.707107I
b = 1.00000
1.64493 −12.0000
u = − 1.414210I
a = 0.707107I
b = 1.00000
1.64493 −12.0000
16
IV. I
v
1
= ha, b + 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
−1
0
a
2
=
1
0
a
8
=
−1
0
a
9
=
−1
0
a
1
=
1
0
a
4
=
1
0
a
10
=
0
−1
a
6
=
−1
1
a
5
=
0
1
a
11
=
1
−1
a
11
=
1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
u
c
4
, c
9
u + 1
c
5
, c
6
, c
10
c
11
u − 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
y
c
4
, c
5
, c
6
c
9
, c
10
, c
11
y − 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −1.00000
−3.28987 −12.0000
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u(u
2
+ 2)(u
14
+ u
13
+ ··· + u + 1)
2
(u
18
− 3u
17
+ ··· − 4u + 2)
c
3
u
3
(u
14
− 3u
13
+ ··· − 7u + 3)
2
(u
18
− 3u
17
+ ··· − 144u
2
+ 16)
c
4
, c
9
((u − 1)
2
)(u + 1)(u
18
+ u
17
+ ··· − u − 1)(u
28
+ u
27
+ ··· − 4u + 3)
c
5
, c
6
, c
10
c
11
(u − 1)(u + 1)
2
(u
18
+ u
17
+ ··· − u − 1)(u
28
+ u
27
+ ··· − 4u + 3)
c
8
u(u
2
+ 2)(u
14
− u
13
+ ··· + 3u + 1)
2
(u
18
+ 3u
17
+ ··· + 24u + 34)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y(y + 2)
2
(y
14
+ 13y
13
+ ··· − y + 1)
2
(y
18
+ 17y
17
+ ··· − 32y + 4)
c
3
y
3
(y
14
+ 5y
13
+ ··· + 23y + 9)
2
(y
18
+ 5y
17
+ ··· − 4608y + 256)
c
4
, c
5
, c
6
c
9
, c
10
, c
11
((y − 1)
3
)(y
18
− 19y
17
+ ··· − 13y + 1)(y
28
− 21y
27
+ ··· + 32y + 9)
c
8
y(y + 2)
2
(y
14
+ y
13
+ ··· − y + 1)
2
· (y
18
+ 5y
17
+ ··· − 4384y + 1156)
22
