11a
229
(K11a
229
)
A knot diagram
1
Linearized knot diagam
6 1 10 9 7 2 5 11 4 3 8
Solving Sequence
2,7
6 1 3 5 8 11 9 4 10
c
6
c
1
c
2
c
5
c
7
c
11
c
8
c
4
c
10
c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
35
− u
34
+ ··· − u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 35 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
= hu
35
− u
34
+ · · · − u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
3
u
5
− u
3
+ u
a
5
=
−u
2
+ 1
−u
2
a
8
=
u
4
− u
2
+ 1
u
4
a
11
=
u
11
− 2u
9
+ 4u
7
− 4u
5
+ 3u
3
u
11
− u
9
+ 2u
7
− u
5
− u
3
+ u
a
9
=
u
18
− 3u
16
+ 8u
14
− 13u
12
+ 17u
10
− 15u
8
+ 10u
6
− 2u
4
− u
2
+ 1
u
18
− 2u
16
+ 5u
14
− 6u
12
+ 5u
10
− 2u
8
− 2u
6
+ 4u
4
− u
2
a
4
=
−u
34
+ 5u
32
+ ··· − u
2
+ 1
−u
34
+ 4u
32
+ ··· + 4u
6
− u
2
a
10
=
u
19
− 2u
17
+ 6u
15
− 8u
13
+ 11u
11
− 10u
9
+ 8u
7
− 4u
5
+ 3u
3
−u
21
+ 3u
19
+ ··· − u
3
+ u
a
10
=
u
19
− 2u
17
+ 6u
15
− 8u
13
+ 11u
11
− 10u
9
+ 8u
7
− 4u
5
+ 3u
3
−u
21
+ 3u
19
+ ··· − u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
33
−4u
32
−16u
31
+20u
30
+64u
29
−76u
28
−160u
27
+204u
26
+356u
25
−440u
24
−624u
23
+
772u
22
+ 948u
21
−1120u
20
−1204u
19
+ 1336u
18
+ 1308u
17
−1304u
16
−1180u
15
+ 984u
14
+
888u
13
−528u
12
−512u
11
+128u
10
+216u
9
+80u
8
−40u
7
−96u
6
−16u
5
+32u
4
+16u
3
+4u−10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
35
− u
34
+ ··· − u
2
+ 1
c
2
, c
5
, c
7
u
35
+ 9u
34
+ ··· + 2u + 1
c
3
, c
4
, c
9
c
10
u
35
− u
34
+ ··· + 2u + 1
c
8
, c
11
u
35
+ 7u
34
+ ··· + 8u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
35
− 9y
34
+ ··· + 2y −1
c
2
, c
5
, c
7
y
35
+ 35y
34
+ ··· + 18y −1
c
3
, c
4
, c
9
c
10
y
35
+ 39y
34
+ ··· + 2y −1
c
8
, c
11
y
35
+ 15y
34
+ ··· − 14y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.962624 + 0.303218I
−3.18298 − 4.64820I −10.32267 + 8.03074I
u = 0.962624 − 0.303218I
−3.18298 + 4.64820I −10.32267 − 8.03074I
u = 0.966916 + 0.178086I
2.77604 + 1.42603I −8.39342 + 0.40844I
u = 0.966916 − 0.178086I
2.77604 − 1.42603I −8.39342 − 0.40844I
u = −0.949626 + 0.247846I
−3.51316 + 0.86929I −12.03394 − 0.57851I
u = −0.949626 − 0.247846I
−3.51316 − 0.86929I −12.03394 + 0.57851I
u = −0.982664 + 0.344890I
3.73413 + 7.15489I −6.21404 − 6.89294I
u = −0.982664 − 0.344890I
3.73413 − 7.15489I −6.21404 + 6.89294I
u = −0.625205 + 0.585600I
8.06862 + 2.14485I 0.03823 − 3.39579I
u = −0.625205 − 0.585600I
8.06862 − 2.14485I 0.03823 + 3.39579I
u = 0.826215 + 0.817094I
3.13686 − 1.06908I −6.00348 + 2.72542I
u = 0.826215 − 0.817094I
3.13686 + 1.06908I −6.00348 − 2.72542I
u = −0.899785 + 0.739431I
7.92591 + 2.80573I −2.67118 − 2.92017I
u = −0.899785 − 0.739431I
7.92591 − 2.80573I −2.67118 + 2.92017I
u = −0.815673 + 0.849045I
4.17141 − 2.71608I −3.22921 + 3.46654I
u = −0.815673 − 0.849045I
4.17141 + 2.71608I −3.22921 − 3.46654I
u = 0.815012 + 0.872021I
11.60150 + 5.24626I −0.28520 − 2.12331I
u = 0.815012 − 0.872021I
11.60150 − 5.24626I −0.28520 + 2.12331I
u = −0.895926 + 0.820169I
7.25366 + 3.06074I 0.53879 − 2.89823I
u = −0.895926 − 0.820169I
7.25366 − 3.06074I 0.53879 + 2.89823I
u = 0.950191 + 0.783875I
2.75474 − 4.93362I −6.65730 + 2.46852I
u = 0.950191 − 0.783875I
2.75474 + 4.93362I −6.65730 − 2.46852I
u = 0.909352 + 0.854322I
15.6759 − 3.1687I 1.84371 + 2.55774I
u = 0.909352 − 0.854322I
15.6759 + 3.1687I 1.84371 − 2.55774I
u = −0.968524 + 0.797329I
3.69689 + 8.85353I −4.28524 − 8.34437I
u = −0.968524 − 0.797329I
3.69689 − 8.85353I −4.28524 + 8.34437I
u = 0.979984 + 0.808991I
11.0850 − 11.4893I −1.26828 + 6.96489I
u = 0.979984 − 0.808991I
11.0850 + 11.4893I −1.26828 − 6.96489I
u = 0.616861 + 0.373834I
0.93698 − 1.48910I −0.78415 + 6.55847I
u = 0.616861 − 0.373834I
0.93698 + 1.48910I −0.78415 − 6.55847I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.163878 + 0.627930I
6.28325 − 3.67948I −0.34607 + 2.46375I
u = −0.163878 − 0.627930I
6.28325 + 3.67948I −0.34607 − 2.46375I
u = −0.621610
−0.791732 −13.6740
u = 0.084932 + 0.544457I
−0.58473 + 1.62274I −4.08967 − 4.27499I
u = 0.084932 − 0.544457I
−0.58473 − 1.62274I −4.08967 + 4.27499I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
35
− u
34
+ ··· − u
2
+ 1
c
2
, c
5
, c
7
u
35
+ 9u
34
+ ··· + 2u + 1
c
3
, c
4
, c
9
c
10
u
35
− u
34
+ ··· + 2u + 1
c
8
, c
11
u
35
+ 7u
34
+ ··· + 8u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
35
− 9y
34
+ ··· + 2y −1
c
2
, c
5
, c
7
y
35
+ 35y
34
+ ··· + 18y −1
c
3
, c
4
, c
9
c
10
y
35
+ 39y
34
+ ··· + 2y −1
c
8
, c
11
y
35
+ 15y
34
+ ··· − 14y −1
8
