11a
362
(K11a
362
)
A knot diagram
1
Linearized knot diagam
8 7 9 1 11 10 2 4 3 6 5
Solving Sequence
3,7
2 8
1,10
6 11 5 9 4
c
2
c
7
c
1
c
6
c
10
c
5
c
9
c
3
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u, u
10
− u
9
+ 7u
8
− 8u
7
+ 17u
6
− 20u
5
+ 14u
4
− 12u
3
+ 4a + 9u + 1,
u
11
+ 8u
9
− u
8
+ 23u
7
− 5u
6
+ 26u
5
− 6u
4
+ 8u
3
+ u
2
+ 2u − 1i
I
u
2
= h−5u
11
− 82u
10
+ ··· + 547b − 41, 572u
11
+ 957u
10
+ ··· + 2735a + 3487,
u
12
+ u
11
+ 6u
10
+ 6u
9
+ 13u
8
+ 11u
7
+ 15u
6
+ 7u
5
+ 17u
4
+ 5u
3
+ 16u
2
+ 6u + 5i
I
u
3
= hb + u, a
2
− a − 1, u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 27 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
= hb − u, u
10
− u
9
+ · · · + 4a + 1, u
11
+ 8u
9
+ · · · + 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
8
=
−u
u
3
+ u
a
1
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
−
1
4
u
10
+
1
4
u
9
+ ··· −
9
4
u −
1
4
u
a
6
=
−
1
2
u
10
− 4u
8
+ ··· + 2u −
1
2
1
4
u
10
−
1
4
u
9
+ ··· +
1
4
u +
1
4
a
11
=
−
1
2
u
10
−
1
2
u
9
+ ··· −
5
2
u
2
− u
1
4
u
10
+
1
4
u
9
+ ··· −
1
4
u +
1
4
a
5
=
1
4
u
10
+
1
4
u
9
+ ··· +
1
4
u +
3
4
1
4
u
10
+
1
4
u
9
+ ··· +
1
4
u −
1
4
a
9
=
−
1
4
u
10
+
1
4
u
9
+ ··· −
5
4
u −
1
4
u
a
4
=
1
4
u
10
+
1
4
u
9
+ ··· +
1
4
u +
3
4
u
2
a
4
=
1
4
u
10
+
1
4
u
9
+ ··· +
1
4
u +
3
4
u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −3u
10
− 2u
9
− 24u
8
− 12u
7
− 66u
6
− 25u
5
− 65u
4
− 23u
3
− 11u
2
− 14u − 13
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
u
11
+ 8u
9
+ u
8
+ 23u
7
+ 5u
6
+ 26u
5
+ 6u
4
+ 8u
3
− u
2
+ 2u + 1
c
4
, c
5
, c
6
c
10
, c
11
u
11
+ 3u
10
+ ··· + 13u + 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
y
11
+ 16y
10
+ ··· + 6y −1
c
4
, c
5
, c
6
c
10
, c
11
y
11
+ 15y
10
+ ··· + 37y −4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.412939 + 0.618853I
a = −1.86851 − 1.24582I
b = 0.412939 + 0.618853I
10.82280 − 1.46957I −5.57474 + 4.71346I
u = 0.412939 − 0.618853I
a = −1.86851 + 1.24582I
b = 0.412939 − 0.618853I
10.82280 + 1.46957I −5.57474 − 4.71346I
u = −0.360154 + 0.393035I
a = 1.25715 − 0.93867I
b = −0.360154 + 0.393035I
1.95559 + 1.25455I −6.26218 − 5.85654I
u = −0.360154 − 0.393035I
a = 1.25715 + 0.93867I
b = −0.360154 − 0.393035I
1.95559 − 1.25455I −6.26218 + 5.85654I
u = −0.07033 + 1.59466I
a = 0.276929 + 0.448902I
b = −0.07033 + 1.59466I
10.55850 + 2.37127I −3.60289 − 2.68530I
u = −0.07033 − 1.59466I
a = 0.276929 − 0.448902I
b = −0.07033 − 1.59466I
10.55850 − 2.37127I −3.60289 + 2.68530I
u = 0.22374 + 1.62996I
a = −0.756490 + 0.157129I
b = 0.22374 + 1.62996I
15.5882 − 6.3668I −0.98879 + 3.90232I
u = 0.22374 − 1.62996I
a = −0.756490 − 0.157129I
b = 0.22374 − 1.62996I
15.5882 + 6.3668I −0.98879 − 3.90232I
u = 0.314433
a = −0.886718
b = 0.314433
−0.496230 −19.9870
u = −0.36341 + 1.67319I
a = 1.034280 − 0.155633I
b = −0.36341 + 1.67319I
−13.1804 + 8.7652I −0.57808 − 3.37097I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.36341 − 1.67319I
a = 1.034280 + 0.155633I
b = −0.36341 − 1.67319I
−13.1804 − 8.7652I −0.57808 + 3.37097I
6
II. I
u
2
= h−5u
11
− 82u
10
+ · · · + 547b − 41, 572u
11
+ 957u
10
+ · · · + 2735a +
3487, u
12
+ u
11
+ · · · + 6u + 5i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
8
=
−u
u
3
+ u
a
1
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
−0.209141u
11
− 0.349909u
10
+ ··· − 1.48702u − 1.27495
0.00914077u
11
+ 0.149909u
10
+ ··· − 1.71298u + 0.0749543
a
6
=
0.0138940u
11
− 0.0921389u
10
+ ··· + 0.116271u − 0.646069
−0.223035u
11
− 0.257770u
10
+ ··· − 0.603291u − 0.628885
a
11
=
0.0277879u
11
− 0.184278u
10
+ ··· − 0.767459u − 1.29214
0.0182815u
11
+ 0.299817u
10
+ ··· − 0.425960u + 0.149909
a
5
=
0.0197441u
11
− 0.236197u
10
+ ··· + 0.0599634u − 0.918099
−0.234004u
11
− 0.237660u
10
+ ··· − 0.747715u − 1.11883
a
9
=
−
1
5
u
11
−
1
5
u
10
+ ··· −
16
5
u −
6
5
0.00914077u
11
+ 0.149909u
10
+ ··· − 1.71298u + 0.0749543
a
4
=
−0.0149909u
11
− 0.00585009u
10
+ ··· + 0.769287u − 0.802925
−0.140768u
11
+ 0.0914077u
10
+ ··· − 0.0201097u − 0.954296
a
4
=
−0.0149909u
11
− 0.00585009u
10
+ ··· + 0.769287u − 0.802925
−0.140768u
11
+ 0.0914077u
10
+ ··· − 0.0201097u − 0.954296
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
828
547
u
11
+
424
547
u
10
−
3252
547
u
9
+
964
547
u
8
−
2920
547
u
7
+
624
547
u
6
−
3248
547
u
5
+
4136
547
u
4
−
9020
547
u
3
+
7924
547
u
2
−
3244
547
u −
882
547
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
u
12
− u
11
+ ··· − 6u + 5
c
4
, c
5
, c
6
c
10
, c
11
(u
6
− u
5
+ 5u
4
− 4u
3
+ 6u
2
− 3u + 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
y
12
+ 11y
11
+ ··· + 124y + 25
c
4
, c
5
, c
6
c
10
, c
11
(y
6
+ 9y
5
+ 29y
4
+ 40y
3
+ 22y
2
+ 3y + 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.778448 + 0.629355I
a = 0.839269 + 0.810995I
b = −0.06243 − 1.43905I
7.93269 − 2.65597I −2.41885 + 3.39809I
u = 0.778448 − 0.629355I
a = 0.839269 − 0.810995I
b = −0.06243 + 1.43905I
7.93269 + 2.65597I −2.41885 − 3.39809I
u = 0.010658 + 1.201250I
a = 0.301274 − 0.265056I
b = −0.293888 − 0.567347I
3.03178 − 1.10871I −7.53615 + 6.18117I
u = 0.010658 − 1.201250I
a = 0.301274 + 0.265056I
b = −0.293888 + 0.567347I
3.03178 + 1.10871I −7.53615 − 6.18117I
u = −1.047750 + 0.669346I
a = −0.79276 + 1.18795I
b = 0.11496 − 1.62096I
18.6443 + 3.4272I −2.04500 − 2.25224I
u = −1.047750 − 0.669346I
a = −0.79276 − 1.18795I
b = 0.11496 + 1.62096I
18.6443 − 3.4272I −2.04500 + 2.25224I
u = −0.293888 + 0.567347I
a = −0.730525 − 0.188448I
b = 0.010658 − 1.201250I
3.03178 + 1.10871I −7.53615 − 6.18117I
u = −0.293888 − 0.567347I
a = −0.730525 + 0.188448I
b = 0.010658 + 1.201250I
3.03178 − 1.10871I −7.53615 + 6.18117I
u = −0.06243 + 1.43905I
a = −0.808537 − 0.064242I
b = 0.778448 − 0.629355I
7.93269 + 2.65597I −2.41885 − 3.39809I
u = −0.06243 − 1.43905I
a = −0.808537 + 0.064242I
b = 0.778448 + 0.629355I
7.93269 − 2.65597I −2.41885 + 3.39809I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.11496 + 1.62096I
a = 1.091280 + 0.055514I
b = −1.047750 − 0.669346I
18.6443 − 3.4272I −2.04500 + 2.25224I
u = 0.11496 − 1.62096I
a = 1.091280 − 0.055514I
b = −1.047750 + 0.669346I
18.6443 + 3.4272I −2.04500 − 2.25224I
11
III. I
u
3
= hb + u, a
2
− a − 1, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
1
a
8
=
−u
0
a
1
=
0
1
a
10
=
a
−u
a
6
=
au + u
a + u
a
11
=
−a − 1
au − a
a
5
=
−au
−au − 1
a
9
=
a − u
−u
a
4
=
−au
−1
a
4
=
−au
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
(u
2
+ 1)
2
c
4
, c
5
, c
6
c
10
, c
11
u
4
+ 3u
2
+ 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
(y + 1)
4
c
4
, c
5
, c
6
c
10
, c
11
(y
2
+ 3y + 1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.618034
b = − 1.000000I
4.27683 0
u = 1.000000I
a = 1.61803
b = − 1.000000I
12.1725 0
u = − 1.000000I
a = −0.618034
b = 1.000000I
4.27683 0
u = − 1.000000I
a = 1.61803
b = 1.000000I
12.1725 0
15
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
((u
2
+ 1)
2
)(u
11
+ 8u
9
+ ··· + 2u + 1)
· (u
12
− u
11
+ ··· − 6u + 5)
c
4
, c
5
, c
6
c
10
, c
11
(u
4
+ 3u
2
+ 1)(u
6
− u
5
+ 5u
4
− 4u
3
+ 6u
2
− 3u + 1)
2
· (u
11
+ 3u
10
+ ··· + 13u + 2)
16
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
9
((y + 1)
4
)(y
11
+ 16y
10
+ ··· + 6y −1)(y
12
+ 11y
11
+ ··· + 124y + 25)
c
4
, c
5
, c
6
c
10
, c
11
(y
2
+ 3y + 1)
2
(y
6
+ 9y
5
+ 29y
4
+ 40y
3
+ 22y
2
+ 3y + 1)
2
· (y
11
+ 15y
10
+ ··· + 37y −4)
17
