11a
106
(K11a
106
)
A knot diagram
1
Linearized knot diagam
5 1 8 9 2 11 3 4 7 6 10
Solving Sequence
6,11 2,7
5 10 1 3 9 4 8
c
6
c
5
c
10
c
11
c
2
c
9
c
4
c
8
c
1
, c
3
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hb − u,
u
17
− u
16
− 3u
15
+ 4u
14
+ 6u
13
− 9u
12
− 4u
11
+ 11u
10
+ 2u
9
− 9u
8
+ 4u
7
+ 4u
6
− 2u
4
+ 4u
3
+ u
2
+ 2a + 2u − 1,
u
19
− u
18
+ ··· − 2u
2
+ 1i
I
u
2
= h−37263u
29
− 111490u
28
+ ··· + 162577b + 113039,
125314u
29
− 274067u
28
+ ··· + 162577a + 438193, u
30
− u
29
+ ··· + 2u − 1i
I
u
3
= hb + 1, a + 2, u − 1i
I
u
4
= hb − 1, a
2
− 4a + 2, u + 1i
* 4 irreducible components of dim
C
= 0, with total 52 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
17
− u
16
+ · · · + 2a − 1, u
19
− u
18
+ · · · − 2u
2
+ 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
−
1
2
u
17
+
1
2
u
16
+ ··· − u +
1
2
u
a
7
=
1
u
2
a
5
=
1
2
u
18
−
1
2
u
17
+ ··· −
1
2
u + 1
−u
2
a
10
=
u
u
a
1
=
−u
3
−u
3
+ u
a
3
=
−
1
2
u
17
+
1
2
u
16
+ ··· − u +
1
2
u
5
− u
3
+ u
a
9
=
u
3
u
5
− u
3
+ u
a
4
=
u
18
− u
17
+ ··· − u + 1
1
2
u
18
−
1
2
u
17
+ ··· +
1
2
u
3
−
1
2
u
a
8
=
u
18
−
3
2
u
17
+ ··· − 2u +
3
2
−
1
2
u
18
+
1
2
u
17
+ ··· −
1
2
u
3
+
1
2
u
a
8
=
u
18
−
3
2
u
17
+ ··· − 2u +
3
2
−
1
2
u
18
+
1
2
u
17
+ ··· −
1
2
u
3
+
1
2
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
18
− u
17
− 9u
16
+ 5u
15
+ 26u
14
− 14u
13
− 43u
12
+ 26u
11
+
51u
10
− 34u
9
− 31u
8
+ 32u
7
+ 12u
6
− 20u
5
+ 6u
4
+ 10u
3
+ 5u
2
− 4u − 1
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
u
19
+ u
18
+ ··· + 2u
2
− 1
c
2
, c
11
u
19
+ 9u
18
+ ··· + 4u + 1
c
3
, c
4
, c
7
c
8
u
19
+ 3u
18
+ ··· + 2u − 2
c
9
u
19
+ 3u
18
+ ··· + 16u − 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
y
19
− 9y
18
+ ··· + 4y −1
c
2
, c
11
y
19
+ 7y
18
+ ··· − 4y −1
c
3
, c
4
, c
7
c
8
y
19
− 21y
18
+ ··· − 4y −4
c
9
y
19
+ 7y
18
+ ··· + 2816y −256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.812789 + 0.553417I
a = −0.76890 − 1.22204I
b = −0.812789 + 0.553417I
1.82665 + 4.33190I 3.09756 − 7.93622I
u = −0.812789 − 0.553417I
a = −0.76890 + 1.22204I
b = −0.812789 − 0.553417I
1.82665 − 4.33190I 3.09756 + 7.93622I
u = 0.865007 + 0.704905I
a = 1.072110 − 0.840866I
b = 0.865007 + 0.704905I
10.08310 − 5.40272I 4.82648 + 5.68964I
u = 0.865007 − 0.704905I
a = 1.072110 + 0.840866I
b = 0.865007 − 0.704905I
10.08310 + 5.40272I 4.82648 − 5.68964I
u = 0.347731 + 0.806765I
a = 0.287964 − 0.269780I
b = 0.347731 + 0.806765I
8.56139 + 2.84598I 6.12727 − 0.57057I
u = 0.347731 − 0.806765I
a = 0.287964 + 0.269780I
b = 0.347731 − 0.806765I
8.56139 − 2.84598I 6.12727 + 0.57057I
u = −1.072710 + 0.432309I
a = −1.91340 − 1.91365I
b = −1.072710 + 0.432309I
0.89681 + 2.96240I −1.25513 − 4.67576I
u = −1.072710 − 0.432309I
a = −1.91340 + 1.91365I
b = −1.072710 − 0.432309I
0.89681 − 2.96240I −1.25513 + 4.67576I
u = 1.135950 + 0.496880I
a = 2.09240 − 1.47882I
b = 1.135950 + 0.496880I
−4.68926 − 6.06103I −4.96256 + 4.06889I
u = 1.135950 − 0.496880I
a = 2.09240 + 1.47882I
b = 1.135950 − 0.496880I
−4.68926 + 6.06103I −4.96256 − 4.06889I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.651125 + 0.371544I
a = −0.115490 − 1.188520I
b = 0.651125 + 0.371544I
−0.69486 − 1.46005I −2.24162 + 4.71190I
u = 0.651125 − 0.371544I
a = −0.115490 + 1.188520I
b = 0.651125 − 0.371544I
−0.69486 + 1.46005I −2.24162 − 4.71190I
u = −1.171910 + 0.539955I
a = −2.14090 − 1.24940I
b = −1.171910 + 0.539955I
−3.93034 + 10.41950I −3.27524 − 9.24443I
u = −1.171910 − 0.539955I
a = −2.14090 + 1.24940I
b = −1.171910 − 0.539955I
−3.93034 − 10.41950I −3.27524 + 9.24443I
u = −0.686077
a = 1.90633
b = −0.686077
2.96406 4.32400
u = −0.296841 + 0.610442I
a = −0.117122 − 0.390719I
b = −0.296841 + 0.610442I
1.19212 − 1.04367I 4.57560 + 2.19936I
u = −0.296841 − 0.610442I
a = −0.117122 + 0.390719I
b = −0.296841 − 0.610442I
1.19212 + 1.04367I 4.57560 − 2.19936I
u = 1.197470 + 0.579281I
a = 2.15018 − 1.07944I
b = 1.197470 + 0.579281I
3.36659 − 13.40010I −0.05434 + 8.12876I
u = 1.197470 − 0.579281I
a = 2.15018 + 1.07944I
b = 1.197470 − 0.579281I
3.36659 + 13.40010I −0.05434 − 8.12876I
6
II.
I
u
2
= h−3.73 × 10
4
u
29
− 1.11 × 10
5
u
28
+ · · · + 1.63 × 10
5
b + 1.13 × 10
5
, 1.25 ×
10
5
u
29
− 2.74 × 10
5
u
28
+ · · · + 1.63 × 10
5
a + 4.38 × 10
5
, u
30
− u
29
+ · · · + 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
−0.770798u
29
+ 1.68577u
28
+ ··· + 0.897808u − 2.69530
0.229202u
29
+ 0.685767u
28
+ ··· − 1.10219u − 0.695295
a
7
=
1
u
2
a
5
=
0.219674u
29
+ 0.569613u
28
+ ··· + 3.03192u − 2.26358
0.914970u
29
− 0.354884u
28
+ ··· − 1.15370u − 0.770798
a
10
=
u
u
a
1
=
−u
3
−u
3
+ u
a
3
=
−0.667228u
29
+ 1.85414u
28
+ ··· + 1.11916u − 3.08601
0.892857u
29
+ 0.684771u
28
+ ··· − 3.48157u − 0.171045
a
9
=
u
3
u
5
− u
3
+ u
a
4
=
0.120681u
29
+ 0.253677u
28
+ ··· + 3.97856u − 2.66124
1.47694u
29
− 0.641395u
28
+ ··· − 1.62083u − 1.34137
a
8
=
−1.35965u
29
+ 0.714234u
28
+ ··· + 4.37797u − 3.99301
0.147635u
29
− 0.397719u
28
+ ··· − 1.70941u − 2.11106
a
8
=
−1.35965u
29
+ 0.714234u
28
+ ··· + 4.37797u − 3.99301
0.147635u
29
− 0.397719u
28
+ ··· − 1.70941u − 2.11106
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
174400
162577
u
29
+
211456
162577
u
28
+ ··· −
402552
162577
u +
413650
162577
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
u
30
+ u
29
+ ··· − 2u − 1
c
2
, c
11
u
30
+ 17u
29
+ ··· + 8u
2
+ 1
c
3
, c
4
, c
7
c
8
(u
15
− u
14
+ ··· − 2u − 1)
2
c
9
(u
15
+ 3u
14
+ ··· − 4u
2
+ 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
y
30
− 17y
29
+ ··· + 8y
2
+ 1
c
2
, c
11
y
30
− 9y
29
+ ··· + 16y + 1
c
3
, c
4
, c
7
c
8
(y
15
− 17y
14
+ ··· + 8y −1)
2
c
9
(y
15
+ 7y
14
+ ··· + 8y −1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.716927 + 0.736174I
a = 0.0379780 − 0.0389976I
b = 0.716927 − 0.736174I
10.5121 5.97706 + 0.I
u = 0.716927 − 0.736174I
a = 0.0379780 + 0.0389976I
b = 0.716927 + 0.736174I
10.5121 5.97706 + 0.I
u = 0.246680 + 0.896428I
a = 0.846092 + 0.456626I
b = 1.131460 − 0.580385I
6.22908 + 8.01682I 3.04132 − 4.89679I
u = 0.246680 − 0.896428I
a = 0.846092 − 0.456626I
b = 1.131460 + 0.580385I
6.22908 − 8.01682I 3.04132 + 4.89679I
u = 1.12548
a = −1.67481
b = −0.786295
−2.69194 4.62820
u = 1.053770 + 0.396631I
a = −0.660279 − 0.334663I
b = 0.170936 − 0.647526I
−1.99092 − 1.64925I −2.39367 + 0.16522I
u = 1.053770 − 0.396631I
a = −0.660279 + 0.334663I
b = 0.170936 + 0.647526I
−1.99092 + 1.64925I −2.39367 − 0.16522I
u = −0.651659 + 0.523428I
a = 0.281100 + 0.225787I
b = −0.651659 − 0.523428I
2.23561 5.03935 + 0.I
u = −0.651659 − 0.523428I
a = 0.281100 − 0.225787I
b = −0.651659 + 0.523428I
2.23561 5.03935 + 0.I
u = −0.212223 + 0.801752I
a = −0.793447 + 0.659092I
b = −1.101980 − 0.506508I
−1.10658 − 5.45324I −0.00468 + 6.35130I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.212223 − 0.801752I
a = −0.793447 − 0.659092I
b = −1.101980 + 0.506508I
−1.10658 + 5.45324I −0.00468 − 6.35130I
u = −1.176320 + 0.122445I
a = 1.120030 − 0.323137I
b = 0.279034 − 0.410677I
3.47397 − 0.15908I 1.79403 − 0.85194I
u = −1.176320 − 0.122445I
a = 1.120030 + 0.323137I
b = 0.279034 + 0.410677I
3.47397 + 0.15908I 1.79403 + 0.85194I
u = 1.087970 + 0.476458I
a = −2.06013 + 0.62143I
b = −1.288900 + 0.283680I
1.23287 − 4.11725I −1.40312 + 3.71929I
u = 1.087970 − 0.476458I
a = −2.06013 − 0.62143I
b = −1.288900 − 0.283680I
1.23287 + 4.11725I −1.40312 − 3.71929I
u = −1.134360 + 0.387877I
a = 1.99836 + 0.59003I
b = 1.209080 + 0.320151I
−5.46412 + 1.81248I −5.85619 − 4.33913I
u = −1.134360 − 0.387877I
a = 1.99836 − 0.59003I
b = 1.209080 − 0.320151I
−5.46412 − 1.81248I −5.85619 + 4.33913I
u = −1.101980 + 0.506508I
a = 0.536960 − 0.457402I
b = −0.212223 − 0.801752I
−1.10658 + 5.45324I −0.00468 − 6.35130I
u = −1.101980 − 0.506508I
a = 0.536960 + 0.457402I
b = −0.212223 + 0.801752I
−1.10658 − 5.45324I −0.00468 + 6.35130I
u = −0.786295
a = 2.39726
b = 1.12548
−2.69194 4.62820
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.209080 + 0.320151I
a = −1.90725 + 0.59253I
b = −1.134360 + 0.387877I
−5.46412 + 1.81248I −5.85619 − 4.33913I
u = 1.209080 − 0.320151I
a = −1.90725 − 0.59253I
b = −1.134360 − 0.387877I
−5.46412 − 1.81248I −5.85619 + 4.33913I
u = 1.131460 + 0.580385I
a = −0.453027 − 0.537511I
b = 0.246680 − 0.896428I
6.22908 − 8.01682I 3.04132 + 4.89679I
u = 1.131460 − 0.580385I
a = −0.453027 + 0.537511I
b = 0.246680 + 0.896428I
6.22908 + 8.01682I 3.04132 − 4.89679I
u = −1.288900 + 0.283680I
a = 1.82798 + 0.63933I
b = 1.087970 + 0.476458I
1.23287 − 4.11725I −1.40312 + 3.71929I
u = −1.288900 − 0.283680I
a = 1.82798 − 0.63933I
b = 1.087970 − 0.476458I
1.23287 + 4.11725I −1.40312 − 3.71929I
u = 0.170936 + 0.647526I
a = 0.672650 + 1.047100I
b = 1.053770 − 0.396631I
−1.99092 + 1.64925I −2.39367 − 0.16522I
u = 0.170936 − 0.647526I
a = 0.672650 − 1.047100I
b = 1.053770 + 0.396631I
−1.99092 − 1.64925I −2.39367 + 0.16522I
u = 0.279034 + 0.410677I
a = −2.30824 + 1.54348I
b = −1.176320 − 0.122445I
3.47397 + 0.15908I 1.79403 + 0.85194I
u = 0.279034 − 0.410677I
a = −2.30824 − 1.54348I
b = −1.176320 + 0.122445I
3.47397 − 0.15908I 1.79403 − 0.85194I
12
III. I
u
3
= hb + 1, a + 2, u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
1
a
2
=
−2
−1
a
7
=
1
1
a
5
=
−1
−1
a
10
=
1
1
a
1
=
−1
0
a
3
=
−1
−1
a
9
=
1
1
a
4
=
−1
−1
a
8
=
1
1
a
8
=
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
6
u − 1
c
2
, c
5
, c
10
c
11
u + 1
c
3
, c
4
, c
7
c
8
, c
9
u
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
10
, c
11
y −1
c
3
, c
4
, c
7
c
8
, c
9
y
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −2.00000
b = −1.00000
−3.28987 −12.0000
16
IV. I
u
4
= hb − 1, a
2
− 4a + 2, u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
−1
a
2
=
a
1
a
7
=
1
1
a
5
=
−a + 1
−1
a
10
=
−1
−1
a
1
=
1
0
a
3
=
a − 1
1
a
9
=
−1
−1
a
4
=
−2a + 3
−a + 1
a
8
=
a + 1
a − 1
a
8
=
a + 1
a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
11
(u + 1)
2
c
3
, c
4
, c
7
c
8
u
2
− 2
c
5
, c
10
(u − 1)
2
c
9
u
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
10
, c
11
(y −1)
2
c
3
, c
4
, c
7
c
8
(y −2)
2
c
9
y
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = 0.585786
b = 1.00000
1.64493 −4.00000
u = −1.00000
a = 3.41421
b = 1.00000
1.64493 −4.00000
20
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
(u − 1)(u + 1)
2
(u
19
+ u
18
+ ··· + 2u
2
− 1)(u
30
+ u
29
+ ··· − 2u − 1)
c
2
, c
11
((u + 1)
3
)(u
19
+ 9u
18
+ ··· + 4u + 1)(u
30
+ 17u
29
+ ··· + 8u
2
+ 1)
c
3
, c
4
, c
7
c
8
u(u
2
− 2)(u
15
− u
14
+ ··· − 2u − 1)
2
(u
19
+ 3u
18
+ ··· + 2u − 2)
c
5
, c
10
((u − 1)
2
)(u + 1)(u
19
+ u
18
+ ··· + 2u
2
− 1)(u
30
+ u
29
+ ··· − 2u − 1)
c
9
u
3
(u
15
+ 3u
14
+ ··· − 4u
2
+ 1)
2
(u
19
+ 3u
18
+ ··· + 16u − 16)
21
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
((y −1)
3
)(y
19
− 9y
18
+ ··· + 4y −1)(y
30
− 17y
29
+ ··· + 8y
2
+ 1)
c
2
, c
11
((y −1)
3
)(y
19
+ 7y
18
+ ··· − 4y −1)(y
30
− 9y
29
+ ··· + 16y + 1)
c
3
, c
4
, c
7
c
8
y(y −2)
2
(y
15
− 17y
14
+ ··· + 8y −1)
2
(y
19
− 21y
18
+ ··· − 4y −4)
c
9
y
3
(y
15
+ 7y
14
+ ··· + 8y −1)
2
(y
19
+ 7y
18
+ ··· + 2816y −256)
22
