11n
170
(K11n
170
)
A knot diagram
1
Linearized knot diagam
6 10 1 11 2 4 1 11 3 5 8
Solving Sequence
2,10 3,5
6 11 1 4 7 9 8
c
2
c
5
c
10
c
1
c
4
c
6
c
9
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−25u
16
− 25u
15
+ ··· + 18b + 137, a − 1, u
17
+ 6u
15
+ ··· − u − 1i
I
u
2
= h−5.20249 × 10
17
u
23
+ 5.01695 × 10
18
u
22
+ ··· + 1.95146 × 10
19
b + 5.92561 × 10
20
,
− 1.39688 × 10
24
u
23
+ 6.26259 × 10
24
u
22
+ ··· + 1.95641 × 10
25
a + 5.44584 × 10
26
,
u
24
− u
23
+ ··· + 224u + 173i
I
u
3
= hu
9
− u
8
+ 5u
7
− 3u
6
+ 12u
5
− 2u
4
+ 10u
3
+ u
2
+ 3b + u − 2, a + 1,
u
10
+ 4u
8
− u
7
+ 6u
6
− 2u
5
+ 2u
4
− u
3
− u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 51 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−25u
16
− 25u
15
+ · · · + 18b + 137, a − 1, u
17
+ 6u
15
+ · · · − u − 1i
(i) Arc colorings
a
2
=
1
0
a
10
=
0
u
a
3
=
1
−u
2
a
5
=
1
1.38889u
16
+ 1.38889u
15
+ ··· + 4.77778u − 7.61111
a
6
=
1.38889u
16
+ 1.38889u
15
+ ··· + 4.77778u − 6.61111
1.38889u
16
+ 1.38889u
15
+ ··· + 4.77778u − 7.61111
a
11
=
u
1.38889u
16
− 1.61111u
15
+ ··· − 5.22222u + 1.38889
a
1
=
−0.277778u
16
+ 1.05556u
15
+ ··· + 3.44444u − 2.61111
−
5
3
u
16
−
1
3
u
15
+ ··· −
4
3
u + 4
a
4
=
u
2
+ 1
−
2
9
u
16
+
25
9
u
15
+ ··· +
68
9
u −
56
9
a
7
=
1
6
u
16
+
1
2
u
15
+ ··· +
7
3
u −
7
6
55
9
u
16
−
23
9
u
15
+ ··· −
43
9
u −
83
9
a
9
=
−u
u
3
+ u
a
8
=
−1.38889u
16
+ 0.611111u
15
+ ··· − 0.777778u + 1.61111
−
26
9
u
16
+
7
9
u
15
+ ··· +
2
9
u +
40
9
a
8
=
−1.38889u
16
+ 0.611111u
15
+ ··· − 0.777778u + 1.61111
−
26
9
u
16
+
7
9
u
15
+ ··· +
2
9
u +
40
9
(ii) Obstruction class = −1
(iii) Cusp Shapes =
103
9
u
16
−
2
9
u
15
+
601
9
u
14
+
122
9
u
13
+
1927
9
u
12
+
542
9
u
11
+
3436
9
u
10
+
1481
9
u
9
+
3799
9
u
8
+
2359
9
u
7
+
2344
9
u
6
+ 257u
5
+ 88u
4
+
862
9
u
3
+
40
3
u
2
+
35
9
u −
170
9
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
17
− 9u
16
+ ··· + 144u − 16
c
2
, c
4
, c
9
c
10
u
17
+ 6u
15
+ ··· − u − 1
c
3
, c
6
u
17
+ 9u
15
+ ··· + 3u
2
− 1
c
7
, c
8
, c
11
u
17
+ 9u
16
+ ··· − 32u − 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
17
+ 15y
16
+ ··· + 1408y −256
c
2
, c
4
, c
9
c
10
y
17
+ 12y
16
+ ··· − y −1
c
3
, c
6
y
17
+ 18y
16
+ ··· + 6y −1
c
7
, c
8
, c
11
y
17
+ 9y
16
+ ··· + 160y −64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.145212 + 0.987929I
a = 1.00000
b = −0.861098 + 1.080220I
−1.58511 + 1.52682I 1.71933 − 1.54413I
u = 0.145212 − 0.987929I
a = 1.00000
b = −0.861098 − 1.080220I
−1.58511 − 1.52682I 1.71933 + 1.54413I
u = 0.594895 + 0.853325I
a = 1.00000
b = −0.888119 − 0.392484I
2.52996 + 1.99554I 7.48406 − 3.24951I
u = 0.594895 − 0.853325I
a = 1.00000
b = −0.888119 + 0.392484I
2.52996 − 1.99554I 7.48406 + 3.24951I
u = 0.455681 + 1.021510I
a = 1.00000
b = −0.09174 − 1.74935I
−12.10840 + 1.93472I 7.26417 − 4.67402I
u = 0.455681 − 1.021510I
a = 1.00000
b = −0.09174 + 1.74935I
−12.10840 − 1.93472I 7.26417 + 4.67402I
u = −0.504262 + 1.174830I
a = 1.00000
b = −1.088960 + 0.356976I
0.48540 − 8.16941I 4.20960 + 6.58024I
u = −0.504262 − 1.174830I
a = 1.00000
b = −1.088960 − 0.356976I
0.48540 + 8.16941I 4.20960 − 6.58024I
u = −0.449425 + 0.466610I
a = 1.00000
b = −0.570876 − 1.008450I
0.75353 + 3.18135I 3.49254 + 0.13841I
u = −0.449425 − 0.466610I
a = 1.00000
b = −0.570876 + 1.008450I
0.75353 − 3.18135I 3.49254 − 0.13841I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.455902 + 0.433518I
a = 1.00000
b = −0.039420 + 0.886123I
−1.82684 − 1.47458I 1.47955 + 5.16393I
u = −0.455902 − 0.433518I
a = 1.00000
b = −0.039420 − 0.886123I
−1.82684 + 1.47458I 1.47955 − 5.16393I
u = −0.71525 + 1.27905I
a = 1.00000
b = −0.35508 + 1.52708I
−3.71302 − 6.55902I 3.96621 + 4.14123I
u = −0.71525 − 1.27905I
a = 1.00000
b = −0.35508 − 1.52708I
−3.71302 + 6.55902I 3.96621 − 4.14123I
u = 0.478551
a = 1.00000
b = −0.344169
0.721984 13.8930
u = 0.68977 + 1.47618I
a = 1.00000
b = −0.43262 − 1.51053I
−5.4582 + 13.6098I 1.93808 − 7.30834I
u = 0.68977 − 1.47618I
a = 1.00000
b = −0.43262 + 1.51053I
−5.4582 − 13.6098I 1.93808 + 7.30834I
6
II. I
u
2
= h−5.20 × 10
17
u
23
+ 5.02 × 10
18
u
22
+ · · · + 1.95 × 10
19
b + 5.93 ×
10
20
, −1.40 × 10
24
u
23
+ 6.26 × 10
24
u
22
+ · · · + 1.96 × 10
25
a + 5.45 ×
10
26
, u
24
− u
23
+ · · · + 224u + 173i
(i) Arc colorings
a
2
=
1
0
a
10
=
0
u
a
3
=
1
−u
2
a
5
=
0.0714002u
23
− 0.320106u
22
+ ··· − 15.5190u − 27.8359
0.0266595u
23
− 0.257087u
22
+ ··· − 18.6780u − 30.3650
a
6
=
0.0980596u
23
− 0.577193u
22
+ ··· − 34.1970u − 58.2008
0.0266595u
23
− 0.257087u
22
+ ··· − 18.6780u − 30.3650
a
11
=
0.470356u
23
− 0.621434u
22
+ ··· + 81.7674u + 16.2383
0.329501u
23
− 0.686697u
22
+ ··· + 33.8837u − 21.2874
a
1
=
0.450732u
23
− 0.314505u
22
+ ··· + 120.111u + 62.4009
0.327683u
23
− 0.520957u
22
+ ··· + 55.3338u + 0.954331
a
4
=
0.0595221u
23
+ 0.166006u
22
+ ··· + 28.1599u + 41.7764
0.497954u
23
− 0.518732u
22
+ ··· + 103.014u + 48.4483
a
7
=
−0.645948u
23
+ 1.30849u
22
+ ··· − 66.6364u + 32.6828
0.142189u
23
+ 0.502228u
22
+ ··· + 106.073u + 111.052
a
9
=
−u
u
3
+ u
a
8
=
0.383897u
23
− 0.657761u
22
+ ··· + 57.2698u + 0.530339
−0.0745968u
23
− 0.255739u
22
+ ··· − 52.0295u − 57.0282
a
8
=
0.383897u
23
− 0.657761u
22
+ ··· + 57.2698u + 0.530339
−0.0745968u
23
− 0.255739u
22
+ ··· − 52.0295u − 57.0282
(ii) Obstruction class = −1
(iii) Cusp Shapes =
57116119689452910512704
113087261740869136389035
u
23
−
196123354323563952367144
113087261740869136389035
u
22
+ ··· −
343977527111163574580764
22617452348173827277807
u −
16520278039745704687355386
113087261740869136389035
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
3
+ u
2
+ 2u + 1)
8
c
2
, c
4
, c
9
c
10
u
24
− u
23
+ ··· + 224u + 173
c
3
, c
6
u
24
− 3u
23
+ ··· − 14u + 19
c
7
, c
8
, c
11
(u
4
− u
3
+ u
2
+ 1)
6
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
3
+ 3y
2
+ 2y −1)
8
c
2
, c
4
, c
9
c
10
y
24
+ 15y
23
+ ··· + 196176y + 29929
c
3
, c
6
y
24
+ 7y
23
+ ··· + 11812y + 361
c
7
, c
8
, c
11
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
6
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.296109 + 0.977179I
a = −1.273900 + 0.388233I
b = 0.569840
−4.03235 − 1.41510I 5.19277 + 4.90874I
u = −0.296109 − 0.977179I
a = −1.273900 − 0.388233I
b = 0.569840
−4.03235 + 1.41510I 5.19277 − 4.90874I
u = −0.850110 + 0.413706I
a = −0.382281 − 1.077960I
b = 0.569840
2.96939 + 3.16396I 8.84625 − 2.56480I
u = −0.850110 − 0.413706I
a = −0.382281 + 1.077960I
b = 0.569840
2.96939 − 3.16396I 8.84625 + 2.56480I
u = −0.338066 + 1.017770I
a = −1.64492 + 0.24451I
b = 0.215080 − 1.307140I
−8.16994 − 1.41302I −1.33649 − 1.92930I
u = −0.338066 − 1.017770I
a = −1.64492 − 0.24451I
b = 0.215080 + 1.307140I
−8.16994 + 1.41302I −1.33649 + 1.92930I
u = 0.770941 + 0.758235I
a = −0.292232 + 0.824041I
b = 0.569840
2.96939 + 3.16396I 8.84625 − 2.56480I
u = 0.770941 − 0.758235I
a = −0.292232 − 0.824041I
b = 0.569840
2.96939 − 3.16396I 8.84625 + 2.56480I
u = 0.105985 + 0.888600I
a = 0.45731 + 1.37162I
b = 0.215080 + 1.307140I
−1.168190 − 0.335841I 2.31698 − 0.41465I
u = 0.105985 − 0.888600I
a = 0.45731 − 1.37162I
b = 0.215080 − 1.307140I
−1.168190 + 0.335841I 2.31698 + 0.41465I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.273584 + 1.104980I
a = −0.168598 − 1.335650I
b = 0.215080 − 1.307140I
−1.16819 − 5.99209I 2.31698 + 5.54425I
u = −0.273584 − 1.104980I
a = −0.168598 + 1.335650I
b = 0.215080 + 1.307140I
−1.16819 + 5.99209I 2.31698 − 5.54425I
u = −1.170350 + 0.551735I
a = 0.218758 − 0.656129I
b = 0.215080 + 1.307140I
−1.168190 − 0.335841I 2.31698 − 0.41465I
u = −1.170350 − 0.551735I
a = 0.218758 + 0.656129I
b = 0.215080 − 1.307140I
−1.168190 + 0.335841I 2.31698 + 0.41465I
u = −0.002161 + 1.359780I
a = −0.718280 + 0.218903I
b = 0.569840
−4.03235 + 1.41510I 5.19277 − 4.90874I
u = −0.002161 − 1.359780I
a = −0.718280 − 0.218903I
b = 0.569840
−4.03235 − 1.41510I 5.19277 + 4.90874I
u = −0.23515 + 1.45919I
a = −0.977489 − 0.499948I
b = 0.215080 − 1.307140I
−8.16994 − 4.24323I −1.33649 + 7.88819I
u = −0.23515 − 1.45919I
a = −0.977489 + 0.499948I
b = 0.215080 + 1.307140I
−8.16994 + 4.24323I −1.33649 − 7.88819I
u = 1.52200 + 0.17911I
a = −0.093025 + 0.736956I
b = 0.215080 − 1.307140I
−1.16819 − 5.99209I 2.31698 + 5.54425I
u = 1.52200 − 0.17911I
a = −0.093025 − 0.736956I
b = 0.215080 + 1.307140I
−1.16819 + 5.99209I 2.31698 − 5.54425I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.95938 + 1.30878I
a = −0.810903 − 0.414746I
b = 0.215080 + 1.307140I
−8.16994 + 4.24323I −1.33649 − 7.88819I
u = 0.95938 − 1.30878I
a = −0.810903 + 0.414746I
b = 0.215080 − 1.307140I
−8.16994 − 4.24323I −1.33649 + 7.88819I
u = 0.30723 + 1.75680I
a = −0.594791 + 0.088414I
b = 0.215080 + 1.307140I
−8.16994 + 1.41302I −1.33649 + 1.92930I
u = 0.30723 − 1.75680I
a = −0.594791 − 0.088414I
b = 0.215080 − 1.307140I
−8.16994 − 1.41302I −1.33649 − 1.92930I
12
III. I
u
3
= hu
9
− u
8
+ · · · + 3b − 2, a + 1, u
10
+ 4u
8
+ · · · − u + 1i
(i) Arc colorings
a
2
=
1
0
a
10
=
0
u
a
3
=
1
−u
2
a
5
=
−1
−
1
3
u
9
+
1
3
u
8
+ ··· −
1
3
u +
2
3
a
6
=
−
1
3
u
9
+
1
3
u
8
+ ··· −
1
3
u −
1
3
−
1
3
u
9
+
1
3
u
8
+ ··· −
1
3
u +
2
3
a
11
=
u
−
1
3
u
9
+
1
3
u
8
+ ··· +
2
3
u −
1
3
a
1
=
u
9
+ 4u
7
− u
6
+ 7u
5
− u
4
+ 5u
3
+ u − 1
2
3
u
9
+
1
3
u
8
+ ··· +
2
3
u −
4
3
a
4
=
−u
2
− 1
−
2
3
u
9
−
1
3
u
8
+ ··· +
1
3
u +
1
3
a
7
=
−
5
3
u
9
−
1
3
u
8
+ ··· +
1
3
u +
4
3
−u
9
− 4u
7
+ u
6
− 7u
5
+ 2u
4
− 4u
3
+ 2u
2
+ 2
a
9
=
−u
u
3
+ u
a
8
=
−
2
3
u
9
−
1
3
u
8
+ ··· −
5
3
u +
1
3
−u
9
− u
8
− 4u
7
− 2u
6
− 5u
5
− u
4
− u
3
+ u
2
+ 1
a
8
=
−
2
3
u
9
−
1
3
u
8
+ ··· −
5
3
u +
1
3
−u
9
− u
8
− 4u
7
− 2u
6
− 5u
5
− u
4
− u
3
+ u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
7
3
u
9
−
11
3
u
8
−
32
3
u
7
−13u
6
−16u
5
−
52
3
u
4
−
16
3
u
3
−
7
3
u
2
+
5
3
u +
23
3
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
10
+ 6u
8
+ 13u
6
− 2u
5
+ 13u
4
− 5u
3
+ 6u
2
− 3u + 2
c
2
, c
10
u
10
+ 4u
8
− u
7
+ 6u
6
− 2u
5
+ 2u
4
− u
3
− u
2
− u + 1
c
3
, c
6
u
10
+ u
8
− u
7
+ 2u
6
+ 2u
5
+ u
4
+ 2u
3
− u
2
− 2u + 1
c
4
, c
9
u
10
+ 4u
8
+ u
7
+ 6u
6
+ 2u
5
+ 2u
4
+ u
3
− u
2
+ u + 1
c
5
u
10
+ 6u
8
+ 13u
6
+ 2u
5
+ 13u
4
+ 5u
3
+ 6u
2
+ 3u + 2
c
7
, c
8
u
10
+ 2u
9
+ 6u
8
+ 8u
7
+ 13u
6
+ 10u
5
+ 11u
4
+ 5u
3
+ 5u
2
+ 1
c
11
u
10
− 2u
9
+ 6u
8
− 8u
7
+ 13u
6
− 10u
5
+ 11u
4
− 5u
3
+ 5u
2
+ 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
10
+ 12y
9
+ ··· + 15y + 4
c
2
, c
4
, c
9
c
10
y
10
+ 8y
9
+ 28y
8
+ 51y
7
+ 46y
6
+ 12y
5
− 6y
4
+ 3y
3
+ 3y
2
− 3y + 1
c
3
, c
6
y
10
+ 2y
9
+ 5y
8
+ 5y
7
+ 8y
6
+ 4y
5
− 13y
4
+ 6y
3
+ 11y
2
− 6y + 1
c
7
, c
8
, c
11
y
10
+ 8y
9
+ ··· + 10y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.389657 + 1.143630I
a = −1.00000
b = 0.14100 + 1.67979I
−12.68460 + 1.69333I −5.30928 + 0.52333I
u = 0.389657 − 1.143630I
a = −1.00000
b = 0.14100 − 1.67979I
−12.68460 − 1.69333I −5.30928 − 0.52333I
u = 0.084751 + 1.224150I
a = −1.00000
b = 0.443974 − 0.385855I
−5.08161 + 0.78317I −2.78080 − 0.34402I
u = 0.084751 − 1.224150I
a = −1.00000
b = 0.443974 + 0.385855I
−5.08161 − 0.78317I −2.78080 + 0.34402I
u = −0.578028 + 0.397630I
a = −1.00000
b = −0.425241 − 1.086470I
0.251695 − 1.343720I 7.28435 + 2.33753I
u = −0.578028 − 0.397630I
a = −1.00000
b = −0.425241 + 1.086470I
0.251695 + 1.343720I 7.28435 − 2.33753I
u = 0.606372 + 0.143048I
a = −1.00000
b = −0.346672 − 0.885333I
1.00791 + 4.33704I 4.62897 − 5.70101I
u = 0.606372 − 0.143048I
a = −1.00000
b = −0.346672 + 0.885333I
1.00791 − 4.33704I 4.62897 + 5.70101I
u = −0.50275 + 1.45896I
a = −1.00000
b = 0.186940 − 1.272060I
−8.16736 − 3.03930I −1.32324 + 1.14176I
u = −0.50275 − 1.45896I
a = −1.00000
b = 0.186940 + 1.272060I
−8.16736 + 3.03930I −1.32324 − 1.14176I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
+ 2u + 1)
8
· (u
10
+ 6u
8
+ 13u
6
− 2u
5
+ 13u
4
− 5u
3
+ 6u
2
− 3u + 2)
· (u
17
− 9u
16
+ ··· + 144u − 16)
c
2
, c
10
(u
10
+ 4u
8
− u
7
+ 6u
6
− 2u
5
+ 2u
4
− u
3
− u
2
− u + 1)
· (u
17
+ 6u
15
+ ··· − u − 1)(u
24
− u
23
+ ··· + 224u + 173)
c
3
, c
6
(u
10
+ u
8
− u
7
+ 2u
6
+ 2u
5
+ u
4
+ 2u
3
− u
2
− 2u + 1)
· (u
17
+ 9u
15
+ ··· + 3u
2
− 1)(u
24
− 3u
23
+ ··· − 14u + 19)
c
4
, c
9
(u
10
+ 4u
8
+ u
7
+ 6u
6
+ 2u
5
+ 2u
4
+ u
3
− u
2
+ u + 1)
· (u
17
+ 6u
15
+ ··· − u − 1)(u
24
− u
23
+ ··· + 224u + 173)
c
5
(u
3
+ u
2
+ 2u + 1)
8
· (u
10
+ 6u
8
+ 13u
6
+ 2u
5
+ 13u
4
+ 5u
3
+ 6u
2
+ 3u + 2)
· (u
17
− 9u
16
+ ··· + 144u − 16)
c
7
, c
8
(u
4
− u
3
+ u
2
+ 1)
6
· (u
10
+ 2u
9
+ 6u
8
+ 8u
7
+ 13u
6
+ 10u
5
+ 11u
4
+ 5u
3
+ 5u
2
+ 1)
· (u
17
+ 9u
16
+ ··· − 32u − 8)
c
11
(u
4
− u
3
+ u
2
+ 1)
6
· (u
10
− 2u
9
+ 6u
8
− 8u
7
+ 13u
6
− 10u
5
+ 11u
4
− 5u
3
+ 5u
2
+ 1)
· (u
17
+ 9u
16
+ ··· − 32u − 8)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
3
+ 3y
2
+ 2y −1)
8
)(y
10
+ 12y
9
+ ··· + 15y + 4)
· (y
17
+ 15y
16
+ ··· + 1408y −256)
c
2
, c
4
, c
9
c
10
(y
10
+ 8y
9
+ 28y
8
+ 51y
7
+ 46y
6
+ 12y
5
− 6y
4
+ 3y
3
+ 3y
2
− 3y + 1)
· (y
17
+ 12y
16
+ ··· − y −1)(y
24
+ 15y
23
+ ··· + 196176y + 29929)
c
3
, c
6
(y
10
+ 2y
9
+ 5y
8
+ 5y
7
+ 8y
6
+ 4y
5
− 13y
4
+ 6y
3
+ 11y
2
− 6y + 1)
· (y
17
+ 18y
16
+ ··· + 6y −1)(y
24
+ 7y
23
+ ··· + 11812y + 361)
c
7
, c
8
, c
11
((y
4
+ y
3
+ 3y
2
+ 2y + 1)
6
)(y
10
+ 8y
9
+ ··· + 10y + 1)
· (y
17
+ 9y
16
+ ··· + 160y −64)
18
