10
100
(K10a
104
)
A knot diagram
1
Linearized knot diagam
5 9 6 1 8 10 4 2 3 7
Solving Sequence
2,8
9
3,6
4 10 5 1 7
c
8
c
2
c
3
c
9
c
5
c
1
c
7
c
4
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−15u
13
+ 70u
12
+ ··· + 2b − 42, 49u
13
− 224u
12
+ ··· + 4a + 132,
u
14
− 6u
13
+ 11u
12
− 3u
11
− u
10
− 22u
9
+ 13u
8
+ 32u
7
− 3u
6
− 28u
5
− 30u
4
+ 36u
3
+ 7u
2
− 2u − 4i
I
u
2
= h−1945u
5
a
3
+ 869u
5
a
2
+ ··· − 1055a − 6821, −u
5
a
3
+ 2u
5
a
2
+ ··· − 14a + 22,
u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1i
I
u
3
= h−u
4
+ 2u
2
+ b, u
5
− 3u
3
+ u
2
+ a + 2u − 1, u
6
− u
5
− 3u
4
+ 3u
3
+ u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 44 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−15u
13
+ 70u
12
+ · · · + 2b − 42, 49u
13
− 224u
12
+ · · · + 4a +
132, u
14
− 6u
13
+ · · · − 2u − 4i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
3
=
u
−u
3
+ u
a
6
=
−
49
4
u
13
+ 56u
12
+ ··· −
151
4
u − 33
15
2
u
13
− 35u
12
+ ··· +
53
2
u + 21
a
4
=
−
7
2
u
13
+
33
2
u
12
+ ··· −
21
2
u −
21
2
3
2
u
13
− 7u
12
+ ··· +
13
2
u + 4
a
10
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
−
19
4
u
13
+ 21u
12
+ ··· −
45
4
u − 12
15
2
u
13
− 35u
12
+ ··· +
53
2
u + 21
a
1
=
2u
13
−
17
2
u
12
+ ··· + 4u +
7
2
−
5
2
u
13
+ 12u
12
+ ··· −
19
2
u − 8
a
7
=
−
3
4
u
13
+ 5u
12
+ ··· −
21
4
u − 4
−
3
2
u
13
+ 6u
12
+ ··· −
3
2
u − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = −14u
13
+ 62u
12
− 57u
11
− 45u
10
− 63u
9
+ 216u
8
+ 154u
7
−
197u
6
− 287u
5
− 60u
4
+ 344u
3
+ 46u
2
− 26u − 34
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
10
u
14
− u
13
+ ··· − 3u + 1
c
2
, c
8
, c
9
u
14
− 6u
13
+ ··· − 2u − 4
c
3
, c
5
u
14
+ u
13
+ ··· + 5u − 1
c
7
u
14
+ 14u
13
+ ··· − 288u − 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
y
14
− 13y
13
+ ··· − 3y + 1
c
2
, c
8
, c
9
y
14
− 14y
13
+ ··· − 60y + 16
c
3
, c
5
y
14
+ 7y
13
+ ··· − 59y + 1
c
7
y
14
+ 2y
13
+ ··· − 41984y + 4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.04049
a = 0.567340
b = −1.20452
0.339162 13.0620
u = −0.748785 + 0.823629I
a = 0.412890 − 0.456902I
b = 0.679306 + 1.137690I
6.90977 − 8.77559I 9.73876 + 7.09449I
u = −0.748785 − 0.823629I
a = 0.412890 + 0.456902I
b = 0.679306 − 1.137690I
6.90977 + 8.77559I 9.73876 − 7.09449I
u = −0.493094 + 1.098780I
a = −0.387144 − 0.128784I
b = 0.098682 − 0.905560I
5.88215 + 2.52726I 13.28929 − 3.43101I
u = −0.493094 − 1.098780I
a = −0.387144 + 0.128784I
b = 0.098682 + 0.905560I
5.88215 − 2.52726I 13.28929 + 3.43101I
u = 0.622591
a = 0.542539
b = 0.127481
0.865875 12.3760
u = 1.45633 + 0.05562I
a = 0.38364 − 1.65172I
b = −0.429494 + 1.051770I
4.42897 + 2.24150I 6.33861 − 3.08717I
u = 1.45633 − 0.05562I
a = 0.38364 + 1.65172I
b = −0.429494 − 1.051770I
4.42897 − 2.24150I 6.33861 + 3.08717I
u = −0.303715 + 0.334799I
a = 0.003671 + 1.353790I
b = −0.729605 − 0.382323I
−1.31044 − 0.99980I −2.51765 + 3.01751I
u = −0.303715 − 0.334799I
a = 0.003671 − 1.353790I
b = −0.729605 + 0.382323I
−1.31044 + 0.99980I −2.51765 − 3.01751I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.62071 + 0.25886I
a = −0.06147 + 1.67177I
b = 1.02771 − 1.53408I
14.7349 + 12.8109I 11.37066 − 6.14968I
u = 1.62071 − 0.25886I
a = −0.06147 − 1.67177I
b = 1.02771 + 1.53408I
14.7349 − 12.8109I 11.37066 + 6.14968I
u = 1.67750 + 0.35344I
a = −0.156526 − 0.920785I
b = −0.608077 + 1.061740I
13.16540 + 3.07431I 13.56108 − 2.64554I
u = 1.67750 − 0.35344I
a = −0.156526 + 0.920785I
b = −0.608077 − 1.061740I
13.16540 − 3.07431I 13.56108 + 2.64554I
6
II. I
u
2
= h−1945u
5
a
3
+ 869u
5
a
2
+ · · · − 1055a − 6821, −u
5
a
3
+ 2u
5
a
2
+ · · · −
14a + 22, u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
3
=
u
−u
3
+ u
a
6
=
a
0.413566a
3
u
5
− 0.184776a
2
u
5
+ ··· + 0.224325a + 1.45035
a
4
=
−0.321072a
3
u
5
− 0.0750585a
2
u
5
+ ··· − 0.0584733a − 1.19796
0.0450776a
3
u
5
− 0.0967468a
2
u
5
+ ··· + 0.253243a + 0.104614
a
10
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
0.413566a
3
u
5
− 0.184776a
2
u
5
+ ··· + 1.22432a + 1.45035
0.413566a
3
u
5
− 0.184776a
2
u
5
+ ··· + 0.224325a + 1.45035
a
1
=
0.503934a
3
u
5
− 0.657027a
2
u
5
+ ··· − 0.0274293a + 2.75441
0.182862a
3
u
5
− 0.732086a
2
u
5
+ ··· − 0.0859026a + 1.55645
a
7
=
0.309802a
3
u
5
− 0.150755a
2
u
5
+ ··· + 1.24516a + 1.17181
−0.0450776a
3
u
5
+ 0.0967468a
2
u
5
+ ··· − 0.253243a + 0.895386
(ii) Obstruction class = −1
(iii) Cusp Shapes =
848
4703
u
5
a
3
−
1820
4703
u
5
a
2
+ ··· +
4764
4703
a +
48998
4703
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
10
u
24
+ u
23
+ ··· − 8u + 1
c
2
, c
8
, c
9
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)
4
c
3
, c
5
u
24
− 7u
23
+ ··· − 372u + 73
c
7
(u
2
− u + 1)
12
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
y
24
− 21y
23
+ ··· + 72y + 1
c
2
, c
8
, c
9
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
4
c
3
, c
5
y
24
+ 11y
23
+ ··· + 52000y + 5329
c
7
(y
2
+ y + 1)
12
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.493180 + 0.575288I
a = 1.067300 − 0.316742I
b = −0.073003 − 0.780422I
1.97456 − 0.05747I 6.57572 − 0.22068I
u = 0.493180 + 0.575288I
a = −0.584086 − 0.249616I
b = −0.678417 + 1.238260I
1.97456 + 4.00229I 6.57572 − 7.14888I
u = 0.493180 + 0.575288I
a = 0.513478 + 1.284170I
b = 0.629282 − 0.637832I
1.97456 + 4.00229I 6.57572 − 7.14888I
u = 0.493180 + 0.575288I
a = −0.136040 − 0.139388I
b = 0.617558 + 0.522759I
1.97456 − 0.05747I 6.57572 − 0.22068I
u = 0.493180 − 0.575288I
a = 1.067300 + 0.316742I
b = −0.073003 + 0.780422I
1.97456 + 0.05747I 6.57572 + 0.22068I
u = 0.493180 − 0.575288I
a = −0.584086 + 0.249616I
b = −0.678417 − 1.238260I
1.97456 − 4.00229I 6.57572 + 7.14888I
u = 0.493180 − 0.575288I
a = 0.513478 − 1.284170I
b = 0.629282 + 0.637832I
1.97456 − 4.00229I 6.57572 + 7.14888I
u = 0.493180 − 0.575288I
a = −0.136040 + 0.139388I
b = 0.617558 − 0.522759I
1.97456 + 0.05747I 6.57572 + 0.22068I
u = −0.483672
a = 1.44157 + 0.74757I
b = 1.09154 − 1.08035I
5.67365 − 2.02988I 15.4168 + 3.4641I
u = −0.483672
a = 1.44157 − 0.74757I
b = 1.09154 + 1.08035I
5.67365 + 2.02988I 15.4168 − 3.4641I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.483672
a = −2.95401 + 1.87206I
b = −0.006188 − 0.799526I
5.67365 − 2.02988I 15.4168 + 3.4641I
u = −0.483672
a = −2.95401 − 1.87206I
b = −0.006188 + 0.799526I
5.67365 + 2.02988I 15.4168 − 3.4641I
u = −1.52087 + 0.16310I
a = 0.299570 − 1.150850I
b = 0.618593 + 0.988703I
8.63038 − 2.56224I 10.58114 − 0.25928I
u = −1.52087 + 0.16310I
a = −0.601099 + 1.113320I
b = 0.554158 − 1.044580I
8.63038 − 2.56224I 10.58114 − 0.25928I
u = −1.52087 + 0.16310I
a = −0.07073 − 1.79722I
b = 0.427101 + 0.945943I
8.63038 − 6.62201I 10.58114 + 6.66892I
u = −1.52087 + 0.16310I
a = 0.18899 + 2.07712I
b = −1.06187 − 1.93363I
8.63038 − 6.62201I 10.58114 + 6.66892I
u = −1.52087 − 0.16310I
a = 0.299570 + 1.150850I
b = 0.618593 − 0.988703I
8.63038 + 2.56224I 10.58114 + 0.25928I
u = −1.52087 − 0.16310I
a = −0.601099 − 1.113320I
b = 0.554158 + 1.044580I
8.63038 + 2.56224I 10.58114 + 0.25928I
u = −1.52087 − 0.16310I
a = −0.07073 + 1.79722I
b = 0.427101 − 0.945943I
8.63038 + 6.62201I 10.58114 − 6.66892I
u = −1.52087 − 0.16310I
a = 0.18899 − 2.07712I
b = −1.06187 + 1.93363I
8.63038 + 6.62201I 10.58114 − 6.66892I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.53904
a = −0.49479 + 1.36564I
b = −0.628935 − 0.898287I
12.59490 − 2.02988I 14.2695 + 3.4641I
u = 1.53904
a = −0.49479 − 1.36564I
b = −0.628935 + 0.898287I
12.59490 + 2.02988I 14.2695 − 3.4641I
u = 1.53904
a = −1.17015 + 1.51812I
b = 2.01019 − 1.49411I
12.59490 − 2.02988I 14.2695 + 3.4641I
u = 1.53904
a = −1.17015 − 1.51812I
b = 2.01019 + 1.49411I
12.59490 + 2.02988I 14.2695 − 3.4641I
12
III.
I
u
3
= h−u
4
+2u
2
+b, u
5
−3u
3
+u
2
+a+2u−1, u
6
−u
5
−3u
4
+3u
3
+u
2
−u+1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
3
=
u
−u
3
+ u
a
6
=
−u
5
+ 3u
3
− u
2
− 2u + 1
u
4
− 2u
2
a
4
=
u
5
− 3u
3
+ 2u
−u
3
+ 2u
a
10
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
−u
5
+ u
4
+ 3u
3
− 3u
2
− 2u + 1
u
4
− 2u
2
a
1
=
u
5
− u
4
− 4u
3
+ 3u
2
+ 3u − 1
u
5
− 3u
3
+ u
2
+ 2u − 1
a
7
=
−u
5
+ u
4
+ 3u
3
− 3u
2
− 2u + 2
−u
5
+ u
4
+ 3u
3
− 3u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
5
+ 2u
4
+ 8u
3
− 4u
2
+ 3u + 7
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
6
− u
5
− 3u
4
+ 3u
3
+ 3u
2
− 3u − 1
c
2
u
6
+ u
5
− 3u
4
− 3u
3
+ u
2
+ u + 1
c
3
, c
5
u
6
+ u
5
+ u
4
+ u
3
− u
2
− u − 1
c
4
, c
10
u
6
+ u
5
− 3u
4
− 3u
3
+ 3u
2
+ 3u − 1
c
7
u
6
− u
5
+ u
4
+ u
3
− u
2
+ u − 1
c
8
, c
9
u
6
− u
5
− 3u
4
+ 3u
3
+ u
2
− u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
y
6
− 7y
5
+ 21y
4
− 35y
3
+ 33y
2
− 15y + 1
c
2
, c
8
, c
9
y
6
− 7y
5
+ 17y
4
− 15y
3
+ y
2
+ y + 1
c
3
, c
5
y
6
+ y
5
− 3y
4
− 3y
3
+ y
2
+ y + 1
c
7
y
6
+ y
5
+ y
4
− 3y
3
− 3y
2
+ y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.847445
a = 0.587994
b = −0.920568
−0.285060 −0.503990
u = 0.251489 + 0.528716I
a = 0.07352 − 1.42421I
b = 0.408651 − 0.646904I
4.59420 − 1.63935I 6.79257 + 0.07886I
u = 0.251489 − 0.528716I
a = 0.07352 + 1.42421I
b = 0.408651 + 0.646904I
4.59420 + 1.63935I 6.79257 − 0.07886I
u = 1.46321 + 0.18726I
a = −0.71355 − 1.48541I
b = −0.077247 + 1.212100I
9.23208 + 4.33255I 12.59516 − 4.05038I
u = 1.46321 − 0.18726I
a = −0.71355 + 1.48541I
b = −0.077247 − 1.212100I
9.23208 − 4.33255I 12.59516 + 4.05038I
u = −1.58196
a = −0.307931
b = 1.25776
12.1109 12.7290
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
6
− u
5
− 3u
4
+ 3u
3
+ 3u
2
− 3u − 1)(u
14
− u
13
+ ··· − 3u + 1)
· (u
24
+ u
23
+ ··· − 8u + 1)
c
2
(u
6
+ u
5
− 3u
4
− 3u
3
+ u
2
+ u + 1)(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)
4
· (u
14
− 6u
13
+ ··· − 2u − 4)
c
3
, c
5
(u
6
+ u
5
+ u
4
+ u
3
− u
2
− u − 1)(u
14
+ u
13
+ ··· + 5u − 1)
· (u
24
− 7u
23
+ ··· − 372u + 73)
c
4
, c
10
(u
6
+ u
5
− 3u
4
− 3u
3
+ 3u
2
+ 3u − 1)(u
14
− u
13
+ ··· − 3u + 1)
· (u
24
+ u
23
+ ··· − 8u + 1)
c
7
(u
2
− u + 1)
12
(u
6
− u
5
+ u
4
+ u
3
− u
2
+ u − 1)
· (u
14
+ 14u
13
+ ··· − 288u − 64)
c
8
, c
9
(u
6
− u
5
− 3u
4
+ 3u
3
+ u
2
− u + 1)(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)
4
· (u
14
− 6u
13
+ ··· − 2u − 4)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
(y
6
− 7y
5
+ ··· − 15y + 1)(y
14
− 13y
13
+ ··· − 3y + 1)
· (y
24
− 21y
23
+ ··· + 72y + 1)
c
2
, c
8
, c
9
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
4
· (y
6
− 7y
5
+ ··· + y + 1)(y
14
− 14y
13
+ ··· − 60y + 16)
c
3
, c
5
(y
6
+ y
5
− 3y
4
− 3y
3
+ y
2
+ y + 1)(y
14
+ 7y
13
+ ··· − 59y + 1)
· (y
24
+ 11y
23
+ ··· + 52000y + 5329)
c
7
(y
2
+ y + 1)
12
(y
6
+ y
5
+ y
4
− 3y
3
− 3y
2
+ y + 1)
· (y
14
+ 2y
13
+ ··· − 41984y + 4096)
18
