10
69
(K10a
38
)
A knot diagram
1
Linearized knot diagam
7 9 1 10 4 2 6 3 8 5
Solving Sequence
1,5
10 4 6
3,8
7 9 2
c
10
c
4
c
5
c
3
c
7
c
9
c
2
c
1
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
18
− 3u
17
+ ··· + b − 3, −3u
18
− 7u
17
+ ··· + 2a − 7, u
19
+ 3u
18
+ ··· + 7u + 2i
I
u
2
= h4u
13
a − 17u
13
+ ··· + a + 22, 2u
13
a − 2u
13
+ ··· − 2a + 2,
u
14
− u
13
− 3u
12
+ 4u
11
+ 4u
10
− 7u
9
− u
8
+ 6u
7
− 2u
6
− 2u
5
+ 2u
4
− u + 1i
I
u
3
= hu
3
+ b, u
2
+ a + u − 1, u
4
− u
2
+ 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−u
18
−3u
17
+· · ·+b −3, −3u
18
−7u
17
+· · ·+2a −7, u
19
+3u
18
+· · ·+7u +2i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
10
=
1
u
2
a
4
=
−u
−u
3
+ u
a
6
=
u
3
u
5
− u
3
+ u
a
3
=
−u
3
−u
3
+ u
a
8
=
3
2
u
18
+
7
2
u
17
+ ··· +
17
2
u +
7
2
u
18
+ 3u
17
+ ··· + 8u + 3
a
7
=
1
2
u
18
+
3
2
u
17
+ ··· +
7
2
u +
3
2
u
17
+ u
16
+ ··· + 2u + 1
a
9
=
−
1
2
u
18
−
3
2
u
17
+ ··· −
7
2
u −
1
2
−u
17
− u
16
+ ··· − 3u − 1
a
2
=
3
2
u
18
+
7
2
u
17
+ ··· +
17
2
u +
7
2
−u
18
− 2u
17
+ ··· − 4u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 12u
18
+ 26u
17
− 24u
16
− 116u
15
− 42u
14
+ 200u
13
+ 222u
12
−
116u
11
−334u
10
−108u
9
+ 228u
8
+ 240u
7
−4u
6
−172u
5
−118u
4
+ 12u
3
+ 78u
2
+ 64u + 30
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
u
19
+ 4u
17
+ ··· + 2u − 1
c
3
u
19
− 9u
18
+ ··· + 157u − 22
c
4
, c
10
u
19
− 3u
18
+ ··· + 7u − 2
c
5
u
19
− 9u
18
+ ··· + 5u − 4
c
7
, c
9
u
19
+ 8u
18
+ ··· − 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
19
+ 8y
18
+ ··· − 2y −1
c
3
y
19
+ 3y
18
+ ··· + 1461y −484
c
4
, c
10
y
19
− 9y
18
+ ··· + 5y −4
c
5
y
19
+ 3y
18
+ ··· + 129y −16
c
7
, c
9
y
19
+ 12y
18
+ ··· + 30y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.656620 + 0.736849I
a = −0.530916 + 0.111769I
b = −0.692991 − 0.514666I
−3.87251 − 6.01197I −0.18591 + 7.59122I
u = −0.656620 − 0.736849I
a = −0.530916 − 0.111769I
b = −0.692991 + 0.514666I
−3.87251 + 6.01197I −0.18591 − 7.59122I
u = 0.833011 + 0.594872I
a = 0.493073 − 0.284708I
b = 0.042413 + 0.483034I
−1.75185 + 2.35707I 4.45005 − 4.73717I
u = 0.833011 − 0.594872I
a = 0.493073 + 0.284708I
b = 0.042413 − 0.483034I
−1.75185 − 2.35707I 4.45005 + 4.73717I
u = −0.342490 + 0.822016I
a = −0.423303 − 0.244228I
b = −0.84616 + 1.72998I
−2.12081 + 8.87474I 0.63360 − 6.11132I
u = −0.342490 − 0.822016I
a = −0.423303 + 0.244228I
b = −0.84616 − 1.72998I
−2.12081 − 8.87474I 0.63360 + 6.11132I
u = −0.954304 + 0.656562I
a = 1.022240 + 0.645581I
b = 0.517413 − 0.115037I
−2.99077 + 0.72249I 1.52455 − 2.82827I
u = −0.954304 − 0.656562I
a = 1.022240 − 0.645581I
b = 0.517413 + 0.115037I
−2.99077 − 0.72249I 1.52455 + 2.82827I
u = 1.178790 + 0.200823I
a = 1.12805 + 1.83215I
b = −0.06929 + 1.61595I
2.86306 − 5.96190I 6.84845 + 4.63798I
u = 1.178790 − 0.200823I
a = 1.12805 − 1.83215I
b = −0.06929 − 1.61595I
2.86306 + 5.96190I 6.84845 − 4.63798I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.160320 + 0.382174I
a = −0.30429 − 1.44141I
b = 0.996422 − 0.904006I
5.16612 + 4.98291I 9.41511 − 6.18167I
u = 1.160320 − 0.382174I
a = −0.30429 + 1.44141I
b = 0.996422 + 0.904006I
5.16612 − 4.98291I 9.41511 + 6.18167I
u = −1.141050 + 0.480142I
a = 0.96822 − 1.32852I
b = −0.00563 − 1.67007I
4.50851 − 3.09886I 9.38086 + 1.28227I
u = −1.141050 − 0.480142I
a = 0.96822 + 1.32852I
b = −0.00563 + 1.67007I
4.50851 + 3.09886I 9.38086 − 1.28227I
u = −1.143800 + 0.588812I
a = −1.12767 + 2.25574I
b = 0.96492 + 2.22818I
0.26882 − 14.12650I 3.54919 + 9.60559I
u = −1.143800 − 0.588812I
a = −1.12767 − 2.25574I
b = 0.96492 − 2.22818I
0.26882 + 14.12650I 3.54919 − 9.60559I
u = −0.085864 + 0.693927I
a = 0.667057 + 0.203041I
b = −0.176244 − 0.940079I
1.57783 − 1.22058I 5.73688 + 3.21713I
u = −0.085864 − 0.693927I
a = 0.667057 − 0.203041I
b = −0.176244 + 0.940079I
1.57783 + 1.22058I 5.73688 − 3.21713I
u = −0.695977
a = 0.715081
b = 0.538288
0.927841 11.2940
6
II. I
u
2
=
h4u
13
a−17u
13
+· · ·+a+22, 2u
13
a−2u
13
+· · ·−2a+2, u
14
−u
13
+· · ·−u+1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
10
=
1
u
2
a
4
=
−u
−u
3
+ u
a
6
=
u
3
u
5
− u
3
+ u
a
3
=
−u
3
−u
3
+ u
a
8
=
a
−0.190476au
13
+ 0.809524u
13
+ ··· − 0.0476190a − 1.04762
a
7
=
−0.190476au
13
− 0.190476u
13
+ ··· + 0.952381a − 0.0476190
0.190476au
13
+ 0.190476u
13
+ ··· + 0.0476190a − 0.952381
a
9
=
−0.190476au
13
− 0.190476u
13
+ ··· + 0.952381a − 0.0476190
−0.619048au
13
+ 0.380952u
13
+ ··· + 0.0952381a − 0.904762
a
2
=
−2u
13
+ 7u
11
− 2u
10
− 12u
9
+ 6u
8
+ 8u
7
− 8u
6
+ 4u
4
− 3u
3
− a + 2
−0.190476au
13
− 0.190476u
13
+ ··· − 0.0476190a + 0.952381
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
13
+ 16u
11
−4u
10
−28u
9
+ 12u
8
+ 20u
7
−16u
6
+ 8u
4
−8u
3
+ 6
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
u
28
− u
27
+ ··· + 2u + 1
c
3
(u
14
+ 3u
13
+ ··· + 7u + 3)
2
c
4
, c
10
(u
14
+ u
13
+ ··· + u + 1)
2
c
5
(u
14
− 7u
13
+ ··· − u + 1)
2
c
7
, c
9
u
28
+ 15u
27
+ ··· + 10u
2
+ 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
28
+ 15y
27
+ ··· + 10y
2
+ 1
c
3
(y
14
+ 5y
13
+ ··· + 23y + 9)
2
c
4
, c
10
(y
14
− 7y
13
+ ··· − y + 1)
2
c
5
(y
14
+ y
13
+ ··· + 7y + 1)
2
c
7
, c
9
y
28
− 5y
27
+ ··· + 20y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.989783 + 0.381937I
a = 0.75275 − 1.27344I
b = 0.090790 − 0.426836I
−1.59516 + 1.40484I 5.50927 − 0.52948I
u = 0.989783 + 0.381937I
a = 1.91833 + 1.38556I
b = 0.20805 + 2.13390I
−1.59516 + 1.40484I 5.50927 − 0.52948I
u = 0.989783 − 0.381937I
a = 0.75275 + 1.27344I
b = 0.090790 + 0.426836I
−1.59516 − 1.40484I 5.50927 + 0.52948I
u = 0.989783 − 0.381937I
a = 1.91833 − 1.38556I
b = 0.20805 − 2.13390I
−1.59516 − 1.40484I 5.50927 + 0.52948I
u = 0.728347 + 0.560551I
a = 0.912076 − 0.177857I
b = 0.443852 + 0.575052I
−1.84948 + 2.19128I 2.76081 − 3.85718I
u = 0.728347 + 0.560551I
a = −0.064777 − 0.599184I
b = −0.371682 + 0.254174I
−1.84948 + 2.19128I 2.76081 − 3.85718I
u = 0.728347 − 0.560551I
a = 0.912076 + 0.177857I
b = 0.443852 − 0.575052I
−1.84948 − 2.19128I 2.76081 + 3.85718I
u = 0.728347 − 0.560551I
a = −0.064777 + 0.599184I
b = −0.371682 − 0.254174I
−1.84948 − 2.19128I 2.76081 + 3.85718I
u = −1.068410 + 0.522447I
a = 1.02538 + 1.04810I
b = 0.439782 + 0.298160I
−2.72606 − 5.07185I 2.32847 + 6.33126I
u = −1.068410 + 0.522447I
a = −0.47730 + 2.74473I
b = 1.89542 + 1.97549I
−2.72606 − 5.07185I 2.32847 + 6.33126I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.068410 − 0.522447I
a = 1.02538 − 1.04810I
b = 0.439782 − 0.298160I
−2.72606 + 5.07185I 2.32847 − 6.33126I
u = −1.068410 − 0.522447I
a = −0.47730 − 2.74473I
b = 1.89542 − 1.97549I
−2.72606 + 5.07185I 2.32847 − 6.33126I
u = −1.157220 + 0.286866I
a = −0.208422 + 0.989667I
b = 0.809510 + 0.540535I
4.53640 + 0.47055I 9.32829 + 0.18349I
u = −1.157220 + 0.286866I
a = 1.17269 − 1.74006I
b = −0.06603 − 1.71504I
4.53640 + 0.47055I 9.32829 + 0.18349I
u = −1.157220 − 0.286866I
a = −0.208422 − 0.989667I
b = 0.809510 − 0.540535I
4.53640 − 0.47055I 9.32829 − 0.18349I
u = −1.157220 − 0.286866I
a = 1.17269 + 1.74006I
b = −0.06603 + 1.71504I
4.53640 − 0.47055I 9.32829 − 0.18349I
u = 0.268039 + 0.757899I
a = 0.805404 − 0.051418I
b = 0.148756 + 0.914884I
0.22261 − 3.62879I 3.66617 + 2.63226I
u = 0.268039 + 0.757899I
a = −0.143310 + 0.427216I
b = −0.80984 − 1.45942I
0.22261 − 3.62879I 3.66617 + 2.63226I
u = 0.268039 − 0.757899I
a = 0.805404 + 0.051418I
b = 0.148756 − 0.914884I
0.22261 + 3.62879I 3.66617 − 2.63226I
u = 0.268039 − 0.757899I
a = −0.143310 − 0.427216I
b = −0.80984 + 1.45942I
0.22261 + 3.62879I 3.66617 − 2.63226I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.142590 + 0.546762I
a = 0.78194 + 1.24283I
b = −0.06519 + 1.60824I
2.77434 + 8.53123I 6.72348 − 6.18031I
u = 1.142590 + 0.546762I
a = −0.88693 − 2.21821I
b = 1.12473 − 1.96518I
2.77434 + 8.53123I 6.72348 − 6.18031I
u = 1.142590 − 0.546762I
a = 0.78194 − 1.24283I
b = −0.06519 − 1.60824I
2.77434 − 8.53123I 6.72348 + 6.18031I
u = 1.142590 − 0.546762I
a = −0.88693 + 2.21821I
b = 1.12473 + 1.96518I
2.77434 − 8.53123I 6.72348 + 6.18031I
u = −0.403136 + 0.584808I
a = −1.142350 + 0.668190I
b = −0.860151 − 0.151246I
−4.65252 + 0.62859I −2.31651 − 1.42251I
u = −0.403136 + 0.584808I
a = −0.445488 − 1.297380I
b = −1.48801 + 1.19980I
−4.65252 + 0.62859I −2.31651 − 1.42251I
u = −0.403136 − 0.584808I
a = −1.142350 − 0.668190I
b = −0.860151 + 0.151246I
−4.65252 − 0.62859I −2.31651 + 1.42251I
u = −0.403136 − 0.584808I
a = −0.445488 + 1.297380I
b = −1.48801 − 1.19980I
−4.65252 − 0.62859I −2.31651 + 1.42251I
12
III. I
u
3
= hu
3
+ b, u
2
+ a + u − 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
10
=
1
u
2
a
4
=
−u
−u
3
+ u
a
6
=
u
3
0
a
3
=
−u
3
−u
3
+ u
a
8
=
−u
2
− u + 1
−u
3
a
7
=
u
3
− u
2
− u + 1
−u
3
a
9
=
−u
2
− u + 2
−u
3
+ u
2
a
2
=
−u
2
+ u + 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
(u
2
+ 1)
2
c
3
, c
4
, c
10
u
4
− u
2
+ 1
c
5
(u
2
− u + 1)
2
c
7
, c
9
(u + 1)
4
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
(y + 1)
4
c
3
, c
4
, c
10
(y
2
− y + 1)
2
c
5
(y
2
+ y + 1)
2
c
7
, c
9
(y −1)
4
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = −0.36603 − 1.36603I
b = − 1.000000I
−3.28987 + 2.02988I −2.00000 − 3.46410I
u = 0.866025 − 0.500000I
a = −0.36603 + 1.36603I
b = 1.000000I
−3.28987 − 2.02988I −2.00000 + 3.46410I
u = −0.866025 + 0.500000I
a = 1.36603 + 0.36603I
b = − 1.000000I
−3.28987 − 2.02988I −2.00000 + 3.46410I
u = −0.866025 − 0.500000I
a = 1.36603 − 0.36603I
b = 1.000000I
−3.28987 + 2.02988I −2.00000 − 3.46410I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
((u
2
+ 1)
2
)(u
19
+ 4u
17
+ ··· + 2u − 1)(u
28
− u
27
+ ··· + 2u + 1)
c
3
(u
4
− u
2
+ 1)(u
14
+ 3u
13
+ ··· + 7u + 3)
2
(u
19
− 9u
18
+ ··· + 157u − 22)
c
4
, c
10
(u
4
− u
2
+ 1)(u
14
+ u
13
+ ··· + u + 1)
2
(u
19
− 3u
18
+ ··· + 7u − 2)
c
5
((u
2
− u + 1)
2
)(u
14
− 7u
13
+ ··· − u + 1)
2
(u
19
− 9u
18
+ ··· + 5u − 4)
c
7
, c
9
((u + 1)
4
)(u
19
+ 8u
18
+ ··· − 2u − 1)(u
28
+ 15u
27
+ ··· + 10u
2
+ 1)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
((y + 1)
4
)(y
19
+ 8y
18
+ ··· − 2y −1)(y
28
+ 15y
27
+ ··· + 10y
2
+ 1)
c
3
((y
2
− y + 1)
2
)(y
14
+ 5y
13
+ ··· + 23y + 9)
2
· (y
19
+ 3y
18
+ ··· + 1461y −484)
c
4
, c
10
((y
2
− y + 1)
2
)(y
14
− 7y
13
+ ··· − y + 1)
2
(y
19
− 9y
18
+ ··· + 5y −4)
c
5
((y
2
+ y + 1)
2
)(y
14
+ y
13
+ ··· + 7y + 1)
2
· (y
19
+ 3y
18
+ ··· + 129y −16)
c
7
, c
9
((y −1)
4
)(y
19
+ 12y
18
+ ··· + 30y −1)(y
28
− 5y
27
+ ··· + 20y + 1)
18
