10
93
(K10a
101
)
A knot diagram
1
Linearized knot diagam
9 6 10 8 3 2 4 1 7 5
Solving Sequence
2,7
6
3,10
4 5 9 1 8
c
6
c
2
c
3
c
5
c
9
c
1
c
8
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.48497 × 10
17
u
34
− 2.74759 × 10
17
u
33
+ ··· + 2.14980 × 10
17
b + 3.71507 × 10
17
,
2.04229 × 10
17
u
34
+ 3.73430 × 10
17
u
33
+ ··· + 2.14980 × 10
17
a − 2.36397 × 10
17
, u
35
+ 2u
34
+ ··· − 2u − 1i
I
u
2
= h3b + u + 2, 3a − 2u − 1, u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 37 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−1.48×10
17
u
34
−2.75×10
17
u
33
+· · ·+2.15×10
17
b+3.72×10
17
, 2.04×
10
17
u
34
+3.73×10
17
u
33
+· · ·+2.15×10
17
a−2.36×10
17
, u
35
+2u
34
+· · ·−2u−1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
−u
2
a
3
=
−u
u
3
+ u
a
10
=
−0.949992u
34
− 1.73705u
33
+ ··· + 6.42492u + 1.09963
0.690747u
34
+ 1.27807u
33
+ ··· − 1.42690u − 1.72810
a
4
=
0.300462u
34
+ 0.653361u
33
+ ··· + 0.171322u − 0.984845
0.369645u
34
+ 0.462967u
33
+ ··· − 2.38683u − 0.219453
a
5
=
u
2
+ 1
−u
4
− 2u
2
a
9
=
−1.64074u
34
− 3.01512u
33
+ ··· + 7.85182u + 2.82773
0.690747u
34
+ 1.27807u
33
+ ··· − 1.42690u − 1.72810
a
1
=
−1.39270u
34
− 2.59706u
33
+ ··· + 7.17623u + 2.38722
0.569891u
34
+ 1.15346u
33
+ ··· − 0.0996613u − 1.67732
a
8
=
−0.604507u
34
− 1.03705u
33
+ ··· + 1.81017u + 1.15186
0.344862u
34
+ 0.434712u
33
+ ··· − 1.72091u − 0.338982
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
43902992914495201
128987874023997969
u
34
−
378946062727999073
214979790039996615
u
33
+ ··· −
1287205910561212151
214979790039996615
u +
3437895448731260974
644939370119989845
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
35
+ 3u
34
+ ··· + 5u − 9
c
2
, c
5
, c
6
u
35
− 2u
34
+ ··· − 2u + 1
c
3
u
35
+ 3u
34
+ ··· − 60u + 36
c
4
, c
7
u
35
− 2u
34
+ ··· + 2u − 1
c
9
3(3u
35
+ 2u
34
+ ··· + 2024u + 529)
c
10
3(3u
35
+ 13u
34
+ ··· − 793u + 173)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
35
− 31y
34
+ ··· + 439y −81
c
2
, c
5
, c
6
y
35
+ 36y
34
+ ··· − 8y −1
c
3
y
35
+ 15y
34
+ ··· − 8136y −1296
c
4
, c
7
y
35
− 24y
34
+ ··· − 8y −1
c
9
9(9y
35
− 280y
34
+ ··· + 2073680y −279841)
c
10
9(9y
35
+ 137y
34
+ ··· + 24387y −29929)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.797949 + 0.618523I
a = 0.441661 − 0.524170I
b = 1.31533 + 0.64336I
7.15893 + 9.08856I 5.28395 − 6.85993I
u = −0.797949 − 0.618523I
a = 0.441661 + 0.524170I
b = 1.31533 − 0.64336I
7.15893 − 9.08856I 5.28395 + 6.85993I
u = 0.319146 + 0.974832I
a = −0.0301867 + 0.0609842I
b = −0.142675 + 0.589069I
0.84892 − 2.27938I −3.03865 + 4.27236I
u = 0.319146 − 0.974832I
a = −0.0301867 − 0.0609842I
b = −0.142675 − 0.589069I
0.84892 + 2.27938I −3.03865 − 4.27236I
u = −0.883803 + 0.527645I
a = −0.151524 − 0.698091I
b = 1.074450 − 0.184550I
6.81152 − 3.53470I 6.64372 + 2.46356I
u = −0.883803 − 0.527645I
a = −0.151524 + 0.698091I
b = 1.074450 + 0.184550I
6.81152 + 3.53470I 6.64372 − 2.46356I
u = 0.890046 + 0.661300I
a = −0.138488 − 0.436432I
b = −0.961888 + 0.317896I
2.19099 − 3.04973I 6.83792 + 5.73006I
u = 0.890046 − 0.661300I
a = −0.138488 + 0.436432I
b = −0.961888 − 0.317896I
2.19099 + 3.04973I 6.83792 − 5.73006I
u = −0.485797 + 0.446415I
a = −1.54295 + 0.61782I
b = −0.767630 − 0.733842I
1.92901 + 4.20671I 2.61467 − 7.67969I
u = −0.485797 − 0.446415I
a = −1.54295 − 0.61782I
b = −0.767630 + 0.733842I
1.92901 − 4.20671I 2.61467 + 7.67969I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.177701 + 0.568169I
a = 0.88046 + 2.71785I
b = 0.844702 + 0.231272I
5.61974 − 1.75521I 9.80898 + 3.99717I
u = 0.177701 − 0.568169I
a = 0.88046 − 2.71785I
b = 0.844702 − 0.231272I
5.61974 + 1.75521I 9.80898 − 3.99717I
u = 0.518141 + 0.274512I
a = 0.865516 + 0.243501I
b = 0.321578 − 0.365013I
−1.063790 − 0.837639I −5.45708 + 2.88305I
u = 0.518141 − 0.274512I
a = 0.865516 − 0.243501I
b = 0.321578 + 0.365013I
−1.063790 + 0.837639I −5.45708 − 2.88305I
u = −0.07117 + 1.42730I
a = −2.02061 + 1.49459I
b = −1.94022 + 1.12557I
7.48516 + 0.26471I 8.26333 + 0.I
u = −0.07117 − 1.42730I
a = −2.02061 − 1.49459I
b = −1.94022 − 1.12557I
7.48516 − 0.26471I 8.26333 + 0.I
u = 0.13283 + 1.44979I
a = 1.51691 + 0.10394I
b = 0.950697 − 0.074489I
4.57837 − 3.04741I 0
u = 0.13283 − 1.44979I
a = 1.51691 − 0.10394I
b = 0.950697 + 0.074489I
4.57837 + 3.04741I 0
u = −0.379190 + 0.370732I
a = 0.133491 + 0.548267I
b = −0.738044 + 0.811910I
1.88873 − 1.15770I 2.26234 − 1.26872I
u = −0.379190 − 0.370732I
a = 0.133491 − 0.548267I
b = −0.738044 − 0.811910I
1.88873 + 1.15770I 2.26234 + 1.26872I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.03075 + 1.47995I
a = −1.46910 − 0.67161I
b = −1.29110 − 1.51306I
7.85287 + 1.23959I 0
u = −0.03075 − 1.47995I
a = −1.46910 + 0.67161I
b = −1.29110 + 1.51306I
7.85287 − 1.23959I 0
u = −0.13948 + 1.49938I
a = −1.99280 − 0.18614I
b = −1.072190 − 0.508436I
8.34974 + 6.42549I 0
u = −0.13948 − 1.49938I
a = −1.99280 + 0.18614I
b = −1.072190 + 0.508436I
8.34974 − 6.42549I 0
u = 0.04304 + 1.53065I
a = 1.29303 + 0.78816I
b = 0.854691 − 0.412838I
12.61950 − 2.50960I 11.52662 + 0.I
u = 0.04304 − 1.53065I
a = 1.29303 − 0.78816I
b = 0.854691 + 0.412838I
12.61950 + 2.50960I 11.52662 + 0.I
u = −0.26639 + 1.57422I
a = 1.85469 − 0.10458I
b = 1.70003 + 0.90521I
14.3602 + 13.0165I 0
u = −0.26639 − 1.57422I
a = 1.85469 + 0.10458I
b = 1.70003 − 0.90521I
14.3602 − 13.0165I 0
u = −0.171298 + 0.343458I
a = −0.06814 + 1.97682I
b = −0.847997 − 0.510070I
1.76589 + 0.63046I 5.20787 + 1.46477I
u = −0.171298 − 0.343458I
a = −0.06814 − 1.97682I
b = −0.847997 + 0.510070I
1.76589 − 0.63046I 5.20787 − 1.46477I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.27157 + 1.59599I
a = −1.399030 − 0.062212I
b = −1.34067 + 0.82337I
9.65156 − 7.25912I 0
u = 0.27157 − 1.59599I
a = −1.399030 + 0.062212I
b = −1.34067 − 0.82337I
9.65156 + 7.25912I 0
u = −0.31084 + 1.58997I
a = 0.998238 − 0.474581I
b = 1.142220 + 0.398928I
13.76820 + 0.95076I 0
u = −0.31084 − 1.58997I
a = 0.998238 + 0.474581I
b = 1.142220 − 0.398928I
13.76820 − 0.95076I 0
u = 0.368379
a = −0.675672
b = 2.46408
3.85534 −11.8900
8
II. I
u
2
= h3b + u + 2, 3a − 2u − 1, u
2
+ u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u + 1
a
3
=
−u
u + 1
a
10
=
2
3
u +
1
3
−
1
3
u −
2
3
a
4
=
−u
u + 1
a
5
=
−u
u + 2
a
9
=
u + 1
−
1
3
u −
2
3
a
1
=
u + 1
2
3
u −
2
3
a
8
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
4
3
u + 5
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
c
2
, c
7
u
2
− u + 1
c
3
u
2
c
4
, c
5
, c
6
u
2
+ u + 1
c
8
(u + 1)
2
c
9
3(3u
2
− 3u + 1)
c
10
3(3u
2
+ 1)
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y −1)
2
c
2
, c
4
, c
5
c
6
, c
7
y
2
+ y + 1
c
3
y
2
c
9
9(9y
2
− 3y + 1)
c
10
9(3y + 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.577350I
b = −0.500000 − 0.288675I
1.64493 + 2.02988I 5.66667 − 1.15470I
u = −0.500000 − 0.866025I
a = − 0.577350I
b = −0.500000 + 0.288675I
1.64493 − 2.02988I 5.66667 + 1.15470I
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
35
+ 3u
34
+ ··· + 5u − 9)
c
2
(u
2
− u + 1)(u
35
− 2u
34
+ ··· − 2u + 1)
c
3
u
2
(u
35
+ 3u
34
+ ··· − 60u + 36)
c
4
(u
2
+ u + 1)(u
35
− 2u
34
+ ··· + 2u − 1)
c
5
, c
6
(u
2
+ u + 1)(u
35
− 2u
34
+ ··· − 2u + 1)
c
7
(u
2
− u + 1)(u
35
− 2u
34
+ ··· + 2u − 1)
c
8
((u + 1)
2
)(u
35
+ 3u
34
+ ··· + 5u − 9)
c
9
9(3u
2
− 3u + 1)(3u
35
+ 2u
34
+ ··· + 2024u + 529)
c
10
9(3u
2
+ 1)(3u
35
+ 13u
34
+ ··· − 793u + 173)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
((y −1)
2
)(y
35
− 31y
34
+ ··· + 439y −81)
c
2
, c
5
, c
6
(y
2
+ y + 1)(y
35
+ 36y
34
+ ··· − 8y −1)
c
3
y
2
(y
35
+ 15y
34
+ ··· − 8136y −1296)
c
4
, c
7
(y
2
+ y + 1)(y
35
− 24y
34
+ ··· − 8y −1)
c
9
81(9y
2
− 3y + 1)(9y
35
− 280y
34
+ ··· + 2073680y −279841)
c
10
81(3y + 1)
2
(9y
35
+ 137y
34
+ ··· + 24387y −29929)
14
