10
116
(K10a
120
)
A knot diagram
1
Linearized knot diagam
8 9 6 1 2 10 4 5 3 7
Solving Sequence
4,7 8,10
1 2 5 6 3 9
c
7
c
10
c
1
c
4
c
6
c
3
c
9
c
2
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−3043u
15
+ 828u
14
+ ··· + 761b − 4040, 1027u
15
− 1203u
14
+ ··· + 761a + 653,
u
16
− u
15
+ u
14
− 2u
13
+ 7u
12
− 8u
11
+ 7u
10
− 6u
9
+ 6u
8
+ 7u
7
− 24u
6
+ 32u
5
− 27u
4
+ 20u
3
− 12u
2
+ 5u − 1i
I
u
2
= h6.18811 × 10
62
u
35
− 2.36237 × 10
62
u
34
+ ··· + 2.97721 × 10
61
b + 3.69879 × 10
62
,
− 3.31586 × 10
63
u
35
+ 1.45172 × 10
63
u
34
+ ··· + 2.97721 × 10
61
a − 1.62016 × 10
63
, u
36
− u
35
+ ··· + 10u − 1i
I
u
3
= hu
3
+ u
2
+ b + 1, −u
4
− 2u
3
− u
2
+ a − u − 1, u
5
+ u
4
+ u
3
+ 2u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 57 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−3043u
15
+ 828u
14
+ · · · + 761b − 4040, 1027u
15
− 1203u
14
+ · · · +
761a + 653, u
16
− u
15
+ · · · + 5u − 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
10
=
−1.34954u
15
+ 1.58081u
14
+ ··· + 8.93955u − 0.858081
3.99869u
15
− 1.08804u
14
+ ··· − 20.1130u + 5.30880
a
1
=
2.64915u
15
+ 0.492773u
14
+ ··· − 11.1735u + 4.45072
3.99869u
15
− 1.08804u
14
+ ··· − 20.1130u + 5.30880
a
2
=
2.30092u
15
+ 1.16163u
14
+ ··· − 4.12089u + 2.28384
3.80158u
15
− 2.29435u
14
+ ··· − 22.0644u + 5.62943
a
5
=
6.61367u
15
− 1.88436u
14
+ ··· − 31.2247u + 9.78844
5.73456u
15
− 1.78449u
14
+ ··· − 25.8279u + 7.37845
a
6
=
3.15112u
15
− 1.87516u
14
+ ··· − 22.0039u + 7.48752
4.22733u
15
+ 0.231275u
14
+ ··· − 12.4494u + 3.57687
a
3
=
4.03022u
15
− 1.97503u
14
+ ··· − 25.4008u + 8.89750
5.50329u
15
− 0.279895u
14
+ ··· − 20.7175u + 6.72799
a
9
=
−5.53482u
15
+ 2.16689u
14
+ ··· + 32.0053u − 10.3167
−7.74901u
15
+ 1.81603u
14
+ ··· + 34.5848u − 9.98160
(ii) Obstruction class = −1
(iii) Cusp Shapes =
13489
761
u
15
+
456
761
u
14
+ ··· −
54502
761
u +
17914
761
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
+ 8u
15
+ ··· − 22u − 4
c
2
, c
6
, c
9
c
10
u
16
− 8u
14
+ ··· + 4u + 1
c
3
u
16
− 12u
15
+ ··· + 112u − 16
c
4
, c
8
u
16
− u
15
+ ··· + 5u − 1
c
5
, c
7
u
16
− u
15
+ ··· + 5u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 2y
15
+ ··· − 44y + 16
c
2
, c
6
, c
9
c
10
y
16
− 16y
15
+ ··· − 18y + 1
c
3
y
16
+ 46y
14
+ ··· + 1632y + 256
c
4
, c
8
y
16
− 11y
15
+ ··· − 17y + 1
c
5
, c
7
y
16
+ y
15
+ ··· − y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.848485 + 0.598766I
a = −0.483988 − 0.792063I
b = 1.362100 + 0.075359I
7.97491 + 0.20600I 9.94793 + 0.07278I
u = 0.848485 − 0.598766I
a = −0.483988 + 0.792063I
b = 1.362100 − 0.075359I
7.97491 − 0.20600I 9.94793 − 0.07278I
u = 0.846121 + 0.652012I
a = −0.284195 + 0.129063I
b = 0.014022 + 0.906951I
−2.23601 − 4.95570I −0.99614 + 6.15512I
u = 0.846121 − 0.652012I
a = −0.284195 − 0.129063I
b = 0.014022 − 0.906951I
−2.23601 + 4.95570I −0.99614 − 6.15512I
u = 0.664815 + 0.989330I
a = 1.38574 + 1.59724I
b = −1.227900 − 0.015479I
6.88399 − 4.31481I 8.84422 + 5.32763I
u = 0.664815 − 0.989330I
a = 1.38574 − 1.59724I
b = −1.227900 + 0.015479I
6.88399 + 4.31481I 8.84422 − 5.32763I
u = −1.20069
a = 0.395416
b = 0.206535
−2.54477 −11.1320
u = −0.207234 + 0.684921I
a = 0.548174 − 0.525931I
b = 0.034860 − 0.480524I
0.24918 + 1.55875I 1.96281 − 3.40867I
u = −0.207234 − 0.684921I
a = 0.548174 + 0.525931I
b = 0.034860 + 0.480524I
0.24918 − 1.55875I 1.96281 + 3.40867I
u = −0.539685 + 1.175220I
a = −1.351880 + 0.225032I
b = 1.48126 + 0.46974I
8.92084 + 7.21911I 9.60333 − 5.50334I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.539685 − 1.175220I
a = −1.351880 − 0.225032I
b = 1.48126 − 0.46974I
8.92084 − 7.21911I 9.60333 + 5.50334I
u = 0.435669 + 0.469034I
a = 1.43102 + 0.27627I
b = −0.975942 − 0.412090I
1.82506 + 0.80819I 2.13059 − 1.11047I
u = 0.435669 − 0.469034I
a = 1.43102 − 0.27627I
b = −0.975942 + 0.412090I
1.82506 − 0.80819I 2.13059 + 1.11047I
u = 0.491705
a = 1.58325
b = 1.37840
7.98963 11.0630
u = −1.19368 + 1.15575I
a = 1.265790 − 0.496149I
b = −1.48086 − 0.47484I
7.3807 + 15.4239I 6.04190 − 8.21765I
u = −1.19368 − 1.15575I
a = 1.265790 + 0.496149I
b = −1.48086 + 0.47484I
7.3807 − 15.4239I 6.04190 + 8.21765I
6
II.
I
u
2
= h6.19×10
62
u
35
−2.36×10
62
u
34
+· · ·+2.98×10
61
b+3.70×10
62
, −3.32×
10
63
u
35
+1.45×10
63
u
34
+· · ·+2.98×10
61
a−1.62×10
63
, u
36
−u
35
+· · ·+10u−1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
10
=
111.375u
35
− 48.7610u
34
+ ··· − 994.024u + 54.4186
−20.7849u
35
+ 7.93485u
34
+ ··· + 169.058u − 12.4237
a
1
=
90.5899u
35
− 40.8261u
34
+ ··· − 824.966u + 41.9949
−20.7849u
35
+ 7.93485u
34
+ ··· + 169.058u − 12.4237
a
2
=
127.801u
35
− 63.0263u
34
+ ··· − 1401.07u + 104.182
−17.1954u
35
+ 3.98736u
34
+ ··· + 56.1564u + 2.58762
a
5
=
139.120u
35
− 113.959u
34
+ ··· − 3359.17u + 420.231
−14.0536u
35
+ 1.68584u
34
+ ··· − 31.6498u + 23.1947
a
6
=
11.6449u
35
− 27.9211u
34
+ ··· − 993.769u + 159.766
11.5499u
35
− 9.32721u
34
+ ··· − 283.605u + 40.5313
a
3
=
212.315u
35
− 128.741u
34
+ ··· − 3334.38u + 333.144
7.82658u
35
− 18.5212u
34
+ ··· − 651.775u + 104.189
a
9
=
−221.628u
35
+ 135.661u
34
+ ··· + 3518.02u − 353.253
−11.7841u
35
+ 22.6573u
34
+ ··· + 774.893u − 121.309
(ii) Obstruction class = −1
(iii) Cusp Shapes = 330.335u
35
− 202.439u
34
+ ··· − 5559.19u + 624.963
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
18
− 4u
17
+ ··· + 7u
2
− 1)
2
c
2
, c
6
, c
9
c
10
u
36
− u
35
+ ··· + 8u − 1
c
3
(u
18
+ 6u
17
+ ··· − 2u + 1)
2
c
4
, c
8
u
36
− u
35
+ ··· + 48u + 11
c
5
, c
7
u
36
− u
35
+ ··· + 10u − 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
18
− 2y
17
+ ··· − 14y + 1)
2
c
2
, c
6
, c
9
c
10
y
36
− 25y
35
+ ··· + 182y
2
+ 1
c
3
(y
18
+ 10y
17
+ ··· − 2y + 1)
2
c
4
, c
8
y
36
− y
35
+ ··· − 2172y + 121
c
5
, c
7
y
36
+ 3y
35
+ ··· − 16y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.158101 + 0.999960I
a = −0.688269 + 0.878262I
b = −0.144717 − 0.202993I
3.61069 + 4.86887I 5.80133 − 5.50961I
u = 0.158101 − 0.999960I
a = −0.688269 − 0.878262I
b = −0.144717 + 0.202993I
3.61069 − 4.86887I 5.80133 + 5.50961I
u = −1.103570 + 0.154303I
a = 0.362077 + 0.101877I
b = 0.191935 + 0.345407I
−2.50163 −7.03291 + 0.I
u = −1.103570 − 0.154303I
a = 0.362077 − 0.101877I
b = 0.191935 − 0.345407I
−2.50163 −7.03291 + 0.I
u = 0.883024 + 0.688109I
a = −0.157240 − 0.022105I
b = 0.337991 − 1.169730I
1.71711 − 9.65993I 2.00000 + 8.40253I
u = 0.883024 − 0.688109I
a = −0.157240 + 0.022105I
b = 0.337991 + 1.169730I
1.71711 + 9.65993I 2.00000 − 8.40253I
u = 0.820566 + 0.255749I
a = 1.57258 − 0.35860I
b = −0.403597 − 0.037486I
2.38258 + 0.03013I 10.67881 + 5.21291I
u = 0.820566 − 0.255749I
a = 1.57258 + 0.35860I
b = −0.403597 + 0.037486I
2.38258 − 0.03013I 10.67881 − 5.21291I
u = −0.921692 + 0.708492I
a = 0.267893 − 0.004765I
b = −0.127834 − 0.725445I
−0.67024 + 2.84508I 0. − 6.07527I
u = −0.921692 − 0.708492I
a = 0.267893 + 0.004765I
b = −0.127834 + 0.725445I
−0.67024 − 2.84508I 0. + 6.07527I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.767470 + 0.046363I
a = −1.032070 + 0.735712I
b = −0.382244 + 0.806713I
1.54929 + 2.22734I 0.12301 − 5.32226I
u = −0.767470 − 0.046363I
a = −1.032070 − 0.735712I
b = −0.382244 − 0.806713I
1.54929 − 2.22734I 0.12301 + 5.32226I
u = 0.834176 + 0.932639I
a = −1.10926 − 0.94801I
b = 1.219430 − 0.325722I
3.61069 − 4.86887I 0
u = 0.834176 − 0.932639I
a = −1.10926 + 0.94801I
b = 1.219430 + 0.325722I
3.61069 + 4.86887I 0
u = 0.921338 + 0.868395I
a = 1.151520 + 0.687508I
b = −1.48314 + 0.56763I
8.10049 − 6.17775I 0
u = 0.921338 − 0.868395I
a = 1.151520 − 0.687508I
b = −1.48314 − 0.56763I
8.10049 + 6.17775I 0
u = 0.701915
a = −1.28298
b = 1.94980
4.48911 −3.44630
u = 0.87912 + 1.26708I
a = −1.66440 − 0.48535I
b = 1.338110 − 0.311895I
3.93390 − 6.62246I 0
u = 0.87912 − 1.26708I
a = −1.66440 + 0.48535I
b = 1.338110 + 0.311895I
3.93390 + 6.62246I 0
u = 0.351282 + 0.272277I
a = −3.31877 − 1.34102I
b = 0.963504 − 0.239682I
−0.67024 − 2.84508I −1.12939 + 6.07527I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.351282 − 0.272277I
a = −3.31877 + 1.34102I
b = 0.963504 + 0.239682I
−0.67024 + 2.84508I −1.12939 − 6.07527I
u = 0.367259 + 0.202636I
a = 0.364325 + 0.477560I
b = −1.48378 + 0.18266I
2.38258 − 0.03013I 10.67881 − 5.21291I
u = 0.367259 − 0.202636I
a = 0.364325 − 0.477560I
b = −1.48378 − 0.18266I
2.38258 + 0.03013I 10.67881 + 5.21291I
u = −0.240979 + 0.319845I
a = −0.517042 − 0.064882I
b = 0.00271 + 1.70162I
3.05645 − 0.82042I 17.9553 − 12.9751I
u = −0.240979 − 0.319845I
a = −0.517042 + 0.064882I
b = 0.00271 − 1.70162I
3.05645 + 0.82042I 17.9553 + 12.9751I
u = 0.318952 + 0.240448I
a = 4.14019 + 3.24927I
b = −1.132980 + 0.371464I
3.93390 − 6.62246I 1.20464 + 6.87903I
u = 0.318952 − 0.240448I
a = 4.14019 − 3.24927I
b = −1.132980 − 0.371464I
3.93390 + 6.62246I 1.20464 − 6.87903I
u = −1.21553 + 1.27399I
a = −1.121660 + 0.382813I
b = 1.281050 + 0.414685I
1.71711 + 9.65993I 0
u = −1.21553 − 1.27399I
a = −1.121660 − 0.382813I
b = 1.281050 − 0.414685I
1.71711 − 9.65993I 0
u = 1.35664 + 1.18816I
a = 1.192410 + 0.304385I
b = −1.262280 + 0.182714I
1.54929 − 2.22734I 0
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.35664 − 1.18816I
a = 1.192410 − 0.304385I
b = −1.262280 − 0.182714I
1.54929 + 2.22734I 0
u = −1.01692 + 1.56813I
a = −1.099020 + 0.434034I
b = 1.297910 − 0.112771I
8.10049 − 6.17775I 0
u = −1.01692 − 1.56813I
a = −1.099020 − 0.434034I
b = 1.297910 + 0.112771I
8.10049 + 6.17775I 0
u = −1.90022
a = 0.385753
b = −1.15448
4.48911 0
u = −0.52514 + 1.99611I
a = 1.105360 − 0.231720I
b = −1.109740 − 0.175458I
3.05645 + 0.82042I 0
u = −0.52514 − 1.99611I
a = 1.105360 + 0.231720I
b = −1.109740 + 0.175458I
3.05645 − 0.82042I 0
13
III.
I
u
3
= hu
3
+ u
2
+ b + 1, −u
4
− 2u
3
− u
2
+ a − u − 1, u
5
+ u
4
+ u
3
+ 2u
2
+ u + 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
10
=
u
4
+ 2u
3
+ u
2
+ u + 1
−u
3
− u
2
− 1
a
1
=
u
4
+ u
3
+ u
−u
3
− u
2
− 1
a
2
=
u
3
+ 1
−u
3
− u
2
− 2
a
5
=
u
3
+ u
2
−u
2
a
6
=
u
4
+ u
3
+ u
2
+ u
−u
4
− u
3
− u
2
− 2u
a
3
=
−u
4
+ u
2
+ u + 1
u
4
+ u
3
+ u − 1
a
9
=
u
3
+ 2u
2
+ 2u + 2
−u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
4
+ 2u
3
+ 6u
2
+ 2u + 16
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
2
, c
10
u
5
− 2u
3
+ u
2
+ 2u − 1
c
3
u
5
− 3u
4
+ 7u
3
− 9u
2
+ 4u − 1
c
4
, c
8
u
5
+ u
4
+ u
3
− 2u
2
− u + 1
c
5
, c
7
u
5
+ u
4
+ u
3
+ 2u
2
+ u + 1
c
6
, c
9
u
5
− 2u
3
− u
2
+ 2u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
2
, c
6
, c
9
c
10
y
5
− 4y
4
+ 8y
3
− 9y
2
+ 6y −1
c
3
y
5
+ 5y
4
+ 3y
3
− 31y
2
− 2y −1
c
4
, c
8
y
5
+ y
4
+ 3y
3
− 8y
2
+ 5y −1
c
5
, c
7
y
5
+ y
4
− y
3
− 4y
2
− 3y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.428550 + 1.039280I
a = −2.07758 − 0.76681I
b = 1.206350 − 0.340852I
5.20316 − 6.77491I 8.84849 + 7.92033I
u = 0.428550 − 1.039280I
a = −2.07758 + 0.76681I
b = 1.206350 + 0.340852I
5.20316 + 6.77491I 8.84849 − 7.92033I
u = −0.276511 + 0.728237I
a = 1.150990 + 0.252750I
b = −0.964913 + 0.621896I
2.50012 − 0.60716I 13.51752 − 1.76382I
u = −0.276511 − 0.728237I
a = 1.150990 − 0.252750I
b = −0.964913 − 0.621896I
2.50012 + 0.60716I 13.51752 + 1.76382I
u = −1.30408
a = −0.146833
b = −0.482881
−2.24708 16.2680
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)(u
16
+ 8u
15
+ ··· − 22u − 4)
· (u
18
− 4u
17
+ ··· + 7u
2
− 1)
2
c
2
, c
10
(u
5
− 2u
3
+ u
2
+ 2u − 1)(u
16
− 8u
14
+ ··· + 4u + 1)
· (u
36
− u
35
+ ··· + 8u − 1)
c
3
(u
5
− 3u
4
+ 7u
3
− 9u
2
+ 4u − 1)(u
16
− 12u
15
+ ··· + 112u − 16)
· (u
18
+ 6u
17
+ ··· − 2u + 1)
2
c
4
, c
8
(u
5
+ u
4
+ u
3
− 2u
2
− u + 1)(u
16
− u
15
+ ··· + 5u − 1)
· (u
36
− u
35
+ ··· + 48u + 11)
c
5
, c
7
(u
5
+ u
4
+ u
3
+ 2u
2
+ u + 1)(u
16
− u
15
+ ··· + 5u − 1)
· (u
36
− u
35
+ ··· + 10u − 1)
c
6
, c
9
(u
5
− 2u
3
− u
2
+ 2u + 1)(u
16
− 8u
14
+ ··· + 4u + 1)
· (u
36
− u
35
+ ··· + 8u − 1)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)(y
16
− 2y
15
+ ··· − 44y + 16)
· (y
18
− 2y
17
+ ··· − 14y + 1)
2
c
2
, c
6
, c
9
c
10
(y
5
− 4y
4
+ 8y
3
− 9y
2
+ 6y −1)(y
16
− 16y
15
+ ··· − 18y + 1)
· (y
36
− 25y
35
+ ··· + 182y
2
+ 1)
c
3
(y
5
+ 5y
4
+ 3y
3
− 31y
2
− 2y −1)(y
16
+ 46y
14
+ ··· + 1632y + 256)
· (y
18
+ 10y
17
+ ··· − 2y + 1)
2
c
4
, c
8
(y
5
+ y
4
+ 3y
3
− 8y
2
+ 5y −1)(y
16
− 11y
15
+ ··· − 17y + 1)
· (y
36
− y
35
+ ··· − 2172y + 121)
c
5
, c
7
(y
5
+ y
4
− y
3
− 4y
2
− 3y −1)(y
16
+ y
15
+ ··· − y + 1)
· (y
36
+ 3y
35
+ ··· − 16y + 1)
19
