10
105
(K10a
72
)
A knot diagram
1
Linearized knot diagam
6 9 1 10 7 2 4 3 5 8
Solving Sequence
2,9 3,6
7 1 4 5 8 10
c
2
c
6
c
1
c
3
c
5
c
8
c
10
c
4
, c
7
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−30u
16
176u
15
+ ··· + 1103b + 331, 1294u
16
1159u
15
+ ··· + 1103a + 2562,
u
17
+ 6u
15
+ u
14
+ 16u
13
+ 4u
12
+ 20u
11
+ 7u
10
+ 7u
9
+ 5u
8
7u
7
+ 3u
6
3u
5
+ u
4
+ 3u
3
+ 2u + 1i
I
u
2
= h−4.51865 × 10
39
u
35
+ 6.97530 × 10
39
u
34
+ ··· + 1.68010 × 10
40
b 7.80705 × 10
39
,
1.24909 × 10
45
u
35
+ 1.82583 × 10
45
u
34
+ ··· + 2.27642 × 10
45
a + 4.03057 × 10
46
,
u
36
u
35
+ ··· + 186u + 43i
I
u
3
= hu
6
+ 4u
4
u
3
+ 4u
2
+ b 2u + 2, u
7
+ u
6
4u
5
+ 5u
4
5u
3
+ 6u
2
+ a 3u + 3,
u
8
+ 4u
6
u
5
+ 5u
4
2u
3
+ 4u
2
u + 1i
* 3 irreducible components of dim
C
= 0, with total 61 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−30u
16
176u
15
+ · · · + 1103b + 331, 1294u
16
1159u
15
+ · · · +
1103a + 2562, u
17
+ 6u
15
+ · · · + 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
u
2
a
6
=
1.17316u
16
+ 1.05077u
15
+ ··· + 0.526745u 2.32276
0.0271985u
16
+ 0.159565u
15
+ ··· + 1.65549u 0.300091
a
7
=
1.20036u
16
+ 0.891206u
15
+ ··· 1.12874u 2.02267
0.0271985u
16
+ 0.159565u
15
+ ··· + 1.65549u 0.300091
a
1
=
0.393472u
16
0.0417044u
15
+ ··· + 0.317316u + 0.407978
1.59383u
16
+ 0.849501u
15
+ ··· 0.811423u 1.61469
a
4
=
u
2
+ 1
1.57298u
16
1.10517u
15
+ ··· + 0.408885u + 1.81142
a
5
=
1
1.16500u
16
+ 1.49864u
15
+ ··· + 1.42339u 0.312783
a
8
=
u
u
3
+ u
a
10
=
u
1.49864u
16
+ 0.407978u
15
+ ··· 1.01723u 1.16500
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1215
1103
u
16
3902
1103
u
15
+ ··· +
52
1103
u
4030
1103
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
17
7u
16
+ ··· 36u + 8
c
2
, c
4
, c
8
c
9
u
17
+ 6u
15
+ ··· + 2u + 1
c
3
, c
7
u
17
u
16
+ ··· u + 1
c
5
u
17
+ 7u
16
+ ··· 48u + 64
c
10
u
17
15u
16
+ ··· + 608u 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
17
7y
16
+ ··· 48y 64
c
2
, c
4
, c
8
c
9
y
17
+ 12y
16
+ ··· + 4y 1
c
3
, c
7
y
17
+ 3y
16
+ ··· 9y 1
c
5
y
17
+ 5y
16
+ ··· + 17664y 4096
c
10
y
17
5y
16
+ ··· + 17408y 4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.099668 + 0.990377I
a = 0.755793 + 0.048508I
b = 0.874913 + 1.017070I
0.65585 3.58827I 5.01554 + 5.19820I
u = 0.099668 0.990377I
a = 0.755793 0.048508I
b = 0.874913 1.017070I
0.65585 + 3.58827I 5.01554 5.19820I
u = 0.397497 + 1.032420I
a = 2.04240 0.79952I
b = 1.30568 + 0.56699I
3.72641 6.77030I 4.91686 + 11.50550I
u = 0.397497 1.032420I
a = 2.04240 + 0.79952I
b = 1.30568 0.56699I
3.72641 + 6.77030I 4.91686 11.50550I
u = 0.749827 + 0.244567I
a = 0.108910 + 0.611388I
b = 0.696825 0.650971I
2.74501 + 0.69000I 3.24547 1.78817I
u = 0.749827 0.244567I
a = 0.108910 0.611388I
b = 0.696825 + 0.650971I
2.74501 0.69000I 3.24547 + 1.78817I
u = 0.346178 + 0.692637I
a = 0.666585 + 0.297186I
b = 0.037067 + 0.756233I
0.24233 + 1.64711I 1.95019 4.12084I
u = 0.346178 0.692637I
a = 0.666585 0.297186I
b = 0.037067 0.756233I
0.24233 1.64711I 1.95019 + 4.12084I
u = 0.736048 + 0.038467I
a = 0.755454 + 0.908610I
b = 0.928563 0.638410I
2.06897 + 4.31656I 2.23828 5.03995I
u = 0.736048 0.038467I
a = 0.755454 0.908610I
b = 0.928563 + 0.638410I
2.06897 4.31656I 2.23828 + 5.03995I
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.285508 + 1.357540I
a = 1.79507 0.11101I
b = 1.375440 0.134825I
10.04230 + 5.59145I 9.61044 4.67516I
u = 0.285508 1.357540I
a = 1.79507 + 0.11101I
b = 1.375440 + 0.134825I
10.04230 5.59145I 9.61044 + 4.67516I
u = 0.52629 + 1.31806I
a = 0.119329 0.266115I
b = 0.352099 0.977016I
3.89694 9.32757I 4.13921 + 5.55906I
u = 0.52629 1.31806I
a = 0.119329 + 0.266115I
b = 0.352099 + 0.977016I
3.89694 + 9.32757I 4.13921 5.55906I
u = 0.59743 + 1.42672I
a = 1.62332 + 0.78900I
b = 1.192940 0.641161I
6.4799 + 15.1817I 6.31050 8.67042I
u = 0.59743 1.42672I
a = 1.62332 0.78900I
b = 1.192940 + 0.641161I
6.4799 15.1817I 6.31050 + 8.67042I
u = 0.438874
a = 1.40978
b = 0.877026
1.63327 4.88280
6
II. I
u
2
= h−4.52 × 10
39
u
35
+ 6.98 × 10
39
u
34
+ · · · + 1.68 × 10
40
b 7.81 ×
10
39
, 1.25 × 10
45
u
35
+ 1.83 × 10
45
u
34
+ · · · + 2.28 × 10
45
a + 4.03 ×
10
46
, u
36
u
35
+ · · · + 186u + 43i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
u
2
a
6
=
0.548710u
35
0.802063u
34
+ ··· 49.1305u 17.7057
0.268951u
35
0.415172u
34
+ ··· 2.22836u + 0.464678
a
7
=
0.279759u
35
0.386891u
34
+ ··· 46.9021u 18.1704
0.268951u
35
0.415172u
34
+ ··· 2.22836u + 0.464678
a
1
=
0.769505u
35
+ 1.07166u
34
+ ··· + 31.1795u + 19.4777
0.393831u
35
+ 0.112167u
34
+ ··· 65.8523u 14.5725
a
4
=
0.637961u
35
+ 0.592755u
34
+ ··· 103.303u 23.1636
0.184491u
35
+ 0.149837u
34
+ ··· 15.4345u + 1.18486
a
5
=
0.359956u
35
+ 0.244025u
34
+ ··· 66.5978u 5.35101
0.294559u
35
0.557722u
34
+ ··· 13.0683u 4.16067
a
8
=
u
u
3
+ u
a
10
=
0.371740u
35
+ 1.03334u
34
+ ··· + 105.667u + 33.5297
0.291646u
35
+ 0.0216178u
34
+ ··· 56.3790u 13.1684
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0.228694u
35
0.643530u
34
+ ··· 255.696u 70.7596
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
6
+ u
5
u
4
2u
3
+ u + 1)
6
c
2
, c
4
, c
8
c
9
u
36
u
35
+ ··· + 186u + 43
c
3
, c
7
u
36
3u
35
+ ··· 16u + 1
c
5
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
6
c
10
(u
3
+ u
2
1)
12
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
6
3y
5
+ 5y
4
4y
3
+ 2y
2
y + 1)
6
c
2
, c
4
, c
8
c
9
y
36
+ 27y
35
+ ··· + 29904y + 1849
c
3
, c
7
y
36
9y
35
+ ··· 36y + 1
c
5
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
6
c
10
(y
3
y
2
+ 2y 1)
12
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.046060 + 0.100110I
a = 0.471095 + 0.739312I
b = 0.428243 0.664531I
0.02007 + 3.75243I 0.77353 3.77367I
u = 1.046060 0.100110I
a = 0.471095 0.739312I
b = 0.428243 + 0.664531I
0.02007 3.75243I 0.77353 + 3.77367I
u = 0.071145 + 1.052640I
a = 2.96217 + 0.54442I
b = 1.002190 0.295542I
3.80128 1.90382I 8.20696 + 2.18522I
u = 0.071145 1.052640I
a = 2.96217 0.54442I
b = 1.002190 + 0.295542I
3.80128 + 1.90382I 8.20696 2.18522I
u = 0.445481 + 0.807833I
a = 0.769672 0.151793I
b = 0.428243 + 0.664531I
0.02007 + 1.90382I 0.77353 2.18522I
u = 0.445481 0.807833I
a = 0.769672 + 0.151793I
b = 0.428243 0.664531I
0.02007 1.90382I 0.77353 + 2.18522I
u = 0.015491 + 1.101610I
a = 0.567110 0.099771I
b = 0.428243 0.664531I
4.15765 + 0.92430I 7.30279 0.79423I
u = 0.015491 1.101610I
a = 0.567110 + 0.099771I
b = 0.428243 + 0.664531I
4.15765 0.92430I 7.30279 + 0.79423I
u = 0.098878 + 1.131130I
a = 1.90200 0.19672I
b = 1.073950 + 0.558752I
1.91067 + 2.86490I 4.49024 2.53112I
u = 0.098878 1.131130I
a = 1.90200 + 0.19672I
b = 1.073950 0.558752I
1.91067 2.86490I 4.49024 + 2.53112I
10
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.196406 + 1.132180I
a = 1.65820 + 1.54999I
b = 1.073950 0.558752I
6.04826 5.69302I 11.01951 + 5.51057I
u = 0.196406 1.132180I
a = 1.65820 1.54999I
b = 1.073950 + 0.558752I
6.04826 + 5.69302I 11.01951 5.51057I
u = 1.031890 + 0.635795I
a = 0.203148 0.430936I
b = 1.002190 + 0.295542I
3.80128 + 1.90382I 8.20696 2.18522I
u = 1.031890 0.635795I
a = 0.203148 + 0.430936I
b = 1.002190 0.295542I
3.80128 1.90382I 8.20696 + 2.18522I
u = 0.444188 + 1.146330I
a = 0.054279 0.572062I
b = 0.428243 0.664531I
0.02007 + 3.75243I 0.77353 3.77367I
u = 0.444188 1.146330I
a = 0.054279 + 0.572062I
b = 0.428243 + 0.664531I
0.02007 3.75243I 0.77353 + 3.77367I
u = 0.560207 + 1.124730I
a = 1.81411 1.13202I
b = 1.002190 + 0.295542I
3.80128 3.75243I 8.20696 + 3.77367I
u = 0.560207 1.124730I
a = 1.81411 + 1.13202I
b = 1.002190 0.295542I
3.80128 + 3.75243I 8.20696 3.77367I
u = 0.598261 + 0.392855I
a = 0.352723 + 0.385946I
b = 1.073950 + 0.558752I
1.91067 + 2.86490I 4.49024 2.53112I
u = 0.598261 0.392855I
a = 0.352723 0.385946I
b = 1.073950 0.558752I
1.91067 2.86490I 4.49024 + 2.53112I
11
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 1.350340 + 0.016723I
a = 0.597073 0.522912I
b = 1.073950 + 0.558752I
1.91067 + 8.52114I 4.49024 8.49002I
u = 1.350340 0.016723I
a = 0.597073 + 0.522912I
b = 1.073950 0.558752I
1.91067 8.52114I 4.49024 + 8.49002I
u = 0.388989 + 1.300350I
a = 2.16057 + 0.72732I
b = 1.073950 0.558752I
1.91067 8.52114I 4.49024 + 8.49002I
u = 0.388989 1.300350I
a = 2.16057 0.72732I
b = 1.073950 + 0.558752I
1.91067 + 8.52114I 4.49024 8.49002I
u = 0.274718 + 0.565739I
a = 0.544610 + 1.141380I
b = 0.428243 + 0.664531I
0.02007 + 1.90382I 0.77353 2.18522I
u = 0.274718 0.565739I
a = 0.544610 1.141380I
b = 0.428243 0.664531I
0.02007 1.90382I 0.77353 + 2.18522I
u = 0.555599 + 1.270020I
a = 0.035250 0.334569I
b = 0.428243 + 0.664531I
4.15765 0.92430I 7.30279 + 0.79423I
u = 0.555599 1.270020I
a = 0.035250 + 0.334569I
b = 0.428243 0.664531I
4.15765 + 0.92430I 7.30279 0.79423I
u = 0.06736 + 1.43539I
a = 1.81428 0.63593I
b = 1.002190 0.295542I
7.93886 + 0.92430I 14.7362 0.7942I
u = 0.06736 1.43539I
a = 1.81428 + 0.63593I
b = 1.002190 + 0.295542I
7.93886 0.92430I 14.7362 + 0.7942I
12
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.216323 + 0.422026I
a = 1.90801 1.66447I
b = 1.002190 0.295542I
3.80128 + 3.75243I 8.20696 3.77367I
u = 0.216323 0.422026I
a = 1.90801 + 1.66447I
b = 1.002190 + 0.295542I
3.80128 3.75243I 8.20696 + 3.77367I
u = 0.80839 + 1.45058I
a = 1.15715 0.89131I
b = 1.073950 + 0.558752I
6.04826 + 5.69302I 0
u = 0.80839 1.45058I
a = 1.15715 + 0.89131I
b = 1.073950 0.558752I
6.04826 5.69302I 0
u = 0.31139 + 1.81407I
a = 1.280070 0.127233I
b = 1.002190 + 0.295542I
7.93886 0.92430I 0
u = 0.31139 1.81407I
a = 1.280070 + 0.127233I
b = 1.002190 0.295542I
7.93886 + 0.92430I 0
13
III. I
u
3
= hu
6
+ 4u
4
u
3
+ 4u
2
+ b 2u + 2, u
7
+ u
6
+ · · · + a + 3, u
8
+
4u
6
u
5
+ 5u
4
2u
3
+ 4u
2
u + 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
u
2
a
6
=
u
7
u
6
+ 4u
5
5u
4
+ 5u
3
6u
2
+ 3u 3
u
6
4u
4
+ u
3
4u
2
+ 2u 2
a
7
=
u
7
+ 4u
5
u
4
+ 4u
3
2u
2
+ u 1
u
6
4u
4
+ u
3
4u
2
+ 2u 2
a
1
=
u
7
+ 3u
5
u
4
+ 2u
3
u
2
+ 3u
2u
7
+ 7u
5
2u
4
+ 6u
3
3u
2
+ 4u 1
a
4
=
u
2
1
u
7
u
6
4u
5
2u
4
4u
3
u
2
2u 1
a
5
=
1
u
7
2u
6
4u
5
6u
4
3u
3
4u
2
u 3
a
8
=
u
u
3
+ u
a
10
=
u
2u
7
+ 7u
5
2u
4
+ 6u
3
3u
2
+ 5u 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
7
+ 6u
6
12u
5
+ 23u
4
18u
3
+ 21u
2
15u + 8
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
2u
6
u
5
+ 3u
4
+ 2u
3
2u
2
u + 1
c
2
, c
9
u
8
+ 4u
6
u
5
+ 5u
4
2u
3
+ 4u
2
u + 1
c
3
, c
7
u
8
+ u
7
u
4
u
3
+ 1
c
4
, c
8
u
8
+ 4u
6
+ u
5
+ 5u
4
+ 2u
3
+ 4u
2
+ u + 1
c
5
u
8
4u
7
+ 10u
6
17u
5
+ 23u
4
22u
3
+ 14u
2
5u + 1
c
6
u
8
2u
6
+ u
5
+ 3u
4
2u
3
2u
2
+ u + 1
c
10
u
8
+ 4u
7
+ 6u
6
+ 4u
5
3u
3
2u
2
+ 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
8
4y
7
+ 10y
6
17y
5
+ 23y
4
22y
3
+ 14y
2
5y + 1
c
2
, c
4
, c
8
c
9
y
8
+ 8y
7
+ 26y
6
+ 47y
5
+ 55y
4
+ 42y
3
+ 22y
2
+ 7y + 1
c
3
, c
7
y
8
y
7
2y
6
+ 2y
5
+ 3y
4
y
3
2y
2
+ 1
c
5
y
8
+ 4y
7
+ 10y
6
+ 23y
5
+ 23y
4
+ 10y
3
+ 22y
2
+ 3y + 1
c
10
y
8
4y
7
+ 4y
6
+ 4y
5
+ 2y
4
+ 3y
3
+ 4y
2
4y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
1(vol +
1CS) Cusp shape
u = 0.484309 + 0.994840I
a = 1.66075 1.39545I
b = 1.136610 + 0.491905I
4.20254 5.73534I 7.16249 + 5.56177I
u = 0.484309 0.994840I
a = 1.66075 + 1.39545I
b = 1.136610 0.491905I
4.20254 + 5.73534I 7.16249 5.56177I
u = 0.487513 + 0.687654I
a = 0.960124 0.950069I
b = 0.612814 + 0.310228I
2.09195 + 2.24783I 2.26438 2.85323I
u = 0.487513 0.687654I
a = 0.960124 + 0.950069I
b = 0.612814 0.310228I
2.09195 2.24783I 2.26438 + 2.85323I
u = 0.110933 + 0.652805I
a = 1.26488 + 0.66485I
b = 0.819536 + 0.880313I
0.32853 + 3.26075I 2.37672 5.45948I
u = 0.110933 0.652805I
a = 1.26488 0.66485I
b = 0.819536 0.880313I
0.32853 3.26075I 2.37672 + 5.45948I
u = 0.11414 + 1.61519I
a = 1.43575 + 0.22209I
b = 0.929887 + 0.300978I
7.19351 + 1.24143I 2.94984 5.90753I
u = 0.11414 1.61519I
a = 1.43575 0.22209I
b = 0.929887 0.300978I
7.19351 1.24143I 2.94984 + 5.90753I
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
6
+ u
5
u
4
2u
3
+ u + 1)
6
)(u
8
2u
6
+ ··· u + 1)
· (u
17
7u
16
+ ··· 36u + 8)
c
2
, c
9
(u
8
+ 4u
6
+ ··· u + 1)(u
17
+ 6u
15
+ ··· + 2u + 1)
· (u
36
u
35
+ ··· + 186u + 43)
c
3
, c
7
(u
8
+ u
7
u
4
u
3
+ 1)(u
17
u
16
+ ··· u + 1)(u
36
3u
35
+ ··· 16u + 1)
c
4
, c
8
(u
8
+ 4u
6
+ ··· + u + 1)(u
17
+ 6u
15
+ ··· + 2u + 1)
· (u
36
u
35
+ ··· + 186u + 43)
c
5
(u
6
+ 3u
5
+ 5u
4
+ 4u
3
+ 2u
2
+ u + 1)
6
· (u
8
4u
7
+ 10u
6
17u
5
+ 23u
4
22u
3
+ 14u
2
5u + 1)
· (u
17
+ 7u
16
+ ··· 48u + 64)
c
6
((u
6
+ u
5
u
4
2u
3
+ u + 1)
6
)(u
8
2u
6
+ ··· + u + 1)
· (u
17
7u
16
+ ··· 36u + 8)
c
10
(u
3
+ u
2
1)
12
(u
8
+ 4u
7
+ 6u
6
+ 4u
5
3u
3
2u
2
+ 1)
· (u
17
15u
16
+ ··· + 608u 64)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
6
3y
5
+ 5y
4
4y
3
+ 2y
2
y + 1)
6
· (y
8
4y
7
+ 10y
6
17y
5
+ 23y
4
22y
3
+ 14y
2
5y + 1)
· (y
17
7y
16
+ ··· 48y 64)
c
2
, c
4
, c
8
c
9
(y
8
+ 8y
7
+ 26y
6
+ 47y
5
+ 55y
4
+ 42y
3
+ 22y
2
+ 7y + 1)
· (y
17
+ 12y
16
+ ··· + 4y 1)(y
36
+ 27y
35
+ ··· + 29904y + 1849)
c
3
, c
7
(y
8
y
7
+ ··· 2y
2
+ 1)(y
17
+ 3y
16
+ ··· 9y 1)
· (y
36
9y
35
+ ··· 36y + 1)
c
5
(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
6
· (y
8
+ 4y
7
+ 10y
6
+ 23y
5
+ 23y
4
+ 10y
3
+ 22y
2
+ 3y + 1)
· (y
17
+ 5y
16
+ ··· + 17664y 4096)
c
10
((y
3
y
2
+ 2y 1)
12
)(y
8
4y
7
+ ··· 4y + 1)
· (y
17
5y
16
+ ··· + 17408y 4096)
19