10
91
(K10a
106
)
A knot diagram
1
Linearized knot diagam
9 7 1 8 2 10 4 5 6 3
Solving Sequence
4,7
8 5
1,9
3 2 10 6
c
7
c
4
c
8
c
3
c
2
c
10
c
6
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h2.01404 × 10
18
u
35
− 4.78501 × 10
18
u
34
+ ··· + 1.28887 × 10
18
b − 6.30993 × 10
17
,
1.95116 × 10
19
u
35
− 6.14010 × 10
19
u
34
+ ··· + 1.41776 × 10
19
a + 2.81287 × 10
18
, u
36
− 3u
35
+ ··· + 3u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 36 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
=
h2.01×10
18
u
35
−4.79×10
18
u
34
+· · ·+1.29×10
18
b−6.31×10
17
, 1.95×10
19
u
35
−
6.14 × 10
19
u
34
+ · · · + 1.42 × 10
19
a + 2.81 × 10
18
, u
36
− 3u
35
+ · · · + 3u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
5
=
u
−u
3
+ u
a
1
=
−1.37623u
35
+ 4.33085u
34
+ ··· − 3.87762u − 0.198403
−1.56264u
35
+ 3.71256u
34
+ ··· − 0.845601u + 0.489570
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
3
=
−1.25056u
35
+ 3.87415u
34
+ ··· − 3.68575u + 0.0424660
−1.35969u
35
+ 3.19917u
34
+ ··· + 0.648916u + 0.386431
a
2
=
0.109127u
35
+ 0.674985u
34
+ ··· − 4.33466u − 0.343965
−1.35969u
35
+ 3.19917u
34
+ ··· + 0.648916u + 0.386431
a
10
=
−0.498455u
35
+ 1.46595u
34
+ ··· − 0.488164u − 0.513350
−0.561499u
35
+ 1.29302u
34
+ ··· − 1.92515u + 0.154877
a
6
=
−0.126393u
35
− 0.0468796u
34
+ ··· − 0.938532u + 0.697640
−0.0671172u
35
+ 0.329351u
34
+ ··· − 1.55309u − 0.241770
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
58911071591979655120
14177581577372014769
u
35
+
138393380035194827072
14177581577372014769
u
34
+ ··· +
178473388351458886120
14177581577372014769
u −
4922018709261351330
14177581577372014769
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
36
+ 11u
35
+ ··· − 6u + 1
c
2
u
36
− 15u
35
+ ··· − 172u + 43
c
3
, c
10
u
36
− u
35
+ ··· − 14u + 1
c
4
, c
7
, c
8
u
36
− 3u
35
+ ··· + 3u
2
+ 1
c
5
u
36
− 3u
35
+ ··· − 4u + 1
c
6
, c
9
u
36
+ u
35
+ ··· + 3u
2
+ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
36
− 151y
35
+ ··· − 50y + 1
c
2
y
36
− 127y
35
+ ··· + 24510y + 1849
c
3
, c
10
y
36
− 23y
35
+ ··· − 134y + 1
c
4
, c
7
, c
8
y
36
− 35y
35
+ ··· + 6y + 1
c
5
y
36
− 3y
35
+ ··· − 46y + 1
c
6
, c
9
y
36
− 27y
35
+ ··· + 6y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.374032 + 0.914066I
a = −0.115745 + 1.064450I
b = 0.39274 + 1.61774I
−0.97788 + 3.67922I 0.14859 − 9.07649I
u = 0.374032 − 0.914066I
a = −0.115745 − 1.064450I
b = 0.39274 − 1.61774I
−0.97788 − 3.67922I 0.14859 + 9.07649I
u = −0.482693 + 0.837528I
a = 0.27444 + 1.43336I
b = −0.48043 + 1.77937I
−6.25192 − 9.33147I −3.94994 + 7.24799I
u = −0.482693 − 0.837528I
a = 0.27444 − 1.43336I
b = −0.48043 − 1.77937I
−6.25192 + 9.33147I −3.94994 − 7.24799I
u = −0.682211 + 0.817416I
a = 0.932948 + 0.700627I
b = −0.21456 + 1.43556I
−5.71207 + 3.85049I −4.56018 − 4.43001I
u = −0.682211 − 0.817416I
a = 0.932948 − 0.700627I
b = −0.21456 − 1.43556I
−5.71207 − 3.85049I −4.56018 + 4.43001I
u = 1.24034
a = 1.44030
b = −0.439862
−2.81937 −4.82430
u = −1.326560 + 0.141059I
a = −0.897495 − 0.822985I
b = 0.382546 − 1.268300I
−1.18988 − 4.20357I −3.06671 + 5.28453I
u = −1.326560 − 0.141059I
a = −0.897495 + 0.822985I
b = 0.382546 + 1.268300I
−1.18988 + 4.20357I −3.06671 − 5.28453I
u = −0.399963 + 0.525370I
a = 1.08446 − 1.08372I
b = 0.289305 + 0.032283I
−1.74249 − 4.24043I −1.82805 + 7.42803I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.399963 − 0.525370I
a = 1.08446 + 1.08372I
b = 0.289305 − 0.032283I
−1.74249 + 4.24043I −1.82805 − 7.42803I
u = 0.545615 + 0.371407I
a = −0.622878 − 0.360163I
b = 0.204444 + 0.269001I
1.145860 + 0.715757I 6.11111 − 2.29185I
u = 0.545615 − 0.371407I
a = −0.622878 + 0.360163I
b = 0.204444 − 0.269001I
1.145860 − 0.715757I 6.11111 + 2.29185I
u = −1.34346
a = −0.912003
b = 2.41867
1.82908 7.56320
u = 1.370890 + 0.090628I
a = 0.660532 − 0.421889I
b = −0.39300 − 1.73201I
3.05261 + 2.19942I 3.77042 − 2.93592I
u = 1.370890 − 0.090628I
a = 0.660532 + 0.421889I
b = −0.39300 + 1.73201I
3.05261 − 2.19942I 3.77042 + 2.93592I
u = −1.39633
a = −0.729782
b = 12.3968
1.61132 108.030
u = 1.46569
a = −0.0582965
b = 1.01413
3.38902 0
u = 0.120769 + 0.518709I
a = −0.34492 − 2.82501I
b = −0.141050 − 1.048610I
−5.66880 + 1.84316I −9.44552 − 3.91915I
u = 0.120769 − 0.518709I
a = −0.34492 + 2.82501I
b = −0.141050 + 1.048610I
−5.66880 − 1.84316I −9.44552 + 3.91915I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.45659 + 0.18746I
a = −0.183193 − 0.880025I
b = −0.350456 − 0.614358I
4.26834 + 6.86007I 0
u = 1.45659 − 0.18746I
a = −0.183193 + 0.880025I
b = −0.350456 + 0.614358I
4.26834 − 6.86007I 0
u = 1.40740 + 0.44440I
a = −0.547365 + 0.331992I
b = 1.19130 + 1.15658I
2.04431 + 1.84068I 0
u = 1.40740 − 0.44440I
a = −0.547365 − 0.331992I
b = 1.19130 − 1.15658I
2.04431 − 1.84068I 0
u = −0.306066 + 0.424951I
a = −0.816894 + 0.202983I
b = −0.749449 + 0.484112I
−1.81388 + 1.13467I −1.97456 + 1.07001I
u = −0.306066 − 0.424951I
a = −0.816894 − 0.202983I
b = −0.749449 − 0.484112I
−1.81388 − 1.13467I −1.97456 − 1.07001I
u = −1.49125 + 0.15772I
a = 0.263366 − 0.575561I
b = 0.010884 − 0.381896I
7.75318 − 2.83746I 0
u = −1.49125 − 0.15772I
a = 0.263366 + 0.575561I
b = 0.010884 + 0.381896I
7.75318 + 2.83746I 0
u = −1.49131 + 0.32149I
a = 0.669876 + 0.507097I
b = −1.25550 + 1.58180I
5.07523 − 8.06301I 0
u = −1.49131 − 0.32149I
a = 0.669876 − 0.507097I
b = −1.25550 − 1.58180I
5.07523 + 8.06301I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.51652 + 0.30390I
a = −0.792548 + 0.567740I
b = 1.12600 + 1.82198I
0.21259 + 13.48700I 0
u = 1.51652 − 0.30390I
a = −0.792548 − 0.567740I
b = 1.12600 − 1.82198I
0.21259 − 13.48700I 0
u = 0.408894
a = 2.87090
b = 1.71340
−3.87788 10.5720
u = −0.149951 + 0.342435I
a = −0.63819 − 2.59470I
b = −0.423633 − 1.031480I
−1.76218 − 0.65074I −4.85797 − 0.85968I
u = −0.149951 − 0.342435I
a = −0.63819 + 2.59470I
b = −0.423633 + 1.031480I
−1.76218 + 0.65074I −4.85797 + 0.85968I
u = 1.70127
a = −0.463910
b = 0.718631
3.00176 0
8
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
36
+ 11u
35
+ ··· − 6u + 1
c
2
u
36
− 15u
35
+ ··· − 172u + 43
c
3
, c
10
u
36
− u
35
+ ··· − 14u + 1
c
4
, c
7
, c
8
u
36
− 3u
35
+ ··· + 3u
2
+ 1
c
5
u
36
− 3u
35
+ ··· − 4u + 1
c
6
, c
9
u
36
+ u
35
+ ··· + 3u
2
+ 1
9
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
36
− 151y
35
+ ··· − 50y + 1
c
2
y
36
− 127y
35
+ ··· + 24510y + 1849
c
3
, c
10
y
36
− 23y
35
+ ··· − 134y + 1
c
4
, c
7
, c
8
y
36
− 35y
35
+ ··· + 6y + 1
c
5
y
36
− 3y
35
+ ··· − 46y + 1
c
6
, c
9
y
36
− 27y
35
+ ··· + 6y + 1
10
