12a
1139
(K12a
1139
)
A knot diagram
1
Linearized knot diagam
4 8 9 10 12 11 3 2 1 7 6 5
Solving Sequence
6,11
7 12 5 1 10 4 2 9 3 8
c
6
c
11
c
5
c
12
c
10
c
4
c
1
c
9
c
3
c
8
c
2
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
50
+ u
49
+ ··· + 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 50 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
= hu
50
+ u
49
+ · · · + 3u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
12
=
u
u
a
5
=
u
2
+ 1
u
2
a
1
=
u
3
+ 2u
u
3
+ u
a
10
=
−u
u
3
+ u
a
4
=
−u
6
− 3u
4
+ 1
u
8
+ 4u
6
+ 4u
4
+ 2u
2
a
2
=
−u
17
− 10u
15
− 37u
13
− 60u
11
− 35u
9
+ 8u
7
+ 16u
5
+ 4u
3
+ u
u
19
+ 11u
17
+ 48u
15
+ 107u
13
+ 133u
11
+ 95u
9
+ 34u
7
+ 2u
5
− u
3
+ u
a
9
=
−u
9
− 6u
7
− 11u
5
− 6u
3
− u
−u
9
− 5u
7
− 7u
5
− 2u
3
+ u
a
3
=
u
26
+ 17u
24
+ ··· + u
2
+ 1
u
26
+ 16u
24
+ ··· + 6u
4
+ u
2
a
8
=
−u
45
− 28u
43
+ ··· − 4u
3
− u
u
47
+ 29u
45
+ ··· − 2u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
49
+ 4u
48
+ ··· + 20u + 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
50
− 11u
49
+ ··· − 971u + 99
c
2
, c
7
, c
8
u
50
− u
49
+ ··· − u + 1
c
3
u
50
+ u
49
+ ··· − 3u + 1
c
4
u
50
− u
49
+ ··· + 135u + 29
c
5
, c
6
, c
10
c
11
, c
12
u
50
− u
49
+ ··· − 3u + 1
c
9
u
50
− 7u
49
+ ··· − 511u + 215
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
50
+ 13y
49
+ ··· + 182789y + 9801
c
2
, c
7
, c
8
y
50
+ 45y
49
+ ··· + y + 1
c
3
y
50
+ y
49
+ ··· + y + 1
c
4
y
50
+ 9y
49
+ ··· − 5523y + 841
c
5
, c
6
, c
10
c
11
, c
12
y
50
+ 65y
49
+ ··· + y + 1
c
9
y
50
+ 17y
49
+ ··· + 738629y + 46225
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.267263 + 0.974653I
−2.52565 − 3.29260I 0
u = −0.267263 − 0.974653I
−2.52565 + 3.29260I 0
u = 0.300039 + 0.917172I
3.68092 + 1.88018I 3.28403 − 3.42848I
u = 0.300039 − 0.917172I
3.68092 − 1.88018I 3.28403 + 3.42848I
u = 0.303413 + 0.993489I
−3.97531 + 7.01696I 0
u = 0.303413 − 0.993489I
−3.97531 − 7.01696I 0
u = −0.228796 + 1.014910I
−2.85501 − 3.56952I 0
u = −0.228796 − 1.014910I
−2.85501 + 3.56952I 0
u = 0.167253 + 1.029960I
−5.48280 + 0.26480I 0
u = 0.167253 − 1.029960I
−5.48280 − 0.26480I 0
u = −0.322805 + 0.992607I
1.41582 − 10.58410I 0
u = −0.322805 − 0.992607I
1.41582 + 10.58410I 0
u = −0.122951 + 1.057210I
−0.72813 + 3.07389I 0
u = −0.122951 − 1.057210I
−0.72813 − 3.07389I 0
u = 0.293582 + 0.669845I
5.06450 + 3.76743I 4.59609 − 5.34956I
u = 0.293582 − 0.669845I
5.06450 − 3.76743I 4.59609 + 5.34956I
u = −0.165448 + 0.666519I
−0.48337 − 1.40800I 0.29896 + 5.97525I
u = −0.165448 − 0.666519I
−0.48337 + 1.40800I 0.29896 − 5.97525I
u = −0.376224 + 0.489617I
4.12836 + 4.50612I 3.44574 − 0.89848I
u = −0.376224 − 0.489617I
4.12836 − 4.50612I 3.44574 + 0.89848I
u = −0.543737 + 0.197520I
5.08510 − 7.63642I 6.10437 + 7.49857I
u = −0.543737 − 0.197520I
5.08510 + 7.63642I 6.10437 − 7.49857I
u = 0.513985 + 0.202878I
−0.28571 + 4.22898I 1.46755 − 7.80159I
u = 0.513985 − 0.202878I
−0.28571 − 4.22898I 1.46755 + 7.80159I
u = 0.334706 + 0.422369I
−1.09545 − 1.33004I −1.86370 + 0.68284I
u = 0.334706 − 0.422369I
−1.09545 + 1.33004I −1.86370 − 0.68284I
u = 0.521502 + 0.099632I
6.77978 − 0.91733I 9.49995 − 0.90455I
u = 0.521502 − 0.099632I
6.77978 + 0.91733I 9.49995 + 0.90455I
u = −0.420230 + 0.281296I
1.13900 − 1.36467I 1.97434 + 4.92900I
u = −0.420230 − 0.281296I
1.13900 + 1.36467I 1.97434 − 4.92900I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.448171 + 0.153855I
0.966748 − 0.838351I 5.97312 + 2.21174I
u = −0.448171 − 0.153855I
0.966748 + 0.838351I 5.97312 − 2.21174I
u = 0.02262 + 1.64150I
−2.97025 + 4.57226I 0
u = 0.02262 − 1.64150I
−2.97025 − 4.57226I 0
u = −0.01192 + 1.65807I
−8.80943 − 1.80374I 0
u = −0.01192 − 1.65807I
−8.80943 + 1.80374I 0
u = 0.07257 + 1.69685I
−5.55279 + 3.30682I 0
u = 0.07257 − 1.69685I
−5.55279 − 3.30682I 0
u = −0.06955 + 1.71380I
−12.07900 − 4.64056I 0
u = −0.06955 − 1.71380I
−12.07900 + 4.64056I 0
u = −0.08449 + 1.71651I
−8.1767 − 12.2216I 0
u = −0.08449 − 1.71651I
−8.1767 + 12.2216I 0
u = 0.07899 + 1.71722I
−13.5884 + 8.5544I 0
u = 0.07899 − 1.71722I
−13.5884 − 8.5544I 0
u = −0.05785 + 1.72253I
−12.61190 − 4.72463I 0
u = −0.05785 − 1.72253I
−12.61190 + 4.72463I 0
u = 0.04441 + 1.72496I
−15.3216 + 1.1374I 0
u = 0.04441 − 1.72496I
−15.3216 − 1.1374I 0
u = −0.03365 + 1.72806I
−10.67560 + 2.41850I 0
u = −0.03365 − 1.72806I
−10.67560 − 2.41850I 0
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
50
− 11u
49
+ ··· − 971u + 99
c
2
, c
7
, c
8
u
50
− u
49
+ ··· − u + 1
c
3
u
50
+ u
49
+ ··· − 3u + 1
c
4
u
50
− u
49
+ ··· + 135u + 29
c
5
, c
6
, c
10
c
11
, c
12
u
50
− u
49
+ ··· − 3u + 1
c
9
u
50
− 7u
49
+ ··· − 511u + 215
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
50
+ 13y
49
+ ··· + 182789y + 9801
c
2
, c
7
, c
8
y
50
+ 45y
49
+ ··· + y + 1
c
3
y
50
+ y
49
+ ··· + y + 1
c
4
y
50
+ 9y
49
+ ··· − 5523y + 841
c
5
, c
6
, c
10
c
11
, c
12
y
50
+ 65y
49
+ ··· + y + 1
c
9
y
50
+ 17y
49
+ ··· + 738629y + 46225
8
