12a
1133
(K12a
1133
)
A knot diagram
1
Linearized knot diagam
4 8 9 10 11 12 3 2 1 7 6 5
Solving Sequence
7,12
6 11 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
79
− u
78
+ ··· + 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 79 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
79
− u
78
+ · · · + 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
6
=
1
u
2
a
11
=
−u
−u
3
+ u
a
5
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
10
=
u
3
− 2u
−u
3
+ u
a
4
=
u
10
− 5u
8
+ 8u
6
− 3u
4
− 3u
2
+ 1
−u
10
+ 4u
8
− 5u
6
+ 3u
2
a
2
=
−u
27
+ 12u
25
+ ··· − 2u
5
+ 5u
3
u
27
− 11u
25
+ ··· − u
3
+ u
a
9
=
u
15
− 6u
13
+ 14u
11
− 14u
9
+ 2u
7
+ 6u
5
− 2u
3
− 2u
u
17
− 7u
15
+ 19u
13
− 22u
11
+ 3u
9
+ 14u
7
− 6u
5
− 4u
3
+ u
a
3
=
−u
42
+ 17u
40
+ ··· − u
2
+ 1
−u
44
+ 18u
42
+ ··· + 5u
4
+ 2u
2
a
8
=
u
71
− 30u
69
+ ··· − 2u
3
− 2u
−u
71
+ 29u
69
+ ··· − 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
77
+ 128u
75
+ ··· + 16u + 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
79
− 17u
78
+ ··· − 26040u + 1697
c
2
, c
7
, c
8
u
79
− u
78
+ ··· + 2u − 1
c
3
u
79
+ u
78
+ ··· + 13u − 2
c
4
u
79
− u
78
+ ··· − 40u − 25
c
5
, c
6
, c
11
u
79
+ u
78
+ ··· + 2u − 1
c
9
u
79
− 7u
78
+ ··· + 4620u + 121
c
10
, c
12
u
79
− 3u
78
+ ··· − 221u + 56
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
79
+ 23y
78
+ ··· − 69562296y −2879809
c
2
, c
7
, c
8
y
79
+ 71y
78
+ ··· − 8y
2
− 1
c
3
y
79
+ 3y
78
+ ··· − 11y −4
c
4
y
79
− 5y
78
+ ··· + 34200y −625
c
5
, c
6
, c
11
y
79
− 65y
78
+ ··· − 4y
2
− 1
c
9
y
79
+ 19y
78
+ ··· + 25448720y −14641
c
10
, c
12
y
79
+ 51y
78
+ ··· + 22297y −3136
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.119910 + 0.269996I
6.31309 + 1.50449I 0
u = 1.119910 − 0.269996I
6.31309 − 1.50449I 0
u = −1.116140 + 0.344098I
3.99592 + 7.01460I 0
u = −1.116140 − 0.344098I
3.99592 − 7.01460I 0
u = 1.129450 + 0.339661I
−1.35951 − 3.44188I 0
u = 1.129450 − 0.339661I
−1.35951 + 3.44188I 0
u = −0.127859 + 0.804619I
0.99138 − 11.20740I 1.90900 + 7.76695I
u = −0.127859 − 0.804619I
0.99138 + 11.20740I 1.90900 − 7.76695I
u = 0.120290 + 0.801749I
−4.42516 + 7.60535I −2.69052 − 7.48919I
u = 0.120290 − 0.801749I
−4.42516 − 7.60535I −2.69052 + 7.48919I
u = −1.151830 + 0.322827I
0.174975 − 0.262644I 0
u = −1.151830 − 0.322827I
0.174975 + 0.262644I 0
u = −0.088144 + 0.798068I
−3.42247 − 4.03212I −1.76280 + 4.49310I
u = −0.088144 − 0.798068I
−3.42247 + 4.03212I −1.76280 − 4.49310I
u = −0.046884 + 0.799298I
−1.44028 + 2.80439I −0.85617 − 2.18147I
u = −0.046884 − 0.799298I
−1.44028 − 2.80439I −0.85617 + 2.18147I
u = 0.065230 + 0.795734I
−6.12113 + 0.61604I −6.03236 + 0.34847I
u = 0.065230 − 0.795734I
−6.12113 − 0.61604I −6.03236 − 0.34847I
u = −0.109674 + 0.789656I
−2.98096 − 3.79614I −0.06060 + 2.39804I
u = −0.109674 − 0.789656I
−2.98096 + 3.79614I −0.06060 − 2.39804I
u = 0.129454 + 0.770426I
3.35446 + 2.37248I 4.39926 − 2.88601I
u = 0.129454 − 0.770426I
3.35446 − 2.37248I 4.39926 + 2.88601I
u = −1.174720 + 0.339826I
−0.109212 − 0.094646I 0
u = −1.174720 − 0.339826I
−0.109212 + 0.094646I 0
u = 1.201820 + 0.343577I
−2.63933 + 3.50252I 0
u = 1.201820 − 0.343577I
−2.63933 − 3.50252I 0
u = −1.217970 + 0.349990I
2.16029 − 6.95203I 0
u = −1.217970 − 0.349990I
2.16029 + 6.95203I 0
u = −1.27536
2.83534 0
u = 1.318290 + 0.071541I
6.31838 + 2.66253I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.318290 − 0.071541I
6.31838 − 2.66253I 0
u = −1.311270 + 0.248102I
3.39241 − 1.40885I 0
u = −1.311270 − 0.248102I
3.39241 + 1.40885I 0
u = 1.296480 + 0.346961I
2.75060 + 1.32326I 0
u = 1.296480 − 0.346961I
2.75060 − 1.32326I 0
u = 0.156652 + 0.634430I
5.00375 + 3.99260I 5.33060 − 4.90046I
u = 0.156652 − 0.634430I
5.00375 − 3.99260I 5.33060 + 4.90046I
u = 1.320350 + 0.276038I
3.78685 + 4.88557I 0
u = 1.320350 − 0.276038I
3.78685 − 4.88557I 0
u = 1.330100 + 0.236506I
8.98594 − 1.62355I 0
u = 1.330100 − 0.236506I
8.98594 + 1.62355I 0
u = −1.310030 + 0.345318I
−1.81920 − 4.72773I 0
u = −1.310030 − 0.345318I
−1.81920 + 4.72773I 0
u = −0.543300 + 0.338999I
5.11761 − 7.49924I 6.46948 + 7.99126I
u = −0.543300 − 0.338999I
5.11761 + 7.49924I 6.46948 − 7.99126I
u = 0.601727 + 0.206736I
6.71860 − 1.01423I 9.60570 − 1.23872I
u = 0.601727 − 0.206736I
6.71860 + 1.01423I 9.60570 + 1.23872I
u = −1.339530 + 0.276387I
9.68534 − 7.36202I 0
u = −1.339530 − 0.276387I
9.68534 + 7.36202I 0
u = 1.324120 + 0.346948I
1.00559 + 8.16070I 0
u = 1.324120 − 0.346948I
1.00559 − 8.16070I 0
u = 1.369290 + 0.043682I
6.62983 + 1.55922I 0
u = 1.369290 − 0.043682I
6.62983 − 1.55922I 0
u = −0.080168 + 0.624756I
−0.62665 − 1.53685I 1.09952 + 5.24112I
u = −0.080168 − 0.624756I
−0.62665 + 1.53685I 1.09952 − 5.24112I
u = 1.337040 + 0.341010I
1.56661 + 7.87869I 0
u = 1.337040 − 0.341010I
1.56661 − 7.87869I 0
u = −1.379070 + 0.061269I
5.59871 − 5.23109I 0
u = −1.379070 − 0.061269I
5.59871 + 5.23109I 0
u = −1.344960 + 0.330309I
7.99521 − 6.35631I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.344960 − 0.330309I
7.99521 + 6.35631I 0
u = −1.343360 + 0.346682I
0.17815 − 11.74890I 0
u = −1.343360 − 0.346682I
0.17815 + 11.74890I 0
u = −1.387760 + 0.032369I
12.77490 + 0.40459I 0
u = −1.387760 − 0.032369I
12.77490 − 0.40459I 0
u = 1.389120 + 0.063240I
11.12760 + 8.64852I 0
u = 1.389120 − 0.063240I
11.12760 − 8.64852I 0
u = 1.347730 + 0.347472I
5.6350 + 15.3639I 0
u = 1.347730 − 0.347472I
5.6350 − 15.3639I 0
u = 0.508944 + 0.322602I
−0.25179 + 4.12095I 1.80082 − 8.29426I
u = 0.508944 − 0.322602I
−0.25179 − 4.12095I 1.80082 + 8.29426I
u = −0.252272 + 0.515953I
4.20461 + 4.40403I 4.02126 − 1.02784I
u = −0.252272 − 0.515953I
4.20461 − 4.40403I 4.02126 + 1.02784I
u = −0.466798 + 0.223035I
0.965294 − 0.777908I 6.33896 + 2.42905I
u = −0.466798 − 0.223035I
0.965294 + 0.777908I 6.33896 − 2.42905I
u = −0.373663 + 0.351639I
1.20042 − 1.33503I 2.25607 + 5.14188I
u = −0.373663 − 0.351639I
1.20042 + 1.33503I 2.25607 − 5.14188I
u = 0.237055 + 0.443394I
−1.04518 − 1.27519I −1.51740 + 0.90528I
u = 0.237055 − 0.443394I
−1.04518 + 1.27519I −1.51740 − 0.90528I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
79
− 17u
78
+ ··· − 26040u + 1697
c
2
, c
7
, c
8
u
79
− u
78
+ ··· + 2u − 1
c
3
u
79
+ u
78
+ ··· + 13u − 2
c
4
u
79
− u
78
+ ··· − 40u − 25
c
5
, c
6
, c
11
u
79
+ u
78
+ ··· + 2u − 1
c
9
u
79
− 7u
78
+ ··· + 4620u + 121
c
10
, c
12
u
79
− 3u
78
+ ··· − 221u + 56
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
79
+ 23y
78
+ ··· − 69562296y −2879809
c
2
, c
7
, c
8
y
79
+ 71y
78
+ ··· − 8y
2
− 1
c
3
y
79
+ 3y
78
+ ··· − 11y −4
c
4
y
79
− 5y
78
+ ··· + 34200y −625
c
5
, c
6
, c
11
y
79
− 65y
78
+ ··· − 4y
2
− 1
c
9
y
79
+ 19y
78
+ ··· + 25448720y −14641
c
10
, c
12
y
79
+ 51y
78
+ ··· + 22297y −3136
9
