12a
1130
(K12a
1130
)
A knot diagram
1
Linearized knot diagam
4 8 9 10 11 12 2 3 1 7 6 5
Solving Sequence
4,9
3 8 2 1 10 5 7 11 12 6
c
3
c
8
c
2
c
1
c
9
c
4
c
7
c
10
c
12
c
6
c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
62
− u
61
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 62 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
62
− u
61
+ · · · + u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
3
=
1
−u
2
a
8
=
u
−u
3
+ u
a
2
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
u
4
− 3u
2
+ 1
u
4
− 2u
2
a
10
=
u
9
− 6u
7
+ 11u
5
− 6u
3
+ u
u
9
− 5u
7
+ 7u
5
− 2u
3
+ u
a
5
=
−u
18
+ 11u
16
− 48u
14
+ 105u
12
− 121u
10
+ 75u
8
− 30u
6
+ 8u
4
− u
2
+ 1
−u
18
+ 10u
16
− 39u
14
+ 74u
12
− 71u
10
+ 38u
8
− 18u
6
+ 4u
4
− u
2
a
7
=
−u
3
+ 2u
u
5
− 3u
3
+ u
a
11
=
u
17
− 10u
15
+ 39u
13
− 74u
11
+ 71u
9
− 38u
7
+ 18u
5
− 4u
3
+ u
−u
19
+ 11u
17
− 48u
15
+ 105u
13
− 121u
11
+ 75u
9
− 30u
7
+ 8u
5
− u
3
+ u
a
12
=
u
32
− 19u
30
+ ··· − 2u
2
+ 1
u
32
− 18u
30
+ ··· + 12u
8
− 2u
2
a
6
=
−u
54
+ 31u
52
+ ··· − 2u
2
+ 1
u
56
− 32u
54
+ ··· + 6u
4
− 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
59
+ 136u
57
+ ··· − 4u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
62
− 17u
61
+ ··· + 1847u − 113
c
2
, c
3
, c
7
c
8
u
62
+ u
61
+ ··· − u + 1
c
4
u
62
− u
61
+ ··· + 15u + 1
c
5
, c
6
, c
11
u
62
+ u
61
+ ··· − u + 1
c
9
u
62
− 5u
61
+ ··· + 640u + 304
c
10
, c
12
u
62
− 3u
61
+ ··· + 55u − 9
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
62
− 11y
61
+ ··· − 256449y + 12769
c
2
, c
3
, c
7
c
8
y
62
− 71y
61
+ ··· − y + 1
c
4
y
62
+ y
61
+ ··· + 127y + 1
c
5
, c
6
, c
11
y
62
− 51y
61
+ ··· − y + 1
c
9
y
62
+ 25y
61
+ ··· − 2665888y + 92416
c
10
, c
12
y
62
+ 41y
61
+ ··· − 2233y + 81
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.708768 + 0.494433I
−0.01088 + 11.34630I 1.00889 − 9.72117I
u = −0.708768 − 0.494433I
−0.01088 − 11.34630I 1.00889 + 9.72117I
u = 0.712691 + 0.482290I
−4.59207 − 7.20372I −3.76784 + 7.81893I
u = 0.712691 − 0.482290I
−4.59207 + 7.20372I −3.76784 − 7.81893I
u = 0.821977 + 0.248060I
−1.60870 + 5.02300I −2.11818 − 2.33854I
u = 0.821977 − 0.248060I
−1.60870 − 5.02300I −2.11818 + 2.33854I
u = −0.717017 + 0.462468I
−1.49252 + 3.04670I −0.95105 − 4.03685I
u = −0.717017 − 0.462468I
−1.49252 − 3.04670I −0.95105 + 4.03685I
u = −0.804271 + 0.274945I
−5.95144 − 0.93191I −6.82947 − 0.41510I
u = −0.804271 − 0.274945I
−5.95144 + 0.93191I −6.82947 + 0.41510I
u = 0.786850 + 0.308644I
−2.51765 − 3.16231I −3.19226 + 4.63064I
u = 0.786850 − 0.308644I
−2.51765 + 3.16231I −3.19226 − 4.63064I
u = 0.645614 + 0.481542I
5.40192 − 4.93284I 5.98347 + 6.95967I
u = 0.645614 − 0.481542I
5.40192 + 4.93284I 5.98347 − 6.95967I
u = −0.661871 + 0.431665I
−0.37286 + 3.82050I 0.80971 − 8.83279I
u = −0.661871 − 0.431665I
−0.37286 − 3.82050I 0.80971 + 8.83279I
u = 0.620723 + 0.337292I
−1.08571 − 1.06603I −2.60164 + 1.01884I
u = 0.620723 − 0.337292I
−1.08571 + 1.06603I −2.60164 − 1.01884I
u = −0.698913
2.99735 1.03130
u = −0.524035 + 0.459452I
3.21307 − 1.54671I 5.20781 − 1.38178I
u = −0.524035 − 0.459452I
3.21307 + 1.54671I 5.20781 + 1.38178I
u = −0.383395 + 0.494306I
3.62071 + 4.90483I 6.55837 − 6.65558I
u = −0.383395 − 0.494306I
3.62071 − 4.90483I 6.55837 + 6.65558I
u = −0.164450 + 0.582453I
1.57732 − 7.67033I 4.62669 + 4.82288I
u = −0.164450 − 0.582453I
1.57732 + 7.67033I 4.62669 − 4.82288I
u = 0.412131 + 0.432363I
−0.75273 − 1.50608I 0.71484 + 5.28376I
u = 0.412131 − 0.432363I
−0.75273 + 1.50608I 0.71484 − 5.28376I
u = 0.147128 + 0.569414I
−2.94806 + 3.60850I −0.16305 − 2.91417I
u = 0.147128 − 0.569414I
−2.94806 − 3.60850I −0.16305 + 2.91417I
u = 0.250782 + 0.527668I
6.54621 + 1.43098I 9.71321 − 0.47730I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.250782 − 0.527668I
6.54621 − 1.43098I 9.71321 + 0.47730I
u = −0.116312 + 0.549646I
0.240300 + 0.413797I 2.99515 − 0.89523I
u = −0.116312 − 0.549646I
0.240300 − 0.413797I 2.99515 + 0.89523I
u = −1.45204
1.51065 0
u = 1.47356 + 0.06742I
−2.33707 − 6.71684I 0
u = 1.47356 − 0.06742I
−2.33707 + 6.71684I 0
u = −1.49480 + 0.05903I
−6.95748 + 3.05756I 0
u = −1.49480 − 0.05903I
−6.95748 − 3.05756I 0
u = 1.50087
−4.52108 0
u = −0.202355 + 0.437640I
0.938163 − 0.711468I 6.55301 + 2.55999I
u = −0.202355 − 0.437640I
0.938163 + 0.711468I 6.55301 − 2.55999I
u = 1.54113
−4.36757 0
u = 1.55617 + 0.10084I
−3.77147 − 0.32838I 0
u = 1.55617 − 0.10084I
−3.77147 + 0.32838I 0
u = −1.58656 + 0.13617I
−2.15018 + 7.19293I 0
u = −1.58656 − 0.13617I
−2.15018 − 7.19293I 0
u = −1.58930 + 0.10190I
−8.66644 + 2.71730I 0
u = −1.58930 − 0.10190I
−8.66644 − 2.71730I 0
u = 1.59484 + 0.12216I
−8.05254 − 5.85903I 0
u = 1.59484 − 0.12216I
−8.05254 + 5.85903I 0
u = 1.60793 + 0.14425I
−7.8739 − 13.7323I 0
u = 1.60793 − 0.14425I
−7.8739 + 13.7323I 0
u = −1.60930 + 0.14013I
−12.4821 + 9.5303I 0
u = −1.60930 − 0.14013I
−12.4821 − 9.5303I 0
u = 1.61037 + 0.13371I
−9.41174 − 5.27661I 0
u = 1.61037 − 0.13371I
−9.41174 + 5.27661I 0
u = −1.62295 + 0.08557I
−10.77130 + 4.64558I 0
u = −1.62295 − 0.08557I
−10.77130 − 4.64558I 0
u = 1.62421 + 0.07686I
−14.2631 − 0.3971I 0
u = 1.62421 − 0.07686I
−14.2631 + 0.3971I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.62511 + 0.06931I
−9.97350 − 3.82516I 0
u = −1.62511 − 0.06931I
−9.97350 + 3.82516I 0
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
62
− 17u
61
+ ··· + 1847u − 113
c
2
, c
3
, c
7
c
8
u
62
+ u
61
+ ··· − u + 1
c
4
u
62
− u
61
+ ··· + 15u + 1
c
5
, c
6
, c
11
u
62
+ u
61
+ ··· − u + 1
c
9
u
62
− 5u
61
+ ··· + 640u + 304
c
10
, c
12
u
62
− 3u
61
+ ··· + 55u − 9
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
62
− 11y
61
+ ··· − 256449y + 12769
c
2
, c
3
, c
7
c
8
y
62
− 71y
61
+ ··· − y + 1
c
4
y
62
+ y
61
+ ··· + 127y + 1
c
5
, c
6
, c
11
y
62
− 51y
61
+ ··· − y + 1
c
9
y
62
+ 25y
61
+ ··· − 2665888y + 92416
c
10
, c
12
y
62
+ 41y
61
+ ··· − 2233y + 81
9
