12a
1024
(K12a
1024
)
A knot diagram
1
Linearized knot diagam
4 7 8 9 11 12 3 2 1 6 5 10
Solving Sequence
2,7
3 8 4 9 5 1 10 12 6 11
c
2
c
7
c
3
c
8
c
4
c
1
c
9
c
12
c
6
c
11
c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
74
+ u
73
+ ··· − u + 1i
* 1 irreducible components of dim
C
= 0, with total 74 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
74
+ u
73
+ · · · − u + 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
−u
2
a
8
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
9
=
−u
3
+ 2u
−u
3
+ u
a
5
=
−u
10
+ 5u
8
− 8u
6
+ 3u
4
+ u
2
+ 1
−u
10
+ 4u
8
− 5u
6
+ 2u
4
− u
2
a
1
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
10
=
u
17
− 8u
15
+ 25u
13
− 36u
11
+ 19u
9
+ 4u
7
− 2u
5
− 4u
3
+ u
−u
19
+ 9u
17
− 32u
15
+ 55u
13
− 43u
11
+ 9u
9
+ 4u
5
− u
3
+ u
a
12
=
u
28
− 13u
26
+ ··· + u
2
+ 1
−u
30
+ 14u
28
+ ··· − 4u
4
− u
2
a
6
=
u
57
− 26u
55
+ ··· + 2u
3
+ u
−u
59
+ 27u
57
+ ··· − u
3
+ u
a
11
=
−u
50
+ 23u
48
+ ··· + u
2
+ 1
−u
50
+ 22u
48
+ ··· − 4u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
72
+ 132u
70
+ ··· − 8u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
74
− 15u
73
+ ··· − 21743u + 1519
c
2
, c
3
, c
7
u
74
+ u
73
+ ··· − u + 1
c
4
u
74
− u
73
+ ··· − 55u + 25
c
5
, c
10
, c
11
u
74
− u
73
+ ··· − u + 1
c
6
u
74
+ u
73
+ ··· − 931u + 457
c
8
u
74
− 3u
73
+ ··· + 15u − 1
c
9
, c
12
u
74
− 11u
73
+ ··· − 267u + 11
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
74
+ 29y
73
+ ··· + 17219705y + 2307361
c
2
, c
3
, c
7
y
74
− 67y
73
+ ··· + y + 1
c
4
y
74
+ 5y
73
+ ··· − 5975y + 625
c
5
, c
10
, c
11
y
74
+ 69y
73
+ ··· + y + 1
c
6
y
74
+ 25y
73
+ ··· + 6053133y + 208849
c
8
y
74
− 7y
73
+ ··· − 195y + 1
c
9
, c
12
y
74
+ 61y
73
+ ··· + 4281y + 121
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.03301
−1.07564 0
u = 1.044940 + 0.102604I
2.61986 + 2.87585I 0
u = 1.044940 − 0.102604I
2.61986 − 2.87585I 0
u = −1.156210 + 0.191012I
2.43321 − 4.72367I 0
u = −1.156210 − 0.191012I
2.43321 + 4.72367I 0
u = 1.158590 + 0.218669I
8.21260 + 7.93871I 0
u = 1.158590 − 0.218669I
8.21260 − 7.93871I 0
u = 1.196130 + 0.144822I
2.98003 + 1.08515I 0
u = 1.196130 − 0.144822I
2.98003 − 1.08515I 0
u = 0.320215 + 0.704487I
8.01003 + 11.14000I 0.39689 − 8.47644I
u = 0.320215 − 0.704487I
8.01003 − 11.14000I 0.39689 + 8.47644I
u = −0.315680 + 0.695529I
2.04162 − 7.74964I −3.30901 + 8.85384I
u = −0.315680 − 0.695529I
2.04162 + 7.74964I −3.30901 − 8.85384I
u = −0.338213 + 0.679862I
8.91437 − 0.94078I 1.86731 + 2.75945I
u = −0.338213 − 0.679862I
8.91437 + 0.94078I 1.86731 − 2.75945I
u = 0.320814 + 0.680420I
2.53500 + 3.64664I −1.83229 − 2.76221I
u = 0.320814 − 0.680420I
2.53500 − 3.64664I −1.83229 + 2.76221I
u = 0.600609 + 0.432783I
9.12086 − 7.18945I 2.91452 + 2.88104I
u = 0.600609 − 0.432783I
9.12086 + 7.18945I 2.91452 − 2.88104I
u = −1.244690 + 0.203790I
8.80185 + 1.44373I 0
u = −1.244690 − 0.203790I
8.80185 − 1.44373I 0
u = 0.255238 + 0.678124I
1.10543 + 6.03198I −4.27580 − 8.07217I
u = 0.255238 − 0.678124I
1.10543 − 6.03198I −4.27580 + 8.07217I
u = −0.545619 + 0.465386I
9.78040 − 2.94455I 3.94521 + 3.50317I
u = −0.545619 − 0.465386I
9.78040 + 2.94455I 3.94521 − 3.50317I
u = −0.580884 + 0.417872I
3.13814 + 3.88721I −0.60973 − 3.22333I
u = −0.580884 − 0.417872I
3.13814 − 3.88721I −0.60973 + 3.22333I
u = −0.229715 + 0.657701I
−3.02571 − 3.01416I −10.84049 + 5.92197I
u = −0.229715 − 0.657701I
−3.02571 + 3.01416I −10.84049 − 5.92197I
u = 0.544204 + 0.430911I
3.50761 + 0.14409I 0.63672 − 3.50408I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.544204 − 0.430911I
3.50761 − 0.14409I 0.63672 + 3.50408I
u = 0.180185 + 0.648822I
0.206108 + 0.208045I −6.68575 − 1.16976I
u = 0.180185 − 0.648822I
0.206108 − 0.208045I −6.68575 + 1.16976I
u = 0.043373 + 0.667655I
4.86508 − 4.63110I −3.42865 + 2.90350I
u = 0.043373 − 0.667655I
4.86508 + 4.63110I −3.42865 − 2.90350I
u = 1.344970 + 0.183030I
3.43197 + 1.12512I 0
u = 1.344970 − 0.183030I
3.43197 − 1.12512I 0
u = −0.354775 + 0.535609I
5.20691 − 1.66335I 3.09565 + 4.27561I
u = −0.354775 − 0.535609I
5.20691 + 1.66335I 3.09565 − 4.27561I
u = −0.055516 + 0.627489I
−0.83877 + 1.62690I −7.90840 − 3.45819I
u = −0.055516 − 0.627489I
−0.83877 − 1.62690I −7.90840 + 3.45819I
u = 0.592806 + 0.205238I
2.64797 − 2.62283I −0.82675 + 2.90416I
u = 0.592806 − 0.205238I
2.64797 + 2.62283I −0.82675 − 2.90416I
u = −1.367910 + 0.115025I
8.34672 + 1.48194I 0
u = −1.367910 − 0.115025I
8.34672 − 1.48194I 0
u = −1.368940 + 0.243993I
5.12052 − 3.43600I 0
u = −1.368940 − 0.243993I
5.12052 + 3.43600I 0
u = −1.385570 + 0.216376I
4.94675 − 3.91535I 0
u = −1.385570 − 0.216376I
4.94675 + 3.91535I 0
u = 1.389990 + 0.255951I
2.13515 + 6.33953I 0
u = 1.389990 − 0.255951I
2.13515 − 6.33953I 0
u = −1.40031 + 0.26526I
6.38349 − 9.46596I 0
u = −1.40031 − 0.26526I
6.38349 + 9.46596I 0
u = 1.42079 + 0.21110I
10.85890 + 4.43876I 0
u = 1.42079 − 0.21110I
10.85890 − 4.43876I 0
u = 0.206283 + 0.524313I
−0.161322 + 1.134130I −2.63011 − 5.69236I
u = 0.206283 − 0.524313I
−0.161322 − 1.134130I −2.63011 + 5.69236I
u = −1.42841 + 0.26365I
8.13467 − 7.09316I 0
u = −1.42841 − 0.26365I
8.13467 + 7.09316I 0
u = −1.44510 + 0.14916I
9.77486 − 2.20808I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44510 − 0.14916I
9.77486 + 2.20808I 0
u = 1.44646 + 0.13855I
9.50233 − 1.95720I 0
u = 1.44646 − 0.13855I
9.50233 + 1.95720I 0
u = 1.42809 + 0.27008I
7.62286 + 11.27000I 0
u = 1.42809 − 0.27008I
7.62286 − 11.27000I 0
u = −1.43094 + 0.27329I
13.6165 − 14.7026I 0
u = −1.43094 − 0.27329I
13.6165 + 14.7026I 0
u = 1.43495 + 0.26103I
14.5965 + 4.3748I 0
u = 1.43495 − 0.26103I
14.5965 − 4.3748I 0
u = −1.45330 + 0.13463I
15.6001 + 5.2588I 0
u = −1.45330 − 0.13463I
15.6001 − 5.2588I 0
u = 1.45302 + 0.15468I
16.1228 + 5.1353I 0
u = 1.45302 − 0.15468I
16.1228 − 5.1353I 0
u = −0.526726
−1.25260 −7.49050
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
74
− 15u
73
+ ··· − 21743u + 1519
c
2
, c
3
, c
7
u
74
+ u
73
+ ··· − u + 1
c
4
u
74
− u
73
+ ··· − 55u + 25
c
5
, c
10
, c
11
u
74
− u
73
+ ··· − u + 1
c
6
u
74
+ u
73
+ ··· − 931u + 457
c
8
u
74
− 3u
73
+ ··· + 15u − 1
c
9
, c
12
u
74
− 11u
73
+ ··· − 267u + 11
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
74
+ 29y
73
+ ··· + 17219705y + 2307361
c
2
, c
3
, c
7
y
74
− 67y
73
+ ··· + y + 1
c
4
y
74
+ 5y
73
+ ··· − 5975y + 625
c
5
, c
10
, c
11
y
74
+ 69y
73
+ ··· + y + 1
c
6
y
74
+ 25y
73
+ ··· + 6053133y + 208849
c
8
y
74
− 7y
73
+ ··· − 195y + 1
c
9
, c
12
y
74
+ 61y
73
+ ··· + 4281y + 121
9
