12a
1282
(K12a
1282
)
A knot diagram
1
Linearized knot diagam
5 9 10 8 1 12 11 4 3 2 7 6
Solving Sequence
6,12
7 1 5 2 11 8 4 9 10 3
c
6
c
12
c
5
c
1
c
11
c
7
c
4
c
8
c
10
c
3
c
2
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
31
+ u
30
+ ··· − 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 31 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
31
+ u
30
+ · · · − 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
7
=
1
u
2
a
1
=
−u
u
a
5
=
u
2
+ 1
−u
2
a
2
=
−u
3
− 2u
u
3
+ u
a
11
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
4
=
u
8
+ 5u
6
+ 7u
4
+ 4u
2
+ 1
u
10
+ 6u
8
+ 11u
6
+ 6u
4
− u
2
a
9
=
u
14
+ 9u
12
+ 30u
10
+ 47u
8
+ 38u
6
+ 16u
4
+ 4u
2
+ 1
u
16
+ 10u
14
+ 38u
12
+ 68u
10
+ 56u
8
+ 14u
6
− 2u
4
+ 2u
2
a
10
=
−u
9
− 6u
7
− 11u
5
− 6u
3
+ u
u
9
+ 5u
7
+ 7u
5
+ 4u
3
+ u
a
3
=
−u
28
− 19u
26
+ ··· + 5u
2
+ 1
u
28
+ 18u
26
+ ··· + 72u
6
+ 19u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
30
+ 4u
29
+ 88u
28
+ 84u
27
+ 856u
26
+ 772u
25
+ 4844u
24
+
4076u
23
+ 17652u
22
+ 13644u
21
+ 43300u
20
+ 30144u
19
+ 72568u
18
+ 44340u
17
+
82620u
16
+ 42724u
15
+ 62520u
14
+ 25864u
13
+ 30820u
12
+ 9340u
11
+ 10724u
10
+
2272u
9
+ 3660u
8
+ 664u
7
+ 1124u
6
+ 108u
5
+ 140u
4
− 44u
3
+ 20u
2
− 28u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
11
, c
12
u
31
+ u
30
+ ··· − 2u − 1
c
2
, c
3
, c
9
u
31
+ u
30
+ ··· + 2u − 1
c
4
, c
8
, c
10
u
31
− 3u
30
+ ··· − 27u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
11
, c
12
y
31
+ 43y
30
+ ··· − 8y −1
c
2
, c
3
, c
9
y
31
− 25y
30
+ ··· − 8y −1
c
4
, c
8
, c
10
y
31
+ 27y
30
+ ··· − 119y −64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.233995 + 1.062500I
2.70695 − 0.12674I 4.66869 − 0.47422I
u = −0.233995 − 1.062500I
2.70695 + 0.12674I 4.66869 + 0.47422I
u = −0.057629 + 1.115900I
4.56522 + 1.48077I 5.55942 − 4.67239I
u = −0.057629 − 1.115900I
4.56522 − 1.48077I 5.55942 + 4.67239I
u = 0.245809 + 1.107520I
−0.77465 − 4.19431I 1.26264 + 4.05555I
u = 0.245809 − 1.107520I
−0.77465 + 4.19431I 1.26264 − 4.05555I
u = −0.250403 + 1.139970I
3.55407 + 8.50807I 5.61234 − 6.50090I
u = −0.250403 − 1.139970I
3.55407 − 8.50807I 5.61234 + 6.50090I
u = 0.093308 + 1.206050I
9.88022 − 3.25617I 10.40235 + 3.78646I
u = 0.093308 − 1.206050I
9.88022 + 3.25617I 10.40235 − 3.78646I
u = −0.497952 + 0.387936I
−1.28060 + 5.95602I 1.10734 − 7.09363I
u = −0.497952 − 0.387936I
−1.28060 − 5.95602I 1.10734 + 7.09363I
u = 0.501664 + 0.346327I
−5.34724 − 1.65915I −3.47730 + 3.92327I
u = 0.501664 − 0.346327I
−5.34724 + 1.65915I −3.47730 − 3.92327I
u = 0.251561 + 0.534036I
4.26948 − 2.12613I 7.78261 + 6.10454I
u = 0.251561 − 0.534036I
4.26948 + 2.12613I 7.78261 − 6.10454I
u = −0.506752 + 0.300569I
−1.53910 − 2.63441I −0.000560 − 0.254726I
u = −0.506752 − 0.300569I
−1.53910 + 2.63441I −0.000560 + 0.254726I
u = 0.385420
2.64216 0.0271240
u = −0.193530 + 0.306617I
0.008601 + 0.713717I 0.31670 − 9.78617I
u = −0.193530 − 0.306617I
0.008601 − 0.713717I 0.31670 + 9.78617I
u = −0.05101 + 1.74665I
12.81940 + 0.99880I 0
u = −0.05101 − 1.74665I
12.81940 − 0.99880I 0
u = 0.05931 + 1.75698I
9.55603 − 5.46146I 0
u = 0.05931 − 1.75698I
9.55603 + 5.46146I 0
u = −0.01191 + 1.76227I
15.0429 + 1.7587I 0
u = −0.01191 − 1.76227I
15.0429 − 1.7587I 0
u = −0.06271 + 1.76571I
14.0570 + 9.8419I 0
u = −0.06271 − 1.76571I
14.0570 − 9.8419I 0
u = 0.02152 + 1.78217I
−18.6689 − 3.7508I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.02152 − 1.78217I
−18.6689 + 3.7508I 0
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
11
, c
12
u
31
+ u
30
+ ··· − 2u − 1
c
2
, c
3
, c
9
u
31
+ u
30
+ ··· + 2u − 1
c
4
, c
8
, c
10
u
31
− 3u
30
+ ··· − 27u + 8
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
11
, c
12
y
31
+ 43y
30
+ ··· − 8y −1
c
2
, c
3
, c
9
y
31
− 25y
30
+ ··· − 8y −1
c
4
, c
8
, c
10
y
31
+ 27y
30
+ ··· − 119y −64
8
