12a
0802
(K12a
0802
)
A knot diagram
1
Linearized knot diagam
3 8 12 1 11 10 9 2 7 6 5 4
Solving Sequence
1,5
4 12 3 2 11 6 10 7 9 8
c
4
c
12
c
3
c
1
c
11
c
5
c
10
c
6
c
9
c
8
c
2
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
23
+ u
22
+ ··· + 4u − 1i
* 1 irreducible components of dim
C
= 0, with total 23 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
23
+ u
22
+ · · · + 4u − 1i
(i) Arc colorings
a
1
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
12
=
u
−u
3
+ u
a
3
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
11
=
−u
3
+ 2u
−u
3
+ u
a
6
=
u
6
− 3u
4
+ 2u
2
+ 1
u
6
− 2u
4
+ u
2
a
10
=
−u
9
+ 4u
7
− 5u
5
+ 3u
−u
9
+ 3u
7
− 3u
5
+ u
a
7
=
u
12
− 5u
10
+ 9u
8
− 4u
6
− 6u
4
+ 5u
2
+ 1
u
12
− 4u
10
+ 6u
8
− 2u
6
− 3u
4
+ 2u
2
a
9
=
−u
15
+ 6u
13
− 14u
11
+ 12u
9
+ 6u
7
− 16u
5
+ 4u
3
+ 4u
−u
15
+ 5u
13
− 10u
11
+ 7u
9
+ 4u
7
− 8u
5
+ 2u
3
+ u
a
8
=
u
18
− 7u
16
+ 20u
14
− 25u
12
+ u
10
+ 31u
8
− 24u
6
− 6u
4
+ 9u
2
+ 1
u
18
− 6u
16
+ 15u
14
− 16u
12
− u
10
+ 18u
8
− 12u
6
− 2u
4
+ 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
21
+ 32u
19
− 4u
18
− 108u
17
+ 28u
16
+ 172u
15
− 80u
14
− 56u
13
+ 96u
12
− 232u
11
+
16u
10
+ 312u
9
− 160u
8
− 8u
7
+ 108u
6
− 208u
5
+ 60u
4
+ 60u
3
− 64u
2
+ 56u − 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
9
, c
10
c
11
u
23
+ 3u
22
+ ··· − 4u − 1
c
2
, c
8
u
23
− u
22
+ ··· + 2u
2
+ 1
c
3
, c
4
, c
12
u
23
− u
22
+ ··· + 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
9
, c
10
c
11
y
23
+ 35y
22
+ ··· + 12y −1
c
2
, c
8
y
23
+ 3y
22
+ ··· − 4y −1
c
3
, c
4
, c
12
y
23
− 17y
22
+ ··· − 4y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.005035 + 0.961413I
−16.4609 − 3.5087I 0.05644 + 2.17240I
u = 0.005035 − 0.961413I
−16.4609 + 3.5087I 0.05644 − 2.17240I
u = 1.09712
−2.03689 −3.73850
u = 1.124750 + 0.248700I
−0.036937 − 1.040240I −3.53344 + 0.53233I
u = 1.124750 − 0.248700I
−0.036937 + 1.040240I −3.53344 − 0.53233I
u = 0.023924 + 0.839260I
10.61860 − 3.02352I 0.20094 + 2.84696I
u = 0.023924 − 0.839260I
10.61860 + 3.02352I 0.20094 − 2.84696I
u = −1.226160 + 0.078178I
−4.38972 + 1.90192I −14.5499 − 5.2542I
u = −1.226160 − 0.078178I
−4.38972 − 1.90192I −14.5499 + 5.2542I
u = −1.229170 + 0.244467I
−0.94527 + 5.21093I −7.03360 − 8.08654I
u = −1.229170 − 0.244467I
−0.94527 − 5.21093I −7.03360 + 8.08654I
u = 1.232150 + 0.405721I
6.90735 − 1.43601I −3.19412 + 0.64909I
u = 1.232150 − 0.405721I
6.90735 + 1.43601I −3.19412 − 0.64909I
u = −1.266670 + 0.390063I
6.62684 + 7.42151I −3.89329 − 6.10029I
u = −1.266670 − 0.390063I
6.62684 − 7.42151I −3.89329 + 6.10029I
u = 0.076206 + 0.610358I
2.98734 − 2.14446I 0.00654 + 4.85802I
u = 0.076206 − 0.610358I
2.98734 + 2.14446I 0.00654 − 4.85802I
u = 1.300390 + 0.478071I
18.9960 − 1.6154I −3.04292 + 0.64980I
u = 1.300390 − 0.478071I
18.9960 + 1.6154I −3.04292 − 0.64980I
u = −1.307350 + 0.473703I
18.9379 + 8.6191I −3.15110 − 4.96250I
u = −1.307350 − 0.473703I
18.9379 − 8.6191I −3.15110 + 4.96250I
u = 0.218328 + 0.243819I
−0.276943 − 0.794269I −6.99628 + 8.47319I
u = 0.218328 − 0.243819I
−0.276943 + 0.794269I −6.99628 − 8.47319I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
9
, c
10
c
11
u
23
+ 3u
22
+ ··· − 4u − 1
c
2
, c
8
u
23
− u
22
+ ··· + 2u
2
+ 1
c
3
, c
4
, c
12
u
23
− u
22
+ ··· + 4u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
9
, c
10
c
11
y
23
+ 35y
22
+ ··· + 12y −1
c
2
, c
8
y
23
+ 3y
22
+ ··· − 4y −1
c
3
, c
4
, c
12
y
23
− 17y
22
+ ··· − 4y −1
7
