12a
1149
(K12a
1149
)
A knot diagram
1
Linearized knot diagam
4 8 9 1 12 11 10 3 2 7 6 5
Solving Sequence
6,12
5 1 4 2 11 7 10 8 9 3
c
5
c
12
c
4
c
1
c
11
c
6
c
10
c
7
c
9
c
3
c
2
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
17
− u
16
+ ··· + u − 1i
* 1 irreducible components of dim
C
= 0, with total 17 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
17
− u
16
+ 14u
15
− 13u
14
+ 79u
13
− 67u
12
+ 230u
11
− 174u
10
+
367u
9
− 239u
8
+ 314u
7
− 166u
6
+ 130u
5
− 50u
4
+ 20u
3
− 4u
2
+ u − 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
5
=
1
−u
2
a
1
=
−u
u
3
+ u
a
4
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
−u
3
− 2u
u
5
+ 3u
3
+ u
a
11
=
u
u
a
7
=
u
2
+ 1
u
2
a
10
=
u
3
+ 2u
u
3
+ u
a
8
=
u
4
+ 3u
2
+ 1
u
4
+ 2u
2
a
9
=
−u
11
− 8u
9
− 22u
7
− 24u
5
− 7u
3
+ 2u
u
13
+ 9u
11
+ 29u
9
+ 40u
7
+ 22u
5
+ 5u
3
+ u
a
3
=
u
13
+ 10u
11
+ 37u
9
+ 62u
7
+ 46u
5
+ 12u
3
− u
u
13
+ 9u
11
+ 29u
9
+ 40u
7
+ 22u
5
+ 5u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
15
+ 4u
14
− 52u
13
+ 48u
12
− 268u
11
+ 224u
10
− 696u
9
+
512u
8
− 956u
7
+ 592u
6
− 664u
5
+ 320u
4
− 200u
3
+ 64u
2
− 16u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
7
, c
10
c
11
, c
12
u
17
− u
16
+ ··· + u − 1
c
2
, c
3
, c
8
u
17
− u
16
+ ··· + u − 1
c
9
u
17
+ 3u
16
+ ··· + u + 21
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
7
, c
10
c
11
, c
12
y
17
+ 27y
16
+ ··· − 7y −1
c
2
, c
3
, c
8
y
17
− 17y
16
+ ··· − 7y −1
c
9
y
17
− 13y
16
+ ··· + 337y −441
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.194186 + 1.026040I
9.51893 − 4.23374I 7.14792 + 4.22195I
u = 0.194186 − 1.026040I
9.51893 + 4.23374I 7.14792 − 4.22195I
u = −0.091284 + 0.918950I
3.67358 + 1.70231I 3.75454 − 4.66095I
u = −0.091284 − 0.918950I
3.67358 − 1.70231I 3.75454 + 4.66095I
u = 0.338270 + 0.473429I
4.74216 − 2.44497I 4.10899 + 5.90559I
u = 0.338270 − 0.473429I
4.74216 + 2.44497I 4.10899 − 5.90559I
u = −0.03492 + 1.49263I
11.95880 + 2.17105I 4.25105 − 3.15879I
u = −0.03492 − 1.49263I
11.95880 − 2.17105I 4.25105 + 3.15879I
u = 0.08539 + 1.53439I
18.3384 − 5.3421I 7.54765 + 3.11558I
u = 0.08539 − 1.53439I
18.3384 + 5.3421I 7.54765 − 3.11558I
u = 0.414876
3.31379 −1.37510
u = −0.212139 + 0.269969I
−0.099174 + 0.746479I −3.08956 − 9.26969I
u = −0.212139 − 0.269969I
−0.099174 − 0.746479I −3.08956 + 9.26969I
u = −0.00824 + 1.86916I
−14.6439 + 2.4029I 4.39001 − 2.67089I
u = −0.00824 − 1.86916I
−14.6439 − 2.4029I 4.39001 + 2.67089I
u = 0.02129 + 1.87890I
−8.00423 − 5.94574I 7.57693 + 2.66715I
u = 0.02129 − 1.87890I
−8.00423 + 5.94574I 7.57693 − 2.66715I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
7
, c
10
c
11
, c
12
u
17
− u
16
+ ··· + u − 1
c
2
, c
3
, c
8
u
17
− u
16
+ ··· + u − 1
c
9
u
17
+ 3u
16
+ ··· + u + 21
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
7
, c
10
c
11
, c
12
y
17
+ 27y
16
+ ··· − 7y −1
c
2
, c
3
, c
8
y
17
− 17y
16
+ ··· − 7y −1
c
9
y
17
− 13y
16
+ ··· + 337y −441
7
