12a
0745
(K12a
0745
)
A knot diagram
1
Linearized knot diagam
3 8 9 12 11 10 1 2 7 6 5 4
Solving Sequence
6,11
5 12 4 1 10 7 8 9 3 2
c
5
c
11
c
4
c
12
c
10
c
6
c
7
c
9
c
3
c
2
c
1
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
29
− u
28
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 29 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
29
− u
28
+ · · · + u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
12
=
−u
u
3
+ u
a
4
=
u
2
+ 1
−u
4
− 2u
2
a
1
=
−u
3
− 2u
u
5
+ 3u
3
+ u
a
10
=
u
u
a
7
=
u
2
+ 1
u
2
a
8
=
−u
10
− 7u
8
− 16u
6
− 13u
4
− u
2
+ 1
u
12
+ 8u
10
+ 22u
8
+ 24u
6
+ 9u
4
+ 2u
2
a
9
=
u
3
+ 2u
u
3
+ u
a
3
=
−u
10
− 7u
8
− 16u
6
− 13u
4
− u
2
+ 1
−u
10
− 6u
8
− 11u
6
− 8u
4
− 3u
2
a
2
=
−u
25
− 18u
23
+ ··· + 4u
3
− 3u
−u
25
− 17u
23
+ ··· + 6u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
27
− 4u
26
+ 84u
25
− 80u
24
+ 772u
23
− 696u
22
+ 4080u
21
− 3456u
20
+ 13704u
19
−
10804u
18
+30524u
17
−22128u
16
+45668u
15
−29956u
14
+45508u
13
−26404u
12
+29320u
11
−
14528u
10
+ 11444u
9
− 4548u
8
+ 2216u
7
− 600u
6
− 40u
5
+ 40u
4
− 80u
3
+ 12u
2
− 8u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
29
+ 15u
28
+ ··· − u − 1
c
2
, c
8
u
29
− u
28
+ ··· − u + 1
c
3
, c
7
u
29
+ u
28
+ ··· + 17u + 13
c
4
, c
5
, c
6
c
9
, c
10
, c
11
c
12
u
29
− u
28
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
− y
28
+ ··· + 15y −1
c
2
, c
8
y
29
+ 15y
28
+ ··· − y −1
c
3
, c
7
y
29
− 17y
28
+ ··· − 413y −169
c
4
, c
5
, c
6
c
9
, c
10
, c
11
c
12
y
29
+ 43y
28
+ ··· − y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.086935 + 0.771881I
2.65370 + 1.94307I 0.30745 − 4.96256I
u = −0.086935 − 0.771881I
2.65370 − 1.94307I 0.30745 + 4.96256I
u = 0.343908 + 0.675511I
−1.94705 − 6.69256I −6.07203 + 8.22032I
u = 0.343908 − 0.675511I
−1.94705 + 6.69256I −6.07203 − 8.22032I
u = 0.117032 + 1.271630I
3.27147 − 0.27468I −5.60472 + 0.I
u = 0.117032 − 1.271630I
3.27147 + 0.27468I −5.60472 + 0.I
u = −0.275093 + 0.647551I
0.83720 + 2.24471I −2.33349 − 5.12953I
u = −0.275093 − 0.647551I
0.83720 − 2.24471I −2.33349 + 5.12953I
u = −0.118947 + 1.334990I
7.41974 + 3.62310I −0.42057 − 2.79694I
u = −0.118947 − 1.334990I
7.41974 − 3.62310I −0.42057 + 2.79694I
u = 0.153448 + 1.339520I
4.70534 − 8.45308I −3.72441 + 6.33593I
u = 0.153448 − 1.339520I
4.70534 + 8.45308I −3.72441 − 6.33593I
u = 0.343286 + 0.551515I
−2.65978 + 1.25239I −7.88493 + 1.60855I
u = 0.343286 − 0.551515I
−2.65978 − 1.25239I −7.88493 − 1.60855I
u = −0.027427 + 1.381600I
9.86986 + 2.32396I 0.90036 − 3.48123I
u = −0.027427 − 1.381600I
9.86986 − 2.32396I 0.90036 + 3.48123I
u = 0.476875 + 0.053551I
−4.16020 − 3.97971I −12.35931 + 4.50350I
u = 0.476875 − 0.053551I
−4.16020 + 3.97971I −12.35931 − 4.50350I
u = −0.400192
−1.12072 −10.0910
u = −0.254330 + 0.235384I
−0.470239 + 0.884635I −8.64771 − 7.43488I
u = −0.254330 − 0.235384I
−0.470239 − 0.884635I −8.64771 + 7.43488I
u = 0.02575 + 1.81070I
14.7006 − 0.9082I 0
u = 0.02575 − 1.81070I
14.7006 + 0.9082I 0
u = −0.02952 + 1.82505I
19.2009 + 4.3355I 0
u = −0.02952 − 1.82505I
19.2009 − 4.3355I 0
u = 0.03812 + 1.82544I
16.4863 − 9.3726I 0
u = 0.03812 − 1.82544I
16.4863 + 9.3726I 0
u = −0.00607 + 1.83542I
−17.5321 + 2.4840I 0
u = −0.00607 − 1.83542I
−17.5321 − 2.4840I 0
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
29
+ 15u
28
+ ··· − u − 1
c
2
, c
8
u
29
− u
28
+ ··· − u + 1
c
3
, c
7
u
29
+ u
28
+ ··· + 17u + 13
c
4
, c
5
, c
6
c
9
, c
10
, c
11
c
12
u
29
− u
28
+ ··· + u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
29
− y
28
+ ··· + 15y −1
c
2
, c
8
y
29
+ 15y
28
+ ··· − y −1
c
3
, c
7
y
29
− 17y
28
+ ··· − 413y −169
c
4
, c
5
, c
6
c
9
, c
10
, c
11
c
12
y
29
+ 43y
28
+ ··· − y −1
7
