12a
1166
(K12a
1166
)
A knot diagram
1
Linearized knot diagam
4 9 8 1 12 11 10 3 2 7 6 5
Solving Sequence
6,12
5 1 4 2 11 7 10 8 3 9
c
5
c
12
c
4
c
1
c
11
c
6
c
10
c
7
c
3
c
9
c
2
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
16
− u
15
+ ··· + 4u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 16 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
16
− u
15
+ 13u
14
− 12u
13
+ 67u
12
− 56u
11
+ 174u
10
− 128u
9
+
239u
8
− 148u
7
+ 166u
6
− 80u
5
+ 50u
4
− 16u
3
+ 4u
2
+ 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
3
=
u
12
+ 9u
10
+ 29u
8
+ 40u
6
+ 22u
4
+ 5u
2
+ 1
u
12
+ 8u
10
+ 22u
8
+ 24u
6
+ 7u
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
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
14
−4u
13
+ 48u
12
−44u
11
+ 224u
10
−184u
9
+ 512u
8
−364u
7
+
592u
6
− 344u
5
+ 320u
4
− 136u
3
+ 64u
2
− 16u + 2
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
16
− u
15
+ ··· + 4u
2
+ 1
c
2
, c
3
, c
8
c
9
u
16
+ u
15
+ ··· + 4u
2
+ 1
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
16
+ 25y
15
+ ··· + 8y + 1
c
2
, c
3
, c
8
c
9
y
16
+ 17y
15
+ ··· + 8y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.266756 + 0.861670I
−2.78433 − 3.76215I −1.09418 + 4.53358I
u = 0.266756 − 0.861670I
−2.78433 + 3.76215I −1.09418 − 4.53358I
u = −0.094119 + 0.885317I
3.49312 + 1.66857I 3.40247 − 4.85811I
u = −0.094119 − 0.885317I
3.49312 − 1.66857I 3.40247 + 4.85811I
u = 0.11360 + 1.44941I
5.02280 − 5.17293I 0.10018 + 3.19792I
u = 0.11360 − 1.44941I
5.02280 + 5.17293I 0.10018 − 3.19792I
u = −0.03738 + 1.46774I
11.53240 + 2.15406I 3.63368 − 3.21855I
u = −0.03738 − 1.46774I
11.53240 − 2.15406I 3.63368 + 3.21855I
u = 0.438466 + 0.268135I
−6.29237 − 1.42936I −6.44952 + 4.15175I
u = 0.438466 − 0.268135I
−6.29237 + 1.42936I −6.44952 − 4.15175I
u = −0.206108 + 0.255692I
−0.105962 + 0.719255I −3.55239 − 9.63825I
u = −0.206108 − 0.255692I
−0.105962 − 0.719255I −3.55239 + 9.63825I
u = 0.02776 + 1.85644I
17.5528 − 5.9083I 0.36622 + 2.67952I
u = 0.02776 − 1.85644I
17.5528 + 5.9083I 0.36622 − 2.67952I
u = −0.00897 + 1.86144I
−15.2590 + 2.3986I 3.59355 − 2.68294I
u = −0.00897 − 1.86144I
−15.2590 − 2.3986I 3.59355 + 2.68294I
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
16
− u
15
+ ··· + 4u
2
+ 1
c
2
, c
3
, c
8
c
9
u
16
+ u
15
+ ··· + 4u
2
+ 1
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
16
+ 25y
15
+ ··· + 8y + 1
c
2
, c
3
, c
8
c
9
y
16
+ 17y
15
+ ··· + 8y + 1
7
