12a
1273
(K12a
1273
)
A knot diagram
1
Linearized knot diagam
5 8 9 10 11 12 1 3 4 2 6 7
Solving Sequence
3,9
4 10 5 8 2 11 6 1 7 12
c
3
c
9
c
4
c
8
c
2
c
10
c
5
c
1
c
7
c
12
c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
30
− u
29
+ ··· − u + 1i
* 1 irreducible components of dim
C
= 0, with total 30 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
30
− u
29
+ · · · − u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
10
=
u
−u
3
+ u
a
5
=
−u
2
+ 1
u
4
− 2u
2
a
8
=
−u
u
a
2
=
−u
2
+ 1
u
2
a
11
=
−u
7
+ 4u
5
− 4u
3
+ 2u
u
7
− 3u
5
+ u
a
6
=
−u
18
+ 11u
16
− 48u
14
+ 107u
12
− 133u
10
+ 95u
8
− 34u
6
+ 2u
4
+ u
2
+ 1
u
18
− 10u
16
+ 37u
14
− 60u
12
+ 35u
10
+ 8u
8
− 16u
6
+ 4u
4
− u
2
a
1
=
−u
8
+ 5u
6
− 7u
4
+ 2u
2
+ 1
u
10
− 6u
8
+ 11u
6
− 6u
4
+ u
2
a
7
=
−u
19
+ 12u
17
− 58u
15
+ 144u
13
− 193u
11
+ 130u
9
− 26u
7
− 14u
5
+ 5u
3
u
21
− 13u
19
+ ··· + u
3
+ u
a
12
=
u
29
− 18u
27
+ ··· − 8u
3
+ u
−u
29
+ 17u
27
+ ··· + u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
27
− 72u
25
+ 560u
23
− 4u
22
− 2464u
21
+ 60u
20
+ 6748u
19
−
376u
18
− 11928u
17
+ 1276u
16
+ 13628u
15
− 2544u
14
− 9672u
13
+ 3024u
12
+ 3680u
11
−
2060u
10
− 256u
9
+ 696u
8
− 296u
7
− 76u
6
+ 52u
5
+ 16u
4
+ 28u
3
− 12u
2
− 12u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
+ 5u
29
+ ··· + 17u + 1
c
2
, c
3
, c
4
c
8
, c
9
u
30
− u
29
+ ··· − u + 1
c
5
, c
6
, c
7
c
11
, c
12
u
30
+ u
29
+ ··· + u + 1
c
10
u
30
− 5u
29
+ ··· − 17u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
30
+ y
29
+ ··· − 209y + 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
11
c
12
y
30
− 39y
29
+ ··· + 3y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.956303 + 0.304469I
5.78714I 0. − 7.32757I
u = 0.956303 − 0.304469I
− 5.78714I 0. + 7.32757I
u = −0.955223 + 0.231940I
3.39527 − 3.00004I 6.38473 + 5.89581I
u = −0.955223 − 0.231940I
3.39527 + 3.00004I 6.38473 − 5.89581I
u = −0.964765 + 0.349999I
−9.41687 − 7.29529I −1.29292 + 5.67601I
u = −0.964765 − 0.349999I
−9.41687 + 7.29529I −1.29292 − 5.67601I
u = 0.928951 + 0.109038I
2.11566 + 0.22358I 2.86129 + 1.31411I
u = 0.928951 − 0.109038I
2.11566 − 0.22358I 2.86129 − 1.31411I
u = −1.09639
−5.79658 1.57890
u = 0.591727 + 0.392754I
−11.51410 − 0.86219I −3.48471 − 2.06303I
u = 0.591727 − 0.392754I
−11.51410 + 0.86219I −3.48471 + 2.06303I
u = −0.555182 + 0.261272I
−2.11566 + 0.22358I −2.86129 + 1.31411I
u = −0.555182 − 0.261272I
−2.11566 − 0.22358I −2.86129 − 1.31411I
u = 0.155952 + 0.575624I
−12.85810 + 4.15601I −6.61449 − 3.95577I
u = 0.155952 − 0.575624I
−12.85810 − 4.15601I −6.61449 + 3.95577I
u = −0.150182 + 0.513339I
−3.39527 − 3.00004I −6.38473 + 5.89581I
u = −0.150182 − 0.513339I
−3.39527 + 3.00004I −6.38473 − 5.89581I
u = 0.151512 + 0.367668I
0.891636I 0. − 7.39939I
u = 0.151512 − 0.367668I
− 0.891636I 0. + 7.39939I
u = −1.61197
−4.27207 −1.99300
u = 1.65244
5.79658 −1.57890
u = −1.70383 + 0.03647I
11.51410 − 0.86219I 0
u = −1.70383 − 0.03647I
11.51410 + 0.86219I 0
u = −1.70626 + 0.07787I
9.41687 − 7.29529I 0. + 5.67601I
u = −1.70626 − 0.07787I
9.41687 + 7.29529I 0. − 5.67601I
u = 1.70771 + 0.05962I
12.85810 + 4.15601I 6.61449 − 3.95577I
u = 1.70771 − 0.05962I
12.85810 − 4.15601I 6.61449 + 3.95577I
u = 1.70693 + 0.09182I
9.05110I 0. − 4.22365I
u = 1.70693 − 0.09182I
− 9.05110I 0. + 4.22365I
u = 1.72865
4.27207 1.99300
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
30
+ 5u
29
+ ··· + 17u + 1
c
2
, c
3
, c
4
c
8
, c
9
u
30
− u
29
+ ··· − u + 1
c
5
, c
6
, c
7
c
11
, c
12
u
30
+ u
29
+ ··· + u + 1
c
10
u
30
− 5u
29
+ ··· − 17u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
30
+ y
29
+ ··· − 209y + 1
c
2
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
11
c
12
y
30
− 39y
29
+ ··· + 3y + 1
7
