12a
1134
(K12a
1134
)
A knot diagram
1
Linearized knot diagam
4 8 9 10 11 12 1 3 2 5 6 7
Solving Sequence
4,9
3 8 2 10 5 11 1 7 12 6
c
3
c
8
c
2
c
9
c
4
c
10
c
1
c
7
c
12
c
6
c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
26
+ u
25
+ ··· + u − 1i
* 1 irreducible components of dim
C
= 0, with total 26 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
26
+ u
25
+ · · · + u − 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
3
=
1
u
2
a
8
=
−u
−u
3
+ u
a
2
=
−u
2
+ 1
−u
4
+ 2u
2
a
10
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
5
=
u
12
− 5u
10
+ 9u
8
− 6u
6
+ u
2
+ 1
u
14
− 6u
12
+ 13u
10
− 10u
8
− 2u
6
+ 4u
4
+ u
2
a
11
=
−u
19
+ 8u
17
− 26u
15
+ 42u
13
− 31u
11
+ 2u
9
+ 8u
7
+ 2u
5
− 5u
3
−u
21
+ 9u
19
+ ··· + u
3
+ u
a
1
=
−u
4
+ u
2
+ 1
−u
4
+ 2u
2
a
7
=
−u
11
+ 4u
9
− 4u
7
− 2u
5
+ 3u
3
−u
11
+ 5u
9
− 8u
7
+ 3u
5
+ u
3
+ u
a
12
=
u
18
− 7u
16
+ 18u
14
− 17u
12
− 5u
10
+ 17u
8
− 4u
6
− 4u
4
+ u
2
+ 1
u
18
− 8u
16
+ 25u
14
− 36u
12
+ 19u
10
+ 4u
8
− 2u
6
− 4u
4
+ u
2
a
6
=
u
25
− 10u
23
+ ··· + 6u
3
+ u
u
25
− 11u
23
+ ··· + 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
23
−40u
21
+ 4u
20
+ 168u
19
−36u
18
−372u
17
+ 132u
16
+ 432u
15
−244u
14
−180u
13
+
220u
12
−112u
11
−60u
10
+104u
9
−24u
8
+44u
7
−12u
6
−60u
5
+32u
4
+4u
3
−12u
2
+8u−10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
− 7u
25
+ ··· + 9u − 1
c
2
, c
3
, c
8
u
26
− u
25
+ ··· − u − 1
c
4
, c
5
, c
6
c
7
, c
10
, c
11
c
12
u
26
+ u
25
+ ··· − u − 1
c
9
u
26
+ 3u
25
+ ··· − u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
− 3y
25
+ ··· − 95y + 1
c
2
, c
3
, c
8
y
26
− 23y
25
+ ··· + y + 1
c
4
, c
5
, c
6
c
7
, c
10
, c
11
c
12
y
26
− 39y
25
+ ··· + y + 1
c
9
y
26
+ 5y
25
+ ··· − 15y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.891799 + 0.372496I
19.3462 − 0.3402I −10.26447 − 1.14724I
u = 0.891799 − 0.372496I
19.3462 + 0.3402I −10.26447 + 1.14724I
u = −0.866485 + 0.257559I
−8.04758 + 0.11056I −10.05758 + 0.78077I
u = −0.866485 − 0.257559I
−8.04758 − 0.11056I −10.05758 − 0.78077I
u = 1.12854
−0.740334 −9.59910
u = 0.228765 + 0.778851I
17.2367 + 4.5531I −12.97139 − 3.36886I
u = 0.228765 − 0.778851I
17.2367 − 4.5531I −12.97139 + 3.36886I
u = −0.215891 + 0.734545I
−10.14730 − 3.92865I −13.03714 + 4.14659I
u = −0.215891 − 0.734545I
−10.14730 + 3.92865I −13.03714 − 4.14659I
u = 0.192441 + 0.646528I
−3.00631 + 2.75009I −12.34966 − 6.37378I
u = 0.192441 − 0.646528I
−3.00631 − 2.75009I −12.34966 + 6.37378I
u = −1.331930 + 0.143170I
3.61530 − 0.91095I −3.48404 − 2.64095I
u = −1.331930 − 0.143170I
3.61530 + 0.91095I −3.48404 + 2.64095I
u = 1.357100 + 0.206224I
4.55876 + 3.52628I 0.01063 − 5.04166I
u = 1.357100 − 0.206224I
4.55876 − 3.52628I 0.01063 + 5.04166I
u = 1.39126
−1.42561 −6.03630
u = −1.367970 + 0.256979I
1.93805 − 6.04513I −6.52131 + 7.17823I
u = −1.367970 − 0.256979I
1.93805 + 6.04513I −6.52131 − 7.17823I
u = 1.38292 + 0.29669I
−5.07741 + 7.66568I −8.32222 − 5.28086I
u = 1.38292 − 0.29669I
−5.07741 − 7.66568I −8.32222 + 5.28086I
u = −1.39494 + 0.31870I
−17.0884 − 8.5238I −8.63563 + 4.48518I
u = −1.39494 − 0.31870I
−17.0884 + 8.5238I −8.63563 − 4.48518I
u = −1.45112
−12.7431 −6.07560
u = −0.148897 + 0.482916I
−0.243470 − 0.910015I −5.42028 + 7.09494I
u = −0.148897 − 0.482916I
−0.243470 + 0.910015I −5.42028 − 7.09494I
u = 0.477495
−1.12957 −8.18280
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
26
− 7u
25
+ ··· + 9u − 1
c
2
, c
3
, c
8
u
26
− u
25
+ ··· − u − 1
c
4
, c
5
, c
6
c
7
, c
10
, c
11
c
12
u
26
+ u
25
+ ··· − u − 1
c
9
u
26
+ 3u
25
+ ··· − u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
26
− 3y
25
+ ··· − 95y + 1
c
2
, c
3
, c
8
y
26
− 23y
25
+ ··· + y + 1
c
4
, c
5
, c
6
c
7
, c
10
, c
11
c
12
y
26
− 39y
25
+ ··· + y + 1
c
9
y
26
+ 5y
25
+ ··· − 15y + 1
7
