12a
1274
(K12a
1274
)
A knot diagram
1
Linearized knot diagam
5 8 9 10 11 12 1 3 4 2 7 6
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
47
− u
46
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 47 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
47
− u
46
+ · · · + 2u − 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
46
− 29u
44
+ ··· + 4u
2
+ 1
−u
46
+ 28u
44
+ ··· − 8u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
44
+ 116u
42
+ ··· − 20u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
47
+ 7u
46
+ ··· + 64u + 23
c
2
, c
3
, c
4
c
8
, c
9
u
47
− u
46
+ ··· + 2u − 1
c
5
, c
7
u
47
+ u
46
+ ··· − 22u − 13
c
6
, c
11
, c
12
u
47
− u
46
+ ··· − 2u
2
− 1
c
10
u
47
− 5u
46
+ ··· + 56u − 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
47
+ 11y
46
+ ··· − 9704y −529
c
2
, c
3
, c
4
c
8
, c
9
y
47
− 61y
46
+ ··· − 4y −1
c
5
, c
7
y
47
− 29y
46
+ ··· − 1076y −169
c
6
, c
11
, c
12
y
47
+ 39y
46
+ ··· − 4y −1
c
10
y
47
− 5y
46
+ ··· + 6176y −256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.935316 + 0.305335I
2.62027 − 2.29094I 4.17636 + 2.98224I
u = −0.935316 − 0.305335I
2.62027 + 2.29094I 4.17636 − 2.98224I
u = 0.966803 + 0.319748I
−0.38211 + 6.33274I 1.15955 − 6.71320I
u = 0.966803 − 0.319748I
−0.38211 − 6.33274I 1.15955 + 6.71320I
u = −0.952629 + 0.220168I
3.38277 − 2.89354I 6.69037 + 6.29889I
u = −0.952629 − 0.220168I
3.38277 + 2.89354I 6.69037 − 6.29889I
u = −0.985625 + 0.326270I
4.24927 − 10.39780I 5.89159 + 8.40345I
u = −0.985625 − 0.326270I
4.24927 + 10.39780I 5.89159 − 8.40345I
u = 0.948541 + 0.084215I
2.09196 + 0.10474I 3.38715 + 0.99978I
u = 0.948541 − 0.084215I
2.09196 − 0.10474I 3.38715 − 0.99978I
u = 1.021670 + 0.243299I
9.32278 + 3.73916I 10.74415 − 4.44796I
u = 1.021670 − 0.243299I
9.32278 − 3.73916I 10.74415 + 4.44796I
u = −1.053170 + 0.103400I
6.61499 + 3.02641I 9.00744 − 2.18164I
u = −1.053170 − 0.103400I
6.61499 − 3.02641I 9.00744 + 2.18164I
u = 0.641912 + 0.301512I
0.98188 + 3.42521I 2.41709 − 5.44099I
u = 0.641912 − 0.301512I
0.98188 − 3.42521I 2.41709 + 5.44099I
u = −0.560169 + 0.321250I
−2.59632 + 0.42907I −1.68504 + 1.57161I
u = −0.560169 − 0.321250I
−2.59632 − 0.42907I −1.68504 − 1.57161I
u = 0.511129 + 0.368669I
1.68279 − 4.29871I 3.25946 + 0.95874I
u = 0.511129 − 0.368669I
1.68279 + 4.29871I 3.25946 − 0.95874I
u = 0.187143 + 0.547043I
0.63696 + 7.42810I 0.40676 − 7.42331I
u = 0.187143 − 0.547043I
0.63696 − 7.42810I 0.40676 + 7.42331I
u = −0.160732 + 0.536483I
−3.84748 − 3.42005I −4.82162 + 5.25079I
u = −0.160732 − 0.536483I
−3.84748 + 3.42005I −4.82162 − 5.25079I
u = 0.118474 + 0.525329I
−0.601586 − 0.534700I −2.02307 − 0.92399I
u = 0.118474 − 0.525329I
−0.601586 + 0.534700I −2.02307 + 0.92399I
u = −0.286692 + 0.438369I
5.28511 − 1.41982I 5.84943 + 4.60268I
u = −0.286692 − 0.438369I
5.28511 + 1.41982I 5.84943 − 4.60268I
u = 0.150071 + 0.356575I
0.004655 + 0.864522I 0.14963 − 7.77782I
u = 0.150071 − 0.356575I
0.004655 − 0.864522I 0.14963 + 7.77782I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.63569
4.98619 0
u = −1.63713 + 0.01674I
8.87485 − 4.16382I 0
u = −1.63713 − 0.01674I
8.87485 + 4.16382I 0
u = 1.70178 + 0.07607I
11.94230 + 3.77271I 0
u = 1.70178 − 0.07607I
11.94230 − 3.77271I 0
u = 1.70759 + 0.05556I
12.84280 + 3.98049I 0
u = 1.70759 − 0.05556I
12.84280 − 3.98049I 0
u = −1.70861 + 0.03317I
11.58770 − 0.66274I 0
u = −1.70861 − 0.03317I
11.58770 + 0.66274I 0
u = −1.70911 + 0.08266I
9.07855 − 7.92982I 0
u = −1.70911 − 0.08266I
9.07855 + 7.92982I 0
u = 1.71430 + 0.08536I
13.8014 + 12.0477I 0
u = 1.71430 − 0.08536I
13.8014 − 12.0477I 0
u = −1.72414 + 0.06236I
19.1056 − 4.9783I 0
u = −1.72414 − 0.06236I
19.1056 + 4.9783I 0
u = 1.72607 + 0.02949I
16.5348 − 2.4638I 0
u = 1.72607 − 0.02949I
16.5348 + 2.4638I 0
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
47
+ 7u
46
+ ··· + 64u + 23
c
2
, c
3
, c
4
c
8
, c
9
u
47
− u
46
+ ··· + 2u − 1
c
5
, c
7
u
47
+ u
46
+ ··· − 22u − 13
c
6
, c
11
, c
12
u
47
− u
46
+ ··· − 2u
2
− 1
c
10
u
47
− 5u
46
+ ··· + 56u − 16
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
47
+ 11y
46
+ ··· − 9704y −529
c
2
, c
3
, c
4
c
8
, c
9
y
47
− 61y
46
+ ··· − 4y −1
c
5
, c
7
y
47
− 29y
46
+ ··· − 1076y −169
c
6
, c
11
, c
12
y
47
+ 39y
46
+ ··· − 4y −1
c
10
y
47
− 5y
46
+ ··· + 6176y −256
8
