12a
0226
(K12a
0226
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 11 2 1 4 12 5 10 8
Solving Sequence
2,6
3 7 4 1 8 9 12 10 11 5
c
2
c
6
c
3
c
1
c
7
c
8
c
12
c
9
c
11
c
5
c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
90
+ u
89
+ ··· + u − 1i
* 1 irreducible components of dim
C
= 0, with total 90 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
90
+ u
89
+ · · · + u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
1
=
u
2
+ 1
−u
4
a
8
=
−u
7
− 2u
5
− 2u
3
u
9
+ u
7
+ u
5
+ u
a
9
=
−u
17
− 4u
15
− 9u
13
− 12u
11
− 11u
9
− 8u
7
− 6u
5
− 4u
3
− u
−u
17
− 3u
15
− 5u
13
− 4u
11
− u
9
+ u
a
12
=
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
−u
14
− 2u
12
− 3u
10
− 2u
8
− 2u
6
− 2u
4
− u
2
a
10
=
u
43
+ 10u
41
+ ··· − 5u
3
− 2u
−u
45
− 9u
43
+ ··· + u
3
+ u
a
11
=
u
74
+ 17u
72
+ ··· + 3u
2
+ 1
−u
76
− 16u
74
+ ··· − 3u
4
− 2u
2
a
5
=
−u
30
− 7u
28
+ ··· − 4u
4
+ 1
−u
30
− 6u
28
+ ··· + 2u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
89
− 4u
88
+ ··· + 4u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
90
+ 41u
89
+ ··· − 3u + 1
c
2
, c
6
u
90
− u
89
+ ··· − u − 1
c
3
u
90
+ u
89
+ ··· + 11u − 1
c
4
, c
8
u
90
− u
89
+ ··· − 3u − 1
c
5
, c
10
u
90
+ u
89
+ ··· − 3u − 1
c
7
, c
12
u
90
− 5u
89
+ ··· + 145u − 21
c
9
, c
11
u
90
+ 31u
89
+ ··· + 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
90
+ 17y
89
+ ··· − 51y + 1
c
2
, c
6
y
90
+ 41y
89
+ ··· − 3y + 1
c
3
y
90
− 7y
89
+ ··· + 125y + 1
c
4
, c
8
y
90
− 51y
89
+ ··· − 83y + 1
c
5
, c
10
y
90
− 31y
89
+ ··· − 3y + 1
c
7
, c
12
y
90
+ 61y
89
+ ··· + 51089y + 441
c
9
, c
11
y
90
+ 57y
89
+ ··· − 3y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.501963 + 0.898997I
1.67262 − 2.04573I 0
u = −0.501963 − 0.898997I
1.67262 + 2.04573I 0
u = 0.016868 + 1.030800I
3.00085 − 2.77316I 0
u = 0.016868 − 1.030800I
3.00085 + 2.77316I 0
u = 0.249218 + 1.008390I
−2.02407 − 1.06219I 0
u = 0.249218 − 1.008390I
−2.02407 + 1.06219I 0
u = −0.355572 + 0.888939I
−0.53261 − 1.53431I 0
u = −0.355572 − 0.888939I
−0.53261 + 1.53431I 0
u = 0.525356 + 0.925869I
0.94370 + 7.33842I 0
u = 0.525356 − 0.925869I
0.94370 − 7.33842I 0
u = 0.177394 + 1.050490I
−1.87659 − 1.33249I 0
u = 0.177394 − 1.050490I
−1.87659 + 1.33249I 0
u = 0.723590 + 0.554540I
3.94277 + 8.63048I −4.05227 − 7.29473I
u = 0.723590 − 0.554540I
3.94277 − 8.63048I −4.05227 + 7.29473I
u = 0.407249 + 1.012720I
−3.09800 + 3.08334I 0
u = 0.407249 − 1.012720I
−3.09800 − 3.08334I 0
u = −0.723374 + 0.544890I
5.04502 − 3.02424I −2.05045 + 2.44739I
u = −0.723374 − 0.544890I
5.04502 + 3.02424I −2.05045 − 2.44739I
u = −0.206935 + 1.078590I
−3.26676 − 3.36781I 0
u = −0.206935 − 1.078590I
−3.26676 + 3.36781I 0
u = 0.141824 + 1.094660I
−0.62220 − 3.55946I 0
u = 0.141824 − 1.094660I
−0.62220 + 3.55946I 0
u = −0.754490 + 0.481579I
8.22286 − 1.43634I 0. + 2.56189I
u = −0.754490 − 0.481579I
8.22286 + 1.43634I 0. − 2.56189I
u = 0.758461 + 0.471953I
8.16996 − 4.24799I 0. + 3.40241I
u = 0.758461 − 0.471953I
8.16996 + 4.24799I 0. − 3.40241I
u = −0.170343 + 1.093900I
−6.56383 + 2.91091I 0
u = −0.170343 − 1.093900I
−6.56383 − 2.91091I 0
u = −0.145257 + 1.104810I
−1.82142 + 9.11969I 0
u = −0.145257 − 1.104810I
−1.82142 − 9.11969I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.692194 + 0.551325I
−0.96504 + 2.69141I −9.30626 − 3.76557I
u = 0.692194 − 0.551325I
−0.96504 − 2.69141I −9.30626 + 3.76557I
u = −0.779428 + 0.408233I
3.15401 + 11.35790I −5.13106 − 7.30784I
u = −0.779428 − 0.408233I
3.15401 − 11.35790I −5.13106 + 7.30784I
u = 0.775037 + 0.413272I
4.33585 − 5.73221I −3.09381 + 2.62769I
u = 0.775037 − 0.413272I
4.33585 + 5.73221I −3.09381 − 2.62769I
u = −0.699433 + 0.507173I
3.25860 − 0.93323I −1.98235 + 2.97328I
u = −0.699433 − 0.507173I
3.25860 + 0.93323I −1.98235 − 2.97328I
u = −0.762752 + 0.398359I
−1.77122 + 5.17263I −10.25794 − 3.78971I
u = −0.762752 − 0.398359I
−1.77122 − 5.17263I −10.25794 + 3.78971I
u = 0.744383 + 0.417449I
2.78033 − 3.35446I −3.31785 + 3.49388I
u = 0.744383 − 0.417449I
2.78033 + 3.35446I −3.31785 − 3.49388I
u = 0.405058 + 1.093730I
−3.77807 + 2.56808I 0
u = 0.405058 − 1.093730I
−3.77807 − 2.56808I 0
u = 0.582288 + 1.013010I
−2.33340 + 2.22713I 0
u = 0.582288 − 1.013010I
−2.33340 − 2.22713I 0
u = −0.727699 + 0.389178I
1.22174 − 1.10018I −7.10486 + 1.96284I
u = −0.727699 − 0.389178I
1.22174 + 1.10018I −7.10486 − 1.96284I
u = −0.400532 + 1.107050I
−5.12142 + 2.61021I 0
u = −0.400532 − 1.107050I
−5.12142 − 2.61021I 0
u = 0.608187 + 1.017900I
2.56703 − 3.54065I 0
u = 0.608187 − 1.017900I
2.56703 + 3.54065I 0
u = 0.441817 + 1.101300I
−3.52532 + 4.80773I 0
u = 0.441817 − 1.101300I
−3.52532 − 4.80773I 0
u = −0.422685 + 1.110300I
−9.04985 − 3.77247I 0
u = −0.422685 − 1.110300I
−9.04985 + 3.77247I 0
u = −0.605703 + 1.024670I
3.62058 − 2.05673I 0
u = −0.605703 − 1.024670I
3.62058 + 2.05673I 0
u = −0.442733 + 1.111360I
−4.83695 − 10.14260I 0
u = −0.442733 − 1.111360I
−4.83695 + 10.14260I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.584864 + 1.044800I
1.66537 − 4.01436I 0
u = −0.584864 − 1.044800I
1.66537 + 4.01436I 0
u = 0.560377 + 1.066900I
0.01118 + 7.69723I 0
u = 0.560377 − 1.066900I
0.01118 − 7.69723I 0
u = −0.473389 + 0.634112I
2.39074 − 2.06952I −2.67251 + 3.85924I
u = −0.473389 − 0.634112I
2.39074 + 2.06952I −2.67251 − 3.85924I
u = 0.556806 + 0.552055I
1.92931 − 2.99812I −4.64252 + 2.70074I
u = 0.556806 − 0.552055I
1.92931 + 2.99812I −4.64252 − 2.70074I
u = −0.607693 + 1.068190I
6.48101 − 3.73161I 0
u = −0.607693 − 1.068190I
6.48101 + 3.73161I 0
u = 0.607083 + 1.073890I
6.38293 + 9.42351I 0
u = 0.607083 − 1.073890I
6.38293 − 9.42351I 0
u = 0.625319 + 0.432375I
1.84509 − 2.98280I −5.82371 + 4.10556I
u = 0.625319 − 0.432375I
1.84509 + 2.98280I −5.82371 − 4.10556I
u = −0.576053 + 1.098500I
−0.85267 − 3.87735I 0
u = −0.576053 − 1.098500I
−0.85267 + 3.87735I 0
u = 0.587200 + 1.093990I
0.78468 + 8.41873I 0
u = 0.587200 − 1.093990I
0.78468 − 8.41873I 0
u = −0.588705 + 1.105070I
−3.85739 − 10.28380I 0
u = −0.588705 − 1.105070I
−3.85739 + 10.28380I 0
u = 0.597219 + 1.103510I
2.29023 + 10.90840I 0
u = 0.597219 − 1.103510I
2.29023 − 10.90840I 0
u = −0.597318 + 1.106640I
1.0834 − 16.5446I 0
u = −0.597318 − 1.106640I
1.0834 + 16.5446I 0
u = −0.625268 + 0.058000I
−1.95110 + 6.19847I −9.59402 − 5.63729I
u = −0.625268 − 0.058000I
−1.95110 − 6.19847I −9.59402 + 5.63729I
u = −0.621508
−6.02816 −14.3370
u = 0.592899 + 0.061563I
−0.725428 − 0.939411I −7.71421 + 0.78565I
u = 0.592899 − 0.061563I
−0.725428 + 0.939411I −7.71421 − 0.78565I
u = 0.374226
−0.816002 −12.1280
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
90
+ 41u
89
+ ··· − 3u + 1
c
2
, c
6
u
90
− u
89
+ ··· − u − 1
c
3
u
90
+ u
89
+ ··· + 11u − 1
c
4
, c
8
u
90
− u
89
+ ··· − 3u − 1
c
5
, c
10
u
90
+ u
89
+ ··· − 3u − 1
c
7
, c
12
u
90
− 5u
89
+ ··· + 145u − 21
c
9
, c
11
u
90
+ 31u
89
+ ··· + 3u + 1
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
90
+ 17y
89
+ ··· − 51y + 1
c
2
, c
6
y
90
+ 41y
89
+ ··· − 3y + 1
c
3
y
90
− 7y
89
+ ··· + 125y + 1
c
4
, c
8
y
90
− 51y
89
+ ··· − 83y + 1
c
5
, c
10
y
90
− 31y
89
+ ··· − 3y + 1
c
7
, c
12
y
90
+ 61y
89
+ ··· + 51089y + 441
c
9
, c
11
y
90
+ 57y
89
+ ··· − 3y + 1
9
