12a
0650
(K12a
0650
)
A knot diagram
1
Linearized knot diagam
3 7 10 11 9 2 1 6 12 5 4 8
Solving Sequence
3,7
2 1 8 6 9 5 12 10 4 11
c
2
c
1
c
7
c
6
c
8
c
5
c
12
c
9
c
3
c
11
c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
82
− u
81
+ ··· − u + 1i
* 1 irreducible components of dim
C
= 0, with total 82 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
82
− u
81
+ · · · − u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
8
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
6
=
u
−u
3
+ u
a
9
=
−u
9
+ 2u
7
− u
5
− 2u
3
+ u
u
11
− 3u
9
+ 4u
7
− u
5
− u
3
+ u
a
5
=
u
17
− 4u
15
+ 7u
13
− 4u
11
− 3u
9
+ 6u
7
− 2u
5
+ u
−u
19
+ 5u
17
− 12u
15
+ 15u
13
− 9u
11
− u
9
+ 4u
7
− 2u
5
− u
3
+ u
a
12
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
10
=
u
27
− 8u
25
+ ··· − 3u
3
+ 2u
u
27
− 7u
25
+ ··· − u
3
+ u
a
4
=
−u
54
+ 15u
52
+ ··· − 2u
2
+ 1
−u
54
+ 14u
52
+ ··· + 2u
4
− u
2
a
11
=
u
63
− 16u
61
+ ··· − 4u
3
+ 2u
−u
65
+ 17u
63
+ ··· − 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
80
− 84u
78
+ ··· + 8u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
82
+ 43u
81
+ ··· + 3u + 1
c
2
, c
6
u
82
− u
81
+ ··· − u + 1
c
3
u
82
+ u
81
+ ··· − 5u + 2
c
4
, c
10
, c
11
u
82
− u
81
+ ··· − u + 1
c
5
, c
8
u
82
− 7u
81
+ ··· − 383u + 37
c
7
, c
12
u
82
− 3u
81
+ ··· − 55u + 56
c
9
u
82
+ 19u
81
+ ··· + 5211u + 283
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
82
− 7y
81
+ ··· + 9y + 1
c
2
, c
6
y
82
− 43y
81
+ ··· − 3y + 1
c
3
y
82
− 3y
81
+ ··· − 25y + 4
c
4
, c
10
, c
11
y
82
+ 73y
81
+ ··· − 3y + 1
c
5
, c
8
y
82
+ 53y
81
+ ··· + 11449y + 1369
c
7
, c
12
y
82
+ 57y
81
+ ··· + 137423y + 3136
c
9
y
82
+ 13y
81
+ ··· + 2040325y + 80089
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.955352 + 0.293882I
−0.49000 − 3.37255I 0. + 7.86263I
u = 0.955352 − 0.293882I
−0.49000 + 3.37255I 0. − 7.86263I
u = 0.816926 + 0.582560I
−0.09685 − 9.75450I 0. + 8.56550I
u = 0.816926 − 0.582560I
−0.09685 + 9.75450I 0. − 8.56550I
u = −0.804317 + 0.580383I
5.07118 + 6.08583I 7.27321 − 7.72699I
u = −0.804317 − 0.580383I
5.07118 − 6.08583I 7.27321 + 7.72699I
u = 0.976357 + 0.106548I
−6.89382 + 1.35042I −8.09485 + 0.I
u = 0.976357 − 0.106548I
−6.89382 − 1.35042I −8.09485 + 0.I
u = 0.780556 + 0.572028I
3.12382 − 2.34167I 4.61313 + 2.84945I
u = 0.780556 − 0.572028I
3.12382 + 2.34167I 4.61313 − 2.84945I
u = −0.813516 + 0.498678I
−3.07012 + 1.93466I 0. − 4.43003I
u = −0.813516 − 0.498678I
−3.07012 − 1.93466I 0. + 4.43003I
u = 0.760520 + 0.575296I
3.18119 − 2.21323I 4.97236 + 4.23790I
u = 0.760520 − 0.575296I
3.18119 + 2.21323I 4.97236 − 4.23790I
u = −0.733948 + 0.585447I
5.27270 − 1.47770I 8.11976 + 0.84952I
u = −0.733948 − 0.585447I
5.27270 + 1.47770I 8.11976 − 0.84952I
u = −1.038490 + 0.247739I
−5.58353 + 6.55182I 0
u = −1.038490 − 0.247739I
−5.58353 − 6.55182I 0
u = 0.718789 + 0.591071I
0.18371 + 5.12454I 3.29871 − 1.93532I
u = 0.718789 − 0.591071I
0.18371 − 5.12454I 3.29871 + 1.93532I
u = −0.870197 + 0.149170I
−1.47910 + 0.55712I −4.57771 − 0.31676I
u = −0.870197 − 0.149170I
−1.47910 − 0.55712I −4.57771 + 0.31676I
u = −1.062130 + 0.425517I
−5.33957 + 6.56153I 0
u = −1.062130 − 0.425517I
−5.33957 − 6.56153I 0
u = 1.093670 + 0.357724I
−0.62091 − 3.37016I 0
u = 1.093670 − 0.357724I
−0.62091 + 3.37016I 0
u = 0.186761 + 0.793781I
−3.11263 + 10.80720I 0.45907 − 6.86198I
u = 0.186761 − 0.793781I
−3.11263 − 10.80720I 0.45907 + 6.86198I
u = −0.190528 + 0.784354I
2.19850 − 7.14289I 5.14145 + 6.39279I
u = −0.190528 − 0.784354I
2.19850 + 7.14289I 5.14145 − 6.39279I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.147130 + 0.343021I
−3.17720 + 0.08534I 0
u = −1.147130 − 0.343021I
−3.17720 − 0.08534I 0
u = 0.189777 + 0.763023I
0.52237 + 3.32831I 2.43416 − 1.63604I
u = 0.189777 − 0.763023I
0.52237 − 3.32831I 2.43416 + 1.63604I
u = −0.149056 + 0.768257I
−5.84541 − 2.27661I −2.42027 + 2.24579I
u = −0.149056 − 0.768257I
−5.84541 + 2.27661I −2.42027 − 2.24579I
u = −0.634881 + 0.451288I
−2.63372 + 2.03081I 2.46981 − 3.49424I
u = −0.634881 − 0.451288I
−2.63372 − 2.03081I 2.46981 + 3.49424I
u = −1.171210 + 0.355781I
−3.48236 + 0.26932I 0
u = −1.171210 − 0.355781I
−3.48236 − 0.26932I 0
u = 0.210213 + 0.746916I
0.80429 + 3.32068I 3.63756 − 3.48400I
u = 0.210213 − 0.746916I
0.80429 − 3.32068I 3.63756 + 3.48400I
u = −0.030138 + 0.769212I
−8.37203 − 4.39350I −4.42980 + 3.66957I
u = −0.030138 − 0.769212I
−8.37203 + 4.39350I −4.42980 − 3.66957I
u = 1.186530 + 0.345924I
−1.93546 + 3.48342I 0
u = 1.186530 − 0.345924I
−1.93546 − 3.48342I 0
u = −0.232794 + 0.720428I
3.19797 + 0.23783I 7.38580 − 1.36908I
u = −0.232794 − 0.720428I
3.19797 − 0.23783I 7.38580 + 1.36908I
u = −1.194950 + 0.346219I
−7.28468 − 7.09304I 0
u = −1.194950 − 0.346219I
−7.28468 + 7.09304I 0
u = 1.187990 + 0.376609I
−9.77179 − 1.54569I 0
u = 1.187990 − 0.376609I
−9.77179 + 1.54569I 0
u = 1.135180 + 0.516102I
−4.27730 − 0.86035I 0
u = 1.135180 − 0.516102I
−4.27730 + 0.86035I 0
u = 0.254021 + 0.705615I
−1.71544 − 3.78990I 2.46470 + 2.68690I
u = 0.254021 − 0.705615I
−1.71544 + 3.78990I 2.46470 − 2.68690I
u = −1.145610 + 0.517637I
0.54284 + 4.45067I 0
u = −1.145610 − 0.517637I
0.54284 − 4.45067I 0
u = 0.024127 + 0.738550I
−2.71130 + 1.67121I −0.69520 − 4.31990I
u = 0.024127 − 0.738550I
−2.71130 − 1.67121I −0.69520 + 4.31990I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.183260 + 0.440258I
−6.16175 + 2.53795I 0
u = −1.183260 − 0.440258I
−6.16175 − 2.53795I 0
u = 1.183560 + 0.457869I
−6.03690 − 6.01989I 0
u = 1.183560 − 0.457869I
−6.03690 + 6.01989I 0
u = 1.158060 + 0.520565I
−1.95947 − 8.07713I 0
u = 1.158060 − 0.520565I
−1.95947 + 8.07713I 0
u = 1.196400 + 0.436391I
−11.94130 + 0.11930I 0
u = 1.196400 − 0.436391I
−11.94130 − 0.11930I 0
u = 1.168870 + 0.519518I
−2.33921 − 8.11453I 0
u = 1.168870 − 0.519518I
−2.33921 + 8.11453I 0
u = −1.194470 + 0.462138I
−11.7595 + 8.8469I 0
u = −1.194470 − 0.462138I
−11.7595 − 8.8469I 0
u = −1.178340 + 0.508340I
−8.84661 + 7.00922I 0
u = −1.178340 − 0.508340I
−8.84661 − 7.00922I 0
u = −1.174810 + 0.524984I
−0.69320 + 12.00310I 0
u = −1.174810 − 0.524984I
−0.69320 − 12.00310I 0
u = 1.178820 + 0.526166I
−6.0335 − 15.6946I 0
u = 1.178820 − 0.526166I
−6.0335 + 15.6946I 0
u = −0.341083 + 0.508049I
−3.35078 − 2.71253I 2.28153 + 2.87054I
u = −0.341083 − 0.508049I
−3.35078 + 2.71253I 2.28153 − 2.87054I
u = 0.428376 + 0.354973I
1.061290 + 0.175167I 9.58671 − 0.79856I
u = 0.428376 − 0.354973I
1.061290 − 0.175167I 9.58671 + 0.79856I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
82
+ 43u
81
+ ··· + 3u + 1
c
2
, c
6
u
82
− u
81
+ ··· − u + 1
c
3
u
82
+ u
81
+ ··· − 5u + 2
c
4
, c
10
, c
11
u
82
− u
81
+ ··· − u + 1
c
5
, c
8
u
82
− 7u
81
+ ··· − 383u + 37
c
7
, c
12
u
82
− 3u
81
+ ··· − 55u + 56
c
9
u
82
+ 19u
81
+ ··· + 5211u + 283
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
82
− 7y
81
+ ··· + 9y + 1
c
2
, c
6
y
82
− 43y
81
+ ··· − 3y + 1
c
3
y
82
− 3y
81
+ ··· − 25y + 4
c
4
, c
10
, c
11
y
82
+ 73y
81
+ ··· − 3y + 1
c
5
, c
8
y
82
+ 53y
81
+ ··· + 11449y + 1369
c
7
, c
12
y
82
+ 57y
81
+ ··· + 137423y + 3136
c
9
y
82
+ 13y
81
+ ··· + 2040325y + 80089
9
