12a
0728
(K12a
0728
)
A knot diagram
1
Linearized knot diagam
3 8 9 10 11 1 2 7 12 5 6 4
Solving Sequence
5,11
6 12 10 4 1 7 9 3 8 2
c
5
c
11
c
10
c
4
c
12
c
6
c
9
c
3
c
8
c
2
c
1
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
66
+ u
65
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 66 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
66
+ u
65
+ · · · + u + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
12
=
u
−u
3
+ u
a
10
=
−u
u
a
4
=
−u
2
+ 1
u
2
a
1
=
u
7
− 4u
5
+ 4u
3
−u
7
+ 3u
5
− 2u
3
+ u
a
7
=
u
16
− 9u
14
+ 31u
12
− 50u
10
+ 37u
8
− 12u
6
+ 4u
4
+ 1
−u
16
+ 8u
14
− 24u
12
+ 34u
10
− 26u
8
+ 14u
6
− 4u
4
a
9
=
u
5
− 2u
3
− u
−u
7
+ 3u
5
− 2u
3
+ u
a
3
=
−u
14
+ 7u
12
− 16u
10
+ 11u
8
+ 2u
6
+ 1
u
16
− 8u
14
+ 24u
12
− 34u
10
+ 26u
8
− 14u
6
+ 4u
4
a
8
=
−u
39
+ 22u
37
+ ··· + 8u
5
− 4u
3
u
39
− 21u
37
+ ··· − 2u
3
+ u
a
2
=
−u
37
+ 20u
35
+ ··· + 6u
3
− u
u
39
− 21u
37
+ ··· − 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
64
+ 148u
62
+ ··· + 8u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
66
+ 23u
65
+ ··· + 3u + 1
c
2
, c
7
u
66
+ u
65
+ ··· + u + 1
c
3
, c
6
u
66
− u
65
+ ··· − 31u + 13
c
4
, c
5
, c
10
c
11
u
66
+ u
65
+ ··· + u + 1
c
9
u
66
+ 17u
65
+ ··· − 47u − 1
c
12
u
66
− 5u
65
+ ··· − 87u + 99
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
66
+ 41y
65
+ ··· + 25y + 1
c
2
, c
7
y
66
− 23y
65
+ ··· − 3y + 1
c
3
, c
6
y
66
− 43y
65
+ ··· − 779y + 169
c
4
, c
5
, c
10
c
11
y
66
− 75y
65
+ ··· − 3y + 1
c
9
y
66
− 3y
65
+ ··· − 1027y + 1
c
12
y
66
+ 13y
65
+ ··· + 97965y + 9801
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.679043 + 0.513026I
−0.55757 + 11.85450I −1.19937 − 10.55626I
u = 0.679043 − 0.513026I
−0.55757 − 11.85450I −1.19937 + 10.55626I
u = −0.677457 + 0.502396I
0.69647 − 6.29635I 0.87137 + 6.02383I
u = −0.677457 − 0.502396I
0.69647 + 6.29635I 0.87137 − 6.02383I
u = −0.827357 + 0.134311I
1.73099 + 5.80754I 2.42706 − 4.28002I
u = −0.827357 − 0.134311I
1.73099 − 5.80754I 2.42706 + 4.28002I
u = 0.651675 + 0.512229I
−5.26765 + 5.51347I −6.43351 − 6.58815I
u = 0.651675 − 0.512229I
−5.26765 − 5.51347I −6.43351 + 6.58815I
u = −0.723236 + 0.392345I
4.90890 − 5.70748I 4.77595 + 8.10333I
u = −0.723236 − 0.392345I
4.90890 + 5.70748I 4.77595 − 8.10333I
u = 0.729599 + 0.367618I
5.06598 + 0.17301I 5.53090 − 1.90980I
u = 0.729599 − 0.367618I
5.06598 − 0.17301I 5.53090 + 1.90980I
u = 0.787704 + 0.158558I
2.78482 − 0.42194I 4.71831 − 0.92383I
u = 0.787704 − 0.158558I
2.78482 + 0.42194I 4.71831 + 0.92383I
u = 0.613057 + 0.504763I
−1.89419 − 0.91996I −3.47927 − 1.04849I
u = 0.613057 − 0.504763I
−1.89419 + 0.91996I −3.47927 + 1.04849I
u = −0.633845 + 0.477974I
−0.41391 − 3.88997I −0.23971 + 6.90287I
u = −0.633845 − 0.477974I
−0.41391 + 3.88997I −0.23971 − 6.90287I
u = −0.792968
−2.47755 −2.65410
u = −0.568943 + 0.415813I
−0.39703 − 3.45284I −3.45398 + 8.62120I
u = −0.568943 − 0.415813I
−0.39703 + 3.45284I −3.45398 − 8.62120I
u = 0.613967 + 0.254014I
1.141260 + 0.707260I 5.14650 − 1.61154I
u = 0.613967 − 0.254014I
1.141260 − 0.707260I 5.14650 + 1.61154I
u = 0.305227 + 0.549680I
−2.79055 + 4.56037I −6.01762 − 5.67931I
u = 0.305227 − 0.549680I
−2.79055 − 4.56037I −6.01762 + 5.67931I
u = 0.257589 + 0.569515I
−6.41719 − 1.79856I −9.70751 + 0.42464I
u = 0.257589 − 0.569515I
−6.41719 + 1.79856I −9.70751 − 0.42464I
u = 0.219617 + 0.585188I
−1.89948 − 8.09919I −4.62425 + 5.17915I
u = 0.219617 − 0.585188I
−1.89948 + 8.09919I −4.62425 − 5.17915I
u = −0.214284 + 0.568263I
−0.65140 + 2.62175I −2.68943 − 0.54084I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.214284 − 0.568263I
−0.65140 − 2.62175I −2.68943 + 0.54084I
u = −0.283990 + 0.514586I
−1.43586 + 0.43361I −4.03138 + 0.14632I
u = −0.283990 − 0.514586I
−1.43586 − 0.43361I −4.03138 − 0.14632I
u = −1.41960
−1.56697 0
u = −1.42823 + 0.03822I
2.50333 − 6.46643I 0
u = −1.42823 − 0.03822I
2.50333 + 6.46643I 0
u = 1.44500 + 0.02800I
3.88317 + 1.19867I 0
u = 1.44500 − 0.02800I
3.88317 − 1.19867I 0
u = −0.022017 + 0.498619I
2.90632 + 2.69811I −0.00578 − 3.20875I
u = −0.022017 − 0.498619I
2.90632 − 2.69811I −0.00578 + 3.20875I
u = −0.289584 + 0.387063I
−1.153330 + 0.503988I −7.19528 − 0.72282I
u = −0.289584 − 0.387063I
−1.153330 − 0.503988I −7.19528 + 0.72282I
u = 1.56691 + 0.04064I
5.24690 + 0.15185I 0
u = 1.56691 − 0.04064I
5.24690 − 0.15185I 0
u = 1.56474 + 0.10431I
6.81950 + 5.27330I 0
u = 1.56474 − 0.10431I
6.81950 − 5.27330I 0
u = −1.57332 + 0.14112I
5.46608 − 1.41931I 0
u = −1.57332 − 0.14112I
5.46608 + 1.41931I 0
u = −1.58537 + 0.07956I
8.69743 − 1.98171I 0
u = −1.58537 − 0.07956I
8.69743 + 1.98171I 0
u = 1.58430 + 0.13594I
7.09486 + 6.13313I 0
u = 1.58430 − 0.13594I
7.09486 − 6.13313I 0
u = −1.58678 + 0.14853I
2.28564 − 7.94476I 0
u = −1.58678 − 0.14853I
2.28564 + 7.94476I 0
u = 1.59661 + 0.14658I
8.39199 + 8.70234I 0
u = 1.59661 − 0.14658I
8.39199 − 8.70234I 0
u = −1.59684 + 0.15037I
7.1378 − 14.3160I 0
u = −1.59684 − 0.15037I
7.1378 + 14.3160I 0
u = −1.60867 + 0.05463I
10.92240 − 0.43188I 0
u = −1.60867 − 0.05463I
10.92240 + 0.43188I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.61183 + 0.04577I
9.98754 − 5.09815I 0
u = 1.61183 − 0.04577I
9.98754 + 5.09815I 0
u = 1.60946 + 0.11086I
12.8693 + 7.5849I 0
u = 1.60946 − 0.11086I
12.8693 − 7.5849I 0
u = −1.61013 + 0.10411I
13.05570 − 1.93744I 0
u = −1.61013 − 0.10411I
13.05570 + 1.93744I 0
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
u
66
+ 23u
65
+ ··· + 3u + 1
c
2
, c
7
u
66
+ u
65
+ ··· + u + 1
c
3
, c
6
u
66
− u
65
+ ··· − 31u + 13
c
4
, c
5
, c
10
c
11
u
66
+ u
65
+ ··· + u + 1
c
9
u
66
+ 17u
65
+ ··· − 47u − 1
c
12
u
66
− 5u
65
+ ··· − 87u + 99
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
66
+ 41y
65
+ ··· + 25y + 1
c
2
, c
7
y
66
− 23y
65
+ ··· − 3y + 1
c
3
, c
6
y
66
− 43y
65
+ ··· − 779y + 169
c
4
, c
5
, c
10
c
11
y
66
− 75y
65
+ ··· − 3y + 1
c
9
y
66
− 3y
65
+ ··· − 1027y + 1
c
12
y
66
+ 13y
65
+ ··· + 97965y + 9801
9
