12a
1125
(K12a
1125
)
A knot diagram
1
Linearized knot diagam
4 8 7 9 11 12 3 2 1 5 6 10
Solving Sequence
5,10
11 6 12 7 1 9 4 2 3 8
c
10
c
5
c
11
c
6
c
12
c
9
c
4
c
1
c
3
c
8
c
2
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
50
+ u
49
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 50 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
50
+ u
49
+ · · · − u − 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
6
=
−u
−u
3
+ u
a
12
=
−u
2
+ 1
−u
4
+ 2u
2
a
7
=
u
3
− 2u
u
5
− 3u
3
+ u
a
1
=
u
4
− 3u
2
+ 1
−u
4
+ 2u
2
a
9
=
u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
4
=
u
17
− 10u
15
+ 39u
13
− 74u
11
+ 71u
9
− 38u
7
+ 18u
5
− 4u
3
+ u
−u
17
+ 9u
15
− 31u
13
+ 50u
11
− 37u
9
+ 12u
7
− 4u
5
+ u
a
2
=
u
30
− 17u
28
+ ··· − 2u
2
+ 1
−u
30
+ 16u
28
+ ··· − 6u
4
+ 3u
2
a
3
=
u
25
− 14u
23
+ ··· − 10u
3
+ u
u
27
− 15u
25
+ ··· + 3u
3
+ u
a
8
=
u
47
− 26u
45
+ ··· + 4u
3
− 2u
u
49
− 27u
47
+ ··· + 2u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
47
+ 104u
45
+ ··· − 4u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
50
− 13u
49
+ ··· − 53u + 3
c
2
, c
3
, c
7
c
8
u
50
− u
49
+ ··· + u − 1
c
4
u
50
− u
49
+ ··· + 35u − 29
c
5
, c
6
, c
10
c
11
u
50
+ u
49
+ ··· − u − 1
c
9
, c
12
u
50
− 9u
49
+ ··· + 279u − 41
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
50
− 3y
49
+ ··· − 187y + 9
c
2
, c
3
, c
7
c
8
y
50
+ 57y
49
+ ··· + y + 1
c
4
y
50
− 11y
49
+ ··· − 11375y + 841
c
5
, c
6
, c
10
c
11
y
50
− 55y
49
+ ··· + y + 1
c
9
, c
12
y
50
+ 29y
49
+ ··· + 16869y + 1681
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.598747 + 0.574890I
−6.17596 − 9.61051I −8.07514 + 7.89257I
u = 0.598747 − 0.574890I
−6.17596 + 9.61051I −8.07514 − 7.89257I
u = −0.579767 + 0.568232I
1.46262 + 7.21330I −5.14859 − 9.60886I
u = −0.579767 − 0.568232I
1.46262 − 7.21330I −5.14859 + 9.60886I
u = −0.799600 + 0.134077I
−10.62720 + 4.36353I −13.8919 − 4.2573I
u = −0.799600 − 0.134077I
−10.62720 − 4.36353I −13.8919 + 4.2573I
u = 0.552380 + 0.559106I
2.72755 − 3.55040I −1.47416 + 3.94014I
u = 0.552380 − 0.559106I
2.72755 + 3.55040I −1.47416 − 3.94014I
u = −0.486892 + 0.584883I
−1.98087 + 1.99888I −4.50156 − 3.58150I
u = −0.486892 − 0.584883I
−1.98087 − 1.99888I −4.50156 + 3.58150I
u = 0.619098 + 0.438297I
−8.73729 − 0.86802I −11.01246 + 3.92491I
u = 0.619098 − 0.438297I
−8.73729 + 0.86802I −11.01246 − 3.92491I
u = 0.726133 + 0.110853I
−2.87515 − 2.61799I −12.7473 + 6.4736I
u = 0.726133 − 0.110853I
−2.87515 + 2.61799I −12.7473 − 6.4736I
u = 0.418082 + 0.569716I
3.12275 − 0.32958I 0.04870 + 3.38032I
u = 0.418082 − 0.569716I
3.12275 + 0.32958I 0.04870 − 3.38032I
u = 0.359261 + 0.608239I
−5.47474 + 5.57708I −6.11056 − 1.82524I
u = 0.359261 − 0.608239I
−5.47474 − 5.57708I −6.11056 + 1.82524I
u = −0.528151 + 0.466800I
−0.81474 + 1.58943I −9.19847 − 3.59943I
u = −0.528151 − 0.466800I
−0.81474 − 1.58943I −9.19847 + 3.59943I
u = −0.381969 + 0.589199I
2.04130 − 3.25118I −3.15587 + 3.30820I
u = −0.381969 − 0.589199I
2.04130 + 3.25118I −3.15587 − 3.30820I
u = −0.607541
−1.09411 −8.24150
u = −1.43710 + 0.11460I
−11.13960 − 3.09747I 0
u = −1.43710 − 0.11460I
−11.13960 + 3.09747I 0
u = 1.46424 + 0.12360I
−3.87403 + 0.83702I 0
u = 1.46424 − 0.12360I
−3.87403 − 0.83702I 0
u = 0.167534 + 0.493668I
−7.46565 − 2.28896I −6.43563 + 2.79578I
u = 0.167534 − 0.493668I
−7.46565 + 2.28896I −6.43563 − 2.79578I
u = −1.48768 + 0.13710I
−3.08950 + 2.74865I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48768 − 0.13710I
−3.08950 − 2.74865I 0
u = 1.50999 + 0.16213I
−8.54473 − 4.64532I 0
u = 1.50999 − 0.16213I
−8.54473 + 4.64532I 0
u = 1.54653 + 0.13709I
−7.79253 − 3.77307I 0
u = 1.54653 − 0.13709I
−7.79253 + 3.77307I 0
u = −1.54628 + 0.16369I
−4.26325 + 6.15786I 0
u = −1.54628 − 0.16369I
−4.26325 − 6.15786I 0
u = 1.55577 + 0.16994I
−5.65936 − 9.90051I 0
u = 1.55577 − 0.16994I
−5.65936 + 9.90051I 0
u = 1.56928
−8.54940 0
u = −1.56295 + 0.17361I
−13.3924 + 12.3497I 0
u = −1.56295 − 0.17361I
−13.3924 − 12.3497I 0
u = −1.56817 + 0.12859I
−16.0981 + 2.9477I 0
u = −1.56817 − 0.12859I
−16.0981 − 2.9477I 0
u = −1.58508 + 0.02052I
−10.70660 + 3.03825I 0
u = −1.58508 − 0.02052I
−10.70660 − 3.03825I 0
u = 1.60009 + 0.02595I
−18.7534 − 4.8844I 0
u = 1.60009 − 0.02595I
−18.7534 + 4.8844I 0
u = −0.135075 + 0.358512I
−0.176711 + 1.051470I −3.23682 − 6.19668I
u = −0.135075 − 0.358512I
−0.176711 − 1.051470I −3.23682 + 6.19668I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
50
− 13u
49
+ ··· − 53u + 3
c
2
, c
3
, c
7
c
8
u
50
− u
49
+ ··· + u − 1
c
4
u
50
− u
49
+ ··· + 35u − 29
c
5
, c
6
, c
10
c
11
u
50
+ u
49
+ ··· − u − 1
c
9
, c
12
u
50
− 9u
49
+ ··· + 279u − 41
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
50
− 3y
49
+ ··· − 187y + 9
c
2
, c
3
, c
7
c
8
y
50
+ 57y
49
+ ··· + y + 1
c
4
y
50
− 11y
49
+ ··· − 11375y + 841
c
5
, c
6
, c
10
c
11
y
50
− 55y
49
+ ··· + y + 1
c
9
, c
12
y
50
+ 29y
49
+ ··· + 16869y + 1681
8
