12n
0106
(K12n
0106
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 9 4 11 12 5 1 8 9
Solving Sequence
2,5 3,9
6 10 1 11 4 7 12 8
c
2
c
5
c
9
c
1
c
10
c
4
c
6
c
12
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.95001 × 10
28
u
46
+ 1.02756 × 10
29
u
45
+ ··· + 4.89243 × 10
27
b − 4.24094 × 10
28
,
5.28780 × 10
28
u
46
+ 1.85724 × 10
29
u
45
+ ··· + 2.44621 × 10
27
a − 1.24073 × 10
29
, u
47
+ 4u
46
+ ··· − 11u − 1i
I
u
2
= hu
2
b + b
2
+ bu − 2u
2
+ b − 3u − 2, a, u
3
+ u
2
− 1i
I
u
3
= hb − 2, a − 1, u − 1i
* 3 irreducible components of dim
C
= 0, with total 54 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
=
h2.95×10
28
u
46
+1.03×10
29
u
45
+· · ·+4.89×10
27
b−4.24×10
28
, 5.29×10
28
u
46
+
1.86 × 10
29
u
45
+ · · · + 2.45 × 10
27
a − 1.24 × 10
29
, u
47
+ 4u
46
+ · · · − 11u − 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u
2
a
9
=
−21.6162u
46
− 75.9230u
45
+ ··· + 433.914u + 50.7202
−6.02975u
46
− 21.0031u
45
+ ··· + 76.8942u + 8.66836
a
6
=
29.5086u
46
+ 104.599u
45
+ ··· − 601.499u − 73.1793
11.4583u
46
+ 40.3975u
45
+ ··· − 214.814u − 25.2675
a
10
=
−21.6162u
46
− 75.9230u
45
+ ··· + 433.914u + 50.7202
−12.4237u
46
− 42.3264u
45
+ ··· + 171.240u + 19.2103
a
1
=
−u
2
+ 1
−u
4
a
11
=
−26.2116u
46
− 91.6779u
45
+ ··· + 523.253u + 61.1104
−10.1373u
46
− 34.3085u
45
+ ··· + 141.882u + 16.1328
a
4
=
u
u
a
7
=
33.2674u
46
+ 117.852u
45
+ ··· − 671.448u − 81.1792
15.2170u
46
+ 53.6510u
45
+ ··· − 284.762u − 33.2674
a
12
=
23.3159u
46
+ 82.6280u
45
+ ··· − 479.630u − 56.3099
5.89371u
46
+ 20.0339u
45
+ ··· − 139.693u − 15.9659
a
8
=
2.05202u
46
+ 7.02641u
45
+ ··· − 34.0094u − 5.57078
5.07530u
46
+ 18.0511u
45
+ ··· − 64.3990u − 8.02822
(ii) Obstruction class = −1
(iii) Cusp Shapes = −19.4717u
46
− 66.4148u
45
+ ··· + 400.531u + 54.1723
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
47
+ 26u
46
+ ··· + 33u + 1
c
2
, c
4
u
47
− 4u
46
+ ··· − 11u + 1
c
3
, c
6
u
47
− 3u
46
+ ··· − 6u + 2
c
5
, c
9
u
47
+ 2u
46
+ ··· − 32u − 64
c
7
, c
8
, c
11
c
12
u
47
− 5u
46
+ ··· − 8u − 1
c
10
u
47
+ 7u
46
+ ··· − 5444u + 89
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
47
− 6y
46
+ ··· + 193y −1
c
2
, c
4
y
47
− 26y
46
+ ··· + 33y −1
c
3
, c
6
y
47
+ 15y
46
+ ··· + 315y
2
− 4
c
5
, c
9
y
47
− 36y
46
+ ··· + 168960y −4096
c
7
, c
8
, c
11
c
12
y
47
− 53y
46
+ ··· + 138y −1
c
10
y
47
+ 31y
46
+ ··· + 25436870y −7921
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.989960 + 0.148170I
a = 0.086218 + 0.547482I
b = 1.057400 − 0.538353I
−1.149640 − 0.628552I −5.94054 − 2.36276I
u = 0.989960 − 0.148170I
a = 0.086218 − 0.547482I
b = 1.057400 + 0.538353I
−1.149640 + 0.628552I −5.94054 + 2.36276I
u = −0.931667 + 0.360435I
a = 0.650552 − 1.137680I
b = 0.506455 − 0.859521I
0.10041 + 3.44087I 0.17183 − 8.28941I
u = −0.931667 − 0.360435I
a = 0.650552 + 1.137680I
b = 0.506455 + 0.859521I
0.10041 − 3.44087I 0.17183 + 8.28941I
u = −0.223147 + 1.003930I
a = −0.312504 + 1.368880I
b = −0.143382 − 0.236139I
5.63196 − 8.09738I 3.35253 + 4.54237I
u = −0.223147 − 1.003930I
a = −0.312504 − 1.368880I
b = −0.143382 + 0.236139I
5.63196 + 8.09738I 3.35253 − 4.54237I
u = 0.951382
a = −0.361021
b = −4.05034
−0.451802 −56.4450
u = −0.108798 + 0.923471I
a = 0.29912 − 1.44151I
b = −0.019834 + 0.147643I
−1.70582 − 5.21126I 0.15580 + 5.73446I
u = −0.108798 − 0.923471I
a = 0.29912 + 1.44151I
b = −0.019834 − 0.147643I
−1.70582 + 5.21126I 0.15580 − 5.73446I
u = 0.375825 + 0.801282I
a = 0.38215 − 1.40610I
b = −0.312468 − 0.166120I
3.28905 + 1.41624I 1.285372 − 0.077907I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.375825 − 0.801282I
a = 0.38215 + 1.40610I
b = −0.312468 + 0.166120I
3.28905 − 1.41624I 1.285372 + 0.077907I
u = −0.754499 + 0.439436I
a = 0.787718 + 0.900721I
b = 1.67009 − 0.64753I
10.33830 + 1.89063I 3.79886 − 2.45073I
u = −0.754499 − 0.439436I
a = 0.787718 − 0.900721I
b = 1.67009 + 0.64753I
10.33830 − 1.89063I 3.79886 + 2.45073I
u = 0.848625
a = 0.348245
b = 5.16287
7.65141 −49.4120
u = −0.874869 + 0.786950I
a = −0.309968 − 0.224071I
b = −0.262520 − 0.143001I
3.72699 + 2.94871I −12.2330 − 7.8683I
u = −0.874869 − 0.786950I
a = −0.309968 + 0.224071I
b = −0.262520 + 0.143001I
3.72699 − 2.94871I −12.2330 + 7.8683I
u = 1.126180 + 0.347504I
a = −0.188549 − 0.855543I
b = −1.147560 − 0.094454I
5.11792 − 1.20868I 0
u = 1.126180 − 0.347504I
a = −0.188549 + 0.855543I
b = −1.147560 + 0.094454I
5.11792 + 1.20868I 0
u = 0.059234 + 0.812807I
a = −0.34521 + 1.50868I
b = 0.186918 − 0.028378I
−2.49343 − 1.08855I −2.03214 + 0.04750I
u = 0.059234 − 0.812807I
a = −0.34521 − 1.50868I
b = 0.186918 + 0.028378I
−2.49343 + 1.08855I −2.03214 − 0.04750I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.144920 + 0.321301I
a = −1.39264 − 0.30017I
b = −2.50504 + 0.05350I
−1.09956 + 1.43032I 0
u = −1.144920 − 0.321301I
a = −1.39264 + 0.30017I
b = −2.50504 − 0.05350I
−1.09956 − 1.43032I 0
u = −1.109420 + 0.477918I
a = −0.225844 + 1.135400I
b = −0.151788 + 0.912718I
6.07282 + 6.30143I 0
u = −1.109420 − 0.477918I
a = −0.225844 − 1.135400I
b = −0.151788 − 0.912718I
6.07282 − 6.30143I 0
u = −0.889179 + 0.911068I
a = 0.567632 + 0.472874I
b = 0.506073 + 0.310758I
10.50090 + 3.30217I 0
u = −0.889179 − 0.911068I
a = 0.567632 − 0.472874I
b = 0.506073 − 0.310758I
10.50090 − 3.30217I 0
u = 1.157290 + 0.591284I
a = 1.109010 − 0.155564I
b = 2.14720 − 0.71964I
0.92342 − 6.68779I 0
u = 1.157290 − 0.591284I
a = 1.109010 + 0.155564I
b = 2.14720 + 0.71964I
0.92342 + 6.68779I 0
u = −1.230280 + 0.438166I
a = 1.292840 + 0.114739I
b = 2.59516 − 0.07060I
−6.29518 + 5.50452I 0
u = −1.230280 − 0.438166I
a = 1.292840 − 0.114739I
b = 2.59516 + 0.07060I
−6.29518 − 5.50452I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.221460 + 0.493956I
a = −1.035260 + 0.239047I
b = −2.17910 + 0.67973I
−5.89684 − 3.67490I 0
u = 1.221460 − 0.493956I
a = −1.035260 − 0.239047I
b = −2.17910 − 0.67973I
−5.89684 + 3.67490I 0
u = 0.669427
a = −0.452367
b = 0.335316
−1.01372 −10.3930
u = −0.178892 + 0.636081I
a = 1.61229 + 0.11889I
b = 0.969029 − 0.433870I
8.67414 − 2.02923I 6.38070 + 1.31837I
u = −0.178892 − 0.636081I
a = 1.61229 − 0.11889I
b = 0.969029 + 0.433870I
8.67414 + 2.02923I 6.38070 − 1.31837I
u = 1.286390 + 0.397327I
a = 0.966983 − 0.333762I
b = 2.17649 − 0.61779I
−6.10647 + 0.63964I 0
u = 1.286390 − 0.397327I
a = 0.966983 + 0.333762I
b = 2.17649 + 0.61779I
−6.10647 − 0.63964I 0
u = −1.251910 + 0.523865I
a = −1.226570 − 0.021764I
b = −2.63642 + 0.05168I
−5.19394 + 10.42330I 0
u = −1.251910 − 0.523865I
a = −1.226570 + 0.021764I
b = −2.63642 − 0.05168I
−5.19394 − 10.42330I 0
u = −1.252930 + 0.595086I
a = 1.168960 − 0.050135I
b = 2.66504 − 0.01710I
2.45160 + 13.84790I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.252930 − 0.595086I
a = 1.168960 + 0.050135I
b = 2.66504 + 0.01710I
2.45160 − 13.84790I 0
u = 1.366130 + 0.294990I
a = −0.908758 + 0.454189I
b = −2.11656 + 0.55334I
0.27703 + 3.60334I 0
u = 1.366130 − 0.294990I
a = −0.908758 − 0.454189I
b = −2.11656 − 0.55334I
0.27703 − 3.60334I 0
u = −0.591311 + 0.089878I
a = −1.40817 + 1.26783I
b = −0.997142 + 0.442455I
1.303350 − 0.477077I 6.44413 + 0.83351I
u = −0.591311 − 0.089878I
a = −1.40817 − 1.26783I
b = −0.997142 − 0.442455I
1.303350 + 0.477077I 6.44413 − 0.83351I
u = −0.275356 + 0.071579I
a = −2.33744 + 1.67178I
b = −0.731969 + 0.318628I
1.33872 − 0.48836I 6.23098 + 1.53144I
u = −0.275356 − 0.071579I
a = −2.33744 − 1.67178I
b = −0.731969 − 0.318628I
1.33872 + 0.48836I 6.23098 − 1.53144I
9
II. I
u
2
= hu
2
b + b
2
+ bu − 2u
2
+ b − 3u − 2, a, u
3
+ u
2
− 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u
2
a
9
=
0
b
a
6
=
0
u
a
10
=
0
b
a
1
=
−u
2
+ 1
−u
2
− u + 1
a
11
=
−u
2
b + bu
−2u
2
b + 2b
a
4
=
u
u
a
7
=
u
2
− 1
u
2
+ u − 1
a
12
=
−u
2
+ 1
−b + 2
a
8
=
u
2
b − bu
2u
2
b + u
2
− 2b + u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
b − bu − u
2
− b − u + 10
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
9
u
6
c
6
(u
3
+ u
2
+ 2u + 1)
2
c
7
, c
8
, c
10
(u
2
− u − 1)
3
c
11
, c
12
(u
2
+ u − 1)
3
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
5
, c
9
y
6
c
7
, c
8
, c
10
c
11
, c
12
(y
2
− 3y + 1)
3
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0
b = −0.546315 + 0.909787I
11.90680 + 2.82812I 7.12010 − 2.78145I
u = −0.877439 + 0.744862I
a = 0
b = 0.208674 − 0.347508I
4.01109 + 2.82812I 12.01538 + 1.83947I
u = −0.877439 − 0.744862I
a = 0
b = −0.546315 − 0.909787I
11.90680 − 2.82812I 7.12010 + 2.78145I
u = −0.877439 − 0.744862I
a = 0
b = 0.208674 + 0.347508I
4.01109 − 2.82812I 12.01538 − 1.83947I
u = 0.754878
a = 0
b = 1.43675
−0.126494 2.87910
u = 0.754878
a = 0
b = −3.76147
7.76919 23.8500
13
III. I
u
3
= hb − 2, a − 1, u − 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
1
a
3
=
1
1
a
9
=
1
2
a
6
=
−1
−1
a
10
=
1
3
a
1
=
0
−1
a
11
=
1
2
a
4
=
1
1
a
7
=
−1
−1
a
12
=
1
1
a
8
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
9
c
11
, c
12
u − 1
c
3
, c
6
u
c
4
, c
5
, c
7
c
8
, c
10
u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
7
, c
8
c
9
, c
10
, c
11
c
12
y −1
c
3
, c
6
y
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 2.00000
0 0
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)(u
3
− u
2
+ 2u − 1)
2
(u
47
+ 26u
46
+ ··· + 33u + 1)
c
2
(u − 1)(u
3
+ u
2
− 1)
2
(u
47
− 4u
46
+ ··· − 11u + 1)
c
3
u(u
3
− u
2
+ 2u − 1)
2
(u
47
− 3u
46
+ ··· − 6u + 2)
c
4
(u + 1)(u
3
− u
2
+ 1)
2
(u
47
− 4u
46
+ ··· − 11u + 1)
c
5
u
6
(u + 1)(u
47
+ 2u
46
+ ··· − 32u − 64)
c
6
u(u
3
+ u
2
+ 2u + 1)
2
(u
47
− 3u
46
+ ··· − 6u + 2)
c
7
, c
8
(u + 1)(u
2
− u − 1)
3
(u
47
− 5u
46
+ ··· − 8u − 1)
c
9
u
6
(u − 1)(u
47
+ 2u
46
+ ··· − 32u − 64)
c
10
(u + 1)(u
2
− u − 1)
3
(u
47
+ 7u
46
+ ··· − 5444u + 89)
c
11
, c
12
(u − 1)(u
2
+ u − 1)
3
(u
47
− 5u
46
+ ··· − 8u − 1)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y −1)(y
3
+ 3y
2
+ 2y −1)
2
(y
47
− 6y
46
+ ··· + 193y −1)
c
2
, c
4
(y −1)(y
3
− y
2
+ 2y −1)
2
(y
47
− 26y
46
+ ··· + 33y −1)
c
3
, c
6
y(y
3
+ 3y
2
+ 2y −1)
2
(y
47
+ 15y
46
+ ··· + 315y
2
− 4)
c
5
, c
9
y
6
(y −1)(y
47
− 36y
46
+ ··· + 168960y −4096)
c
7
, c
8
, c
11
c
12
(y −1)(y
2
− 3y + 1)
3
(y
47
− 53y
46
+ ··· + 138y −1)
c
10
(y −1)(y
2
− 3y + 1)
3
(y
47
+ 31y
46
+ ··· + 2.54369 × 10
7
y −7921)
19
