12n
0093
(K12n
0093
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 9 4 11 6 12 7 9 10
Solving Sequence
4,6 7,11
8 9 12 3 5 2 1 10
c
6
c
7
c
8
c
11
c
3
c
5
c
2
c
1
c
10
c
4
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h8.15753 × 10
41
u
22
− 3.72668 × 10
42
u
21
+ ··· + 7.71580 × 10
42
b + 1.17939 × 10
43
,
1.10388 × 10
43
u
22
− 4.86462 × 10
43
u
21
+ ··· + 1.54316 × 10
43
a + 2.96744 × 10
44
, u
23
− 4u
22
+ ··· − 36u + 8i
I
u
2
= h−u
8
+ 2u
7
− 3u
6
+ 3u
5
− 4u
4
+ 4u
3
− 3u
2
+ b + 2u − 1,
− 3u
8
+ 4u
7
− 8u
6
+ 7u
5
− 13u
4
+ 9u
3
− 11u
2
+ a + 6u − 6, u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
I
u
3
= h−2u
2
a − au − u
2
+ b − u, −2u
2
a + a
2
− au − 11u
2
− 2a − 5u − 19, u
3
+ u
2
+ 2u + 1i
I
v
1
= ha, 5v
2
+ 7b − 49v + 11, v
3
− 10v
2
+ 5v −1i
* 4 irreducible components of dim
C
= 0, with total 41 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
=
h8.16×10
41
u
22
−3.73×10
42
u
21
+· · ·+7.72×10
42
b+1.18×10
43
, 1.10×10
43
u
22
−
4.86 × 10
43
u
21
+ · · · + 1.54 × 10
43
a + 2.97 × 10
44
, u
23
− 4u
22
+ · · · − 36u + 8i
(i) Arc colorings
a
4
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
11
=
−0.715334u
22
+ 3.15238u
21
+ ··· + 69.0282u − 19.2296
−0.105725u
22
+ 0.482993u
21
+ ··· + 14.9531u − 1.52853
a
8
=
−0.186391u
22
+ 0.803680u
21
+ ··· + 9.92260u − 5.79288
−0.0258071u
22
+ 0.120060u
21
+ ··· + 3.37054u − 0.131649
a
9
=
−0.212198u
22
+ 0.923740u
21
+ ··· + 13.2931u − 5.92453
−0.0258071u
22
+ 0.120060u
21
+ ··· + 3.37054u − 0.131649
a
12
=
−0.576767u
22
+ 2.56286u
21
+ ··· + 55.9572u − 14.4153
−0.115767u
22
+ 0.522790u
21
+ ··· + 12.7973u − 1.57836
a
3
=
u
u
3
+ u
a
5
=
0.0635667u
22
− 0.259763u
21
+ ··· − 11.3894u + 1.71111
0.00786141u
22
− 0.0482210u
21
+ ··· + 1.53688u − 0.150885
a
2
=
−0.0506560u
22
+ 0.189656u
21
+ ··· + 13.6327u − 1.90596
0.0232321u
22
− 0.108930u
21
+ ··· + 2.18167u − 0.0911079
a
1
=
−0.0557053u
22
+ 0.211542u
21
+ ··· + 12.9263u − 1.86199
0.0193035u
22
− 0.0931377u
21
+ ··· + 1.57646u − 0.0606498
a
10
=
−0.714037u
22
+ 3.15386u
21
+ ··· + 67.7812u − 18.4298
−0.108857u
22
+ 0.493167u
21
+ ··· + 15.1831u − 1.58195
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4.74869u
22
+ 21.0543u
21
+ ··· + 605.964u − 98.1244
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
+ 23u
22
+ ··· + 12783u + 1
c
2
, c
4
u
23
− 7u
22
+ ··· − 113u − 1
c
3
, c
6
u
23
− 4u
22
+ ··· − 36u + 8
c
5
, c
8
u
23
+ 3u
22
+ ··· − 32u − 64
c
7
, c
10
u
23
+ 5u
22
+ ··· + 4608u − 512
c
9
, c
11
, c
12
u
23
− 14u
22
+ ··· + 247u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
− 39y
22
+ ··· + 163240279y −1
c
2
, c
4
y
23
− 23y
22
+ ··· + 12783y −1
c
3
, c
6
y
23
− 12y
22
+ ··· + 7568y −64
c
5
, c
8
y
23
+ 37y
22
+ ··· + 234496y −4096
c
7
, c
10
y
23
− 111y
22
+ ··· + 71041024y −262144
c
9
, c
11
, c
12
y
23
− 48y
22
+ ··· + 59963y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.810706 + 0.505931I
a = −0.375875 − 0.573416I
b = −0.094068 − 0.572082I
−0.87687 + 1.52898I −6.60742 − 3.54271I
u = −0.810706 − 0.505931I
a = −0.375875 + 0.573416I
b = −0.094068 + 0.572082I
−0.87687 − 1.52898I −6.60742 + 3.54271I
u = −0.273102 + 1.253150I
a = 0.905694 + 0.280329I
b = −1.78345 − 1.11930I
2.20419 + 2.68521I 2.70136 + 6.44368I
u = −0.273102 − 1.253150I
a = 0.905694 − 0.280329I
b = −1.78345 + 1.11930I
2.20419 − 2.68521I 2.70136 − 6.44368I
u = −0.282905 + 0.561433I
a = 0.025171 + 0.255386I
b = 0.116102 − 1.176160I
1.45854 + 3.25209I −3.51442 − 11.82565I
u = −0.282905 − 0.561433I
a = 0.025171 − 0.255386I
b = 0.116102 + 1.176160I
1.45854 − 3.25209I −3.51442 + 11.82565I
u = 0.904186 + 1.051940I
a = −0.346587 − 0.098446I
b = −0.141661 + 0.415462I
−5.12106 − 6.15902I −10.50715 + 1.63362I
u = 0.904186 − 1.051940I
a = −0.346587 + 0.098446I
b = −0.141661 − 0.415462I
−5.12106 + 6.15902I −10.50715 − 1.63362I
u = 0.603575
a = 4.66294
b = 0.0529154
−9.92701 35.8110
u = −0.518673
a = 1.24139
b = 0.270054
−1.19404 −8.40790
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.271589 + 0.441556I
a = 0.17891 − 4.69126I
b = −0.423841 + 0.717638I
−2.85899 + 0.09109I −11.2448 − 8.7640I
u = −0.271589 − 0.441556I
a = 0.17891 + 4.69126I
b = −0.423841 − 0.717638I
−2.85899 − 0.09109I −11.2448 + 8.7640I
u = −0.439625
a = −12.6495
b = −2.20680
−2.87501 −99.4720
u = 0.0940545
a = −7.89489
b = 0.510696
−1.10354 −8.74790
u = 1.16222 + 1.51464I
a = −0.789835 + 0.935119I
b = −0.43899 − 2.10734I
15.7088 − 13.9110I −11.35191 + 5.40734I
u = 1.16222 − 1.51464I
a = −0.789835 − 0.935119I
b = −0.43899 + 2.10734I
15.7088 + 13.9110I −11.35191 − 5.40734I
u = −1.41200 + 1.76863I
a = −0.536030 − 0.772744I
b = −0.24550 + 2.28839I
19.7178 + 6.1351I 0
u = −1.41200 − 1.76863I
a = −0.536030 + 0.772744I
b = −0.24550 − 2.28839I
19.7178 − 6.1351I 0
u = 2.39957 + 0.70874I
a = 0.624715 − 0.384715I
b = 0.36478 + 1.74735I
−14.2988 − 3.5584I 0
u = 2.39957 − 0.70874I
a = 0.624715 + 0.384715I
b = 0.36478 − 1.74735I
−14.2988 + 3.5584I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −2.52063
a = 0.877307
b = 0.551360
18.9120 0
u = 1.97498 + 1.71262I
a = −0.304781 + 0.587751I
b = 0.05752 − 2.27275I
14.2364 + 2.5672I 0
u = 1.97498 − 1.71262I
a = −0.304781 − 0.587751I
b = 0.05752 + 2.27275I
14.2364 − 2.5672I 0
7
II. I
u
2
= h−u
8
+ 2u
7
+ · · · + b − 1, −3u
8
+ 4u
7
+ · · · + a − 6, u
9
− u
8
+ 2u
7
−
u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
(i) Arc colorings
a
4
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
11
=
3u
8
− 4u
7
+ 8u
6
− 7u
5
+ 13u
4
− 9u
3
+ 11u
2
− 6u + 6
u
8
− 2u
7
+ 3u
6
− 3u
5
+ 4u
4
− 4u
3
+ 3u
2
− 2u + 1
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
12
=
3u
8
− 4u
7
+ 8u
6
− 7u
5
+ 13u
4
− 9u
3
+ 10u
2
− 6u + 5
u
8
− 2u
7
+ 3u
6
− 3u
5
+ 4u
4
− 4u
3
+ 2u
2
− 2u + 1
a
3
=
u
u
3
+ u
a
5
=
u
4
+ u
2
+ 1
u
4
a
2
=
−u
6
− u
4
− 2u
2
− 1
−u
8
− 2u
6
− 2u
4
− 2u
2
a
1
=
−u
2
− 1
−u
2
a
10
=
3u
8
− 4u
7
+ 8u
6
− 7u
5
+ 13u
4
− 9u
3
+ 11u
2
− 6u + 6
u
8
− 2u
7
+ 3u
6
− 3u
5
+ 4u
4
− 4u
3
+ 3u
2
− 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 45u
8
−63u
7
+ 119u
6
−104u
5
+ 184u
4
−133u
3
+ 157u
2
−83u + 73
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
2
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
3
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
4
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
5
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
c
6
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
7
, c
10
u
9
c
8
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
9
(u − 1)
9
c
11
, c
12
(u + 1)
9
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
2
, c
4
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
3
, c
6
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
5
, c
8
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
7
, c
10
y
9
c
9
, c
11
, c
12
(y −1)
9
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140343 + 0.966856I
a = 0.920144 − 0.598375I
b = −1.004430 + 0.297869I
0.13850 + 2.09337I −6.65973 − 4.50528I
u = −0.140343 − 0.966856I
a = 0.920144 + 0.598375I
b = −1.004430 − 0.297869I
0.13850 − 2.09337I −6.65973 + 4.50528I
u = −0.628449 + 0.875112I
a = −0.590648 − 0.449402I
b = −0.275254 + 0.816341I
−2.26187 + 2.45442I −9.69685 − 4.13179I
u = −0.628449 − 0.875112I
a = −0.590648 + 0.449402I
b = −0.275254 − 0.816341I
−2.26187 − 2.45442I −9.69685 + 4.13179I
u = 0.796005 + 0.733148I
a = −0.719281 − 0.119276I
b = 0.070080 − 0.850995I
−6.01628 + 1.33617I −13.00050 − 1.13735I
u = 0.796005 − 0.733148I
a = −0.719281 + 0.119276I
b = 0.070080 + 0.850995I
−6.01628 − 1.33617I −13.00050 + 1.13735I
u = 0.728966 + 0.986295I
a = −0.365868 + 0.247975I
b = −0.195086 − 0.635552I
−5.24306 − 7.08493I −11.6081 + 10.4867I
u = 0.728966 − 0.986295I
a = −0.365868 − 0.247975I
b = −0.195086 + 0.635552I
−5.24306 + 7.08493I −11.6081 − 10.4867I
u = −0.512358
a = 14.5113
b = 3.80937
−2.84338 193.930
11
III. I
u
3
=
h−2u
2
a−au−u
2
+b−u, −2u
2
a+a
2
−au−11u
2
−2a−5u−19, u
3
+u
2
+2u+1i
(i) Arc colorings
a
4
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
11
=
a
2u
2
a + au + u
2
+ u
a
8
=
−u
2
a − au − 3u
2
− a − 2u − 4
0
a
9
=
−u
2
a − au − 3u
2
− a − 2u − 4
0
a
12
=
−2u
2
a − 2au − 4u
2
− a − 3u − 5
2u
2
a + au + u
2
+ u
a
3
=
u
−u
2
− u − 1
a
5
=
1
0
a
2
=
−u
2
− 1
−u
2
− u − 1
a
1
=
−1
−u
2
a
10
=
u
2
a + au + u
2
+ a + u
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12u
2
a − 21u
2
− 3a − 13u − 44
12
(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
8
u
6
c
6
(u
3
+ u
2
+ 2u + 1)
2
c
7
, c
9
(u
2
+ u − 1)
3
c
10
, c
11
, c
12
(u
2
− u − 1)
3
13
(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
8
y
6
c
7
, c
9
, c
10
c
11
, c
12
(y
2
− 3y + 1)
3
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = −1.284420 − 0.112842I
b = 2.68975 + 0.90979I
2.03717 + 2.82812I −27.3018 − 15.7639I
u = −0.215080 + 1.307140I
a = −0.255377 + 0.295424I
b = −1.027390 − 0.347508I
−5.85852 + 2.82812I −12.61597 − 1.90115I
u = −0.215080 − 1.307140I
a = −1.284420 + 0.112842I
b = 2.68975 − 0.90979I
2.03717 − 2.82812I −27.3018 + 15.7639I
u = −0.215080 − 1.307140I
a = −0.255377 − 0.295424I
b = −1.027390 + 0.347508I
−5.85852 − 2.82812I −12.61597 + 1.90115I
u = −0.569840
a = −3.52133
b = −0.525405
−2.10041 −19.1260
u = −0.569840
a = 5.60092
b = 0.200687
−9.99610 −82.0390
15
IV. I
v
1
= ha, 5v
2
+ 7b − 49v + 11, v
3
− 10v
2
+ 5v − 1i
(i) Arc colorings
a
4
=
v
0
a
6
=
1
0
a
7
=
1
0
a
11
=
0
−
5
7
v
2
+ 7v −
11
7
a
8
=
1
−
2
7
v
2
+ 3v −
17
7
a
9
=
−
2
7
v
2
+ 3v −
10
7
−
2
7
v
2
+ 3v −
17
7
a
12
=
−1
−
2
7
v
2
+ 3v −
17
7
a
3
=
v
0
a
5
=
5
7
v
2
− 7v +
25
7
v
2
− 10v + 5
a
2
=
−
5
7
v
2
+ 8v −
25
7
−v
2
+ 10v − 5
a
1
=
−
5
7
v
2
+ 7v −
25
7
−v
2
+ 10v − 5
a
10
=
−
5
7
v
2
+ 7v −
11
7
−
5
7
v
2
+ 7v −
11
7
(ii) Obstruction class = 1
(iii) Cusp Shapes =
30
7
v
2
− 33v +
3
7
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
6
u
3
c
4
(u + 1)
3
c
5
u
3
+ 3u
2
+ 2u − 1
c
7
u
3
− u
2
+ 2u − 1
c
8
u
3
− 3u
2
+ 2u + 1
c
9
u
3
+ u
2
− 1
c
10
u
3
+ u
2
+ 2u + 1
c
11
, c
12
u
3
− u
2
+ 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
3
c
3
, c
6
y
3
c
5
, c
8
y
3
− 5y
2
+ 10y − 1
c
7
, c
10
y
3
+ 3y
2
+ 2y − 1
c
9
, c
11
, c
12
y
3
− y
2
+ 2y − 1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.258045 + 0.197115I
a = 0
b = 0.215080 + 1.307140I
1.37919 − 2.82812I −7.96807 − 6.06881I
v = 0.258045 − 0.197115I
a = 0
b = 0.215080 − 1.307140I
1.37919 + 2.82812I −7.96807 + 6.06881I
v = 9.48391
a = 0
b = 0.569840
−2.75839 72.9360
19
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
3
(u
3
− u
2
+ 2u − 1)
2
· (u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
23
+ 23u
22
+ ··· + 12783u + 1)
c
2
(u − 1)
3
(u
3
+ u
2
− 1)
2
(u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1)
· (u
23
− 7u
22
+ ··· − 113u − 1)
c
3
u
3
(u
3
− u
2
+ 2u − 1)
2
(u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1)
· (u
23
− 4u
22
+ ··· − 36u + 8)
c
4
(u + 1)
3
(u
3
− u
2
+ 1)
2
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
23
− 7u
22
+ ··· − 113u − 1)
c
5
u
6
(u
3
+ 3u
2
+ 2u − 1)
· (u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
23
+ 3u
22
+ ··· − 32u − 64)
c
6
u
3
(u
3
+ u
2
+ 2u + 1)
2
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
23
− 4u
22
+ ··· − 36u + 8)
c
7
u
9
(u
2
+ u − 1)
3
(u
3
− u
2
+ 2u − 1)(u
23
+ 5u
22
+ ··· + 4608u − 512)
c
8
u
6
(u
3
− 3u
2
+ 2u + 1)
· (u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
23
+ 3u
22
+ ··· − 32u − 64)
c
9
((u − 1)
9
)(u
2
+ u − 1)
3
(u
3
+ u
2
− 1)(u
23
− 14u
22
+ ··· + 247u + 1)
c
10
u
9
(u
2
− u − 1)
3
(u
3
+ u
2
+ 2u + 1)(u
23
+ 5u
22
+ ··· + 4608u − 512)
c
11
, c
12
((u + 1)
9
)(u
2
− u − 1)
3
(u
3
− u
2
+ 1)(u
23
− 14u
22
+ ··· + 247u + 1)
20
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
3
(y
3
+ 3y
2
+ 2y − 1)
2
· (y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y − 1)
· (y
23
− 39y
22
+ ··· + 163240279y − 1)
c
2
, c
4
(y − 1)
3
(y
3
− y
2
+ 2y − 1)
2
· (y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y − 1)
· (y
23
− 23y
22
+ ··· + 12783y − 1)
c
3
, c
6
y
3
(y
3
+ 3y
2
+ 2y − 1)
2
· (y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y − 1)
· (y
23
− 12y
22
+ ··· + 7568y − 64)
c
5
, c
8
y
6
(y
3
− 5y
2
+ 10y − 1)
· (y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y − 1)
· (y
23
+ 37y
22
+ ··· + 234496y − 4096)
c
7
, c
10
y
9
(y
2
− 3y + 1)
3
(y
3
+ 3y
2
+ 2y − 1)
· (y
23
− 111y
22
+ ··· + 71041024y − 262144)
c
9
, c
11
, c
12
(y − 1)
9
(y
2
− 3y + 1)
3
(y
3
− y
2
+ 2y − 1)
· (y
23
− 48y
22
+ ··· + 59963y − 1)
21
