12n
0196
(K12n
0196
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 12 11 4 12 1 5 6 9
Solving Sequence
5,12 3,6
2 1 4 11 7 8 9 10
c
5
c
2
c
1
c
4
c
11
c
6
c
7
c
8
c
9
c
3
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h5.91245 × 10
25
u
28
+ 1.63252 × 10
26
u
27
+ ··· + 3.02573 × 10
27
b + 2.88635 × 10
27
,
− 5.15849 × 10
26
u
28
− 3.76417 × 10
26
u
27
+ ··· + 1.81544 × 10
28
a − 1.59875 × 10
28
,
u
29
+ 2u
28
+ ··· + 24u + 8i
I
u
2
= h−4a
2
u − 6a
2
+ 8au + 17b + 12a − 2u − 20, 4a
3
− 6a
2
u − 8a
2
+ 2au + u − 6, u
2
+ 2i
I
u
3
= hb + 1, 3a − 2u − 1, u
2
+ u + 1i
I
v
1
= ha, −v
2
+ b − 3v + 1, v
3
+ 2v
2
− 3v + 1i
* 4 irreducible components of dim
C
= 0, with total 40 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
= h5.91 × 10
25
u
28
+ 1.63 × 10
26
u
27
+ · · · + 3.03 × 10
27
b + 2.89 ×
10
27
, −5.16 × 10
26
u
28
− 3.76 × 10
26
u
27
+ · · · + 1.82 × 10
28
a − 1.60 ×
10
28
, u
29
+ 2u
28
+ · · · + 24u + 8i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
3
=
0.0284146u
28
+ 0.0207342u
27
+ ··· − 6.48402u + 0.880639
−0.0195406u
28
− 0.0539545u
27
+ ··· − 0.120108u − 0.953934
a
6
=
1
−u
2
a
2
=
0.00887400u
28
− 0.0332203u
27
+ ··· − 6.60412u − 0.0732946
−0.0195406u
28
− 0.0539545u
27
+ ··· − 0.120108u − 0.953934
a
1
=
−0.00109364u
28
+ 0.00268100u
27
+ ··· − 2.31580u − 1.18662
−0.0151700u
28
− 0.0423430u
27
+ ··· + 2.22414u + 0.186334
a
4
=
0.0301055u
28
+ 0.0216495u
27
+ ··· − 8.00531u + 0.779890
−0.0370743u
28
− 0.0881628u
27
+ ··· + 0.425213u − 0.704192
a
11
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
−0.0385391u
28
− 0.0826420u
27
+ ··· + 2.43382u − 0.756874
0.0271306u
28
+ 0.0472982u
27
+ ··· − 2.96732u − 0.287921
a
9
=
−0.0385391u
28
− 0.0826420u
27
+ ··· + 2.43382u − 0.756874
0.0222755u
28
+ 0.0429799u
27
+ ··· − 2.52548u − 0.243412
a
10
=
u
3
+ 2u
−u
3
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
5380338557971956323782944785
27231580801980091699413843348
u
28
−
382789047733408314358823614
756432800055002547205940093
u
27
+
··· −
24975710409590861685346874876
6807895200495022924853460837
u −
79653205793763175879382867786
6807895200495022924853460837
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
29
+ 24u
28
+ ··· − 533u + 81
c
2
, c
4
u
29
− 6u
28
+ ··· + 5u − 9
c
3
, c
7
u
29
+ 2u
28
+ ··· + 36u − 36
c
5
, c
6
, c
11
u
29
+ 2u
28
+ ··· + 24u + 8
c
8
, c
9
, c
12
u
29
+ 5u
28
+ ··· + 371u − 49
c
10
u
29
− 2u
28
+ ··· + 109624u + 17960
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
− 32y
28
+ ··· + 729751y −6561
c
2
, c
4
y
29
− 24y
28
+ ··· − 533y −81
c
3
, c
7
y
29
− 6y
28
+ ··· + 7416y −1296
c
5
, c
6
, c
11
y
29
+ 42y
28
+ ··· + 1472y −64
c
8
, c
9
, c
12
y
29
− 39y
28
+ ··· + 313551y −2401
c
10
y
29
+ 126y
28
+ ··· + 874175296y −322561600
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.056486 + 1.108600I
a = 0.509763 + 0.504736I
b = 0.907095 − 0.525537I
−1.48252 + 4.21157I −5.04918 − 7.08997I
u = 0.056486 − 1.108600I
a = 0.509763 − 0.504736I
b = 0.907095 + 0.525537I
−1.48252 − 4.21157I −5.04918 + 7.08997I
u = −0.388139 + 1.131690I
a = 0.13323 + 1.59492I
b = −0.279564 − 0.842912I
−6.31420 − 2.62388I −7.82173 + 3.53782I
u = −0.388139 − 1.131690I
a = 0.13323 − 1.59492I
b = −0.279564 + 0.842912I
−6.31420 + 2.62388I −7.82173 − 3.53782I
u = −1.26121
a = −1.32815
b = 1.48540
−8.96674 −10.0380
u = 0.596916 + 1.218910I
a = −0.248187 + 0.135692I
b = 1.167880 + 0.296850I
−1.89970 + 1.08021I −8.90087 + 2.30906I
u = 0.596916 − 1.218910I
a = −0.248187 − 0.135692I
b = 1.167880 − 0.296850I
−1.89970 − 1.08021I −8.90087 − 2.30906I
u = 0.246173 + 0.558581I
a = 0.428232 − 0.225932I
b = 0.080951 + 0.316217I
−0.137288 + 1.167630I −1.98849 − 5.87802I
u = 0.246173 − 0.558581I
a = 0.428232 + 0.225932I
b = 0.080951 − 0.316217I
−0.137288 − 1.167630I −1.98849 + 5.87802I
u = 0.229637 + 1.393650I
a = −0.24130 − 1.45930I
b = −1.306470 + 0.114811I
−9.08630 + 0.60306I −9.48302 + 0.55490I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.229637 − 1.393650I
a = −0.24130 + 1.45930I
b = −1.306470 − 0.114811I
−9.08630 − 0.60306I −9.48302 − 0.55490I
u = −0.92622 + 1.09424I
a = −0.679131 − 1.154340I
b = 1.50364 + 0.34882I
−12.14260 − 7.09236I −9.88548 + 4.43112I
u = −0.92622 − 1.09424I
a = −0.679131 + 1.154340I
b = 1.50364 − 0.34882I
−12.14260 + 7.09236I −9.88548 − 4.43112I
u = 0.032332 + 0.523301I
a = −2.28494 + 0.79922I
b = −1.045540 − 0.191235I
−2.84144 − 0.79516I −13.03610 − 2.36785I
u = 0.032332 − 0.523301I
a = −2.28494 − 0.79922I
b = −1.045540 + 0.191235I
−2.84144 + 0.79516I −13.03610 + 2.36785I
u = −0.06536 + 1.54556I
a = 0.658215 − 0.546986I
b = −0.451198 + 0.592359I
−7.37261 + 1.38935I −7.45295 − 4.42658I
u = −0.06536 − 1.54556I
a = 0.658215 + 0.546986I
b = −0.451198 − 0.592359I
−7.37261 − 1.38935I −7.45295 + 4.42658I
u = 0.434195 + 0.049760I
a = −0.72855 − 1.30157I
b = 0.901341 + 0.657097I
1.84827 − 2.56654I 3.67854 + 0.07862I
u = 0.434195 − 0.049760I
a = −0.72855 + 1.30157I
b = 0.901341 − 0.657097I
1.84827 + 2.56654I 3.67854 − 0.07862I
u = −0.352396
a = 5.25680
b = −0.489012
−2.50392 5.38240
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.210444
a = 3.27498
b = −0.852919
−1.24667 −7.81580
u = −0.31071 + 1.78442I
a = −0.039698 − 1.223290I
b = 1.49818 + 0.64361I
17.7563 − 12.2354I 0
u = −0.31071 − 1.78442I
a = −0.039698 + 1.223290I
b = 1.49818 − 0.64361I
17.7563 + 12.2354I 0
u = −0.14116 + 1.80910I
a = −0.144818 + 1.112790I
b = −0.015590 − 1.360440I
−16.9778 − 5.1847I 0
u = −0.14116 − 1.80910I
a = −0.144818 − 1.112790I
b = −0.015590 + 1.360440I
−16.9778 + 5.1847I 0
u = 0.04856 + 1.88123I
a = 0.226652 − 0.888720I
b = −1.55643 + 0.68836I
17.7608 + 2.1451I 0
u = 0.04856 − 1.88123I
a = 0.226652 + 0.888720I
b = −1.55643 − 0.68836I
17.7608 − 2.1451I 0
u = 0.09931 + 1.89084I
a = −0.024622 + 0.392844I
b = 1.52399 − 0.23863I
−13.8756 + 4.6395I 0
u = 0.09931 − 1.89084I
a = −0.024622 − 0.392844I
b = 1.52399 + 0.23863I
−13.8756 − 4.6395I 0
7
II. I
u
2
=
h−4a
2
u−6a
2
+8au+17b+12a−2u−20, 4a
3
−6a
2
u−8a
2
+2au+u−6, u
2
+2i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
3
=
a
0.235294a
2
u − 0.470588au + ··· − 0.705882a + 1.17647
a
6
=
1
2
a
2
=
0.235294a
2
u − 0.470588au + ··· + 0.294118a + 1.17647
0.235294a
2
u − 0.470588au + ··· − 0.705882a + 1.17647
a
1
=
1
2
u
0.352941a
2
u + 0.294118au + ··· + 0.941176a + 1.76471
a
4
=
−0.411765a
2
u + 0.823529au + ··· + 0.235294a − 0.0588235
0.117647a
2
u + 0.764706au + ··· + 1.64706a − 0.411765
a
11
=
−u
−u
a
7
=
−1
0
a
8
=
1
2
u
0.352941a
2
u + 0.294118au + ··· + 0.941176a + 1.76471
a
9
=
1
2
u
0.352941a
2
u + 0.294118au + ··· + 0.941176a + 1.76471
a
10
=
0
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
16
17
a
2
u +
24
17
a
2
−
32
17
au −
48
17
a +
8
17
u −
124
17
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
+ u
2
− 1)
2
c
3
(u
3
+ u
2
+ 2u + 1)
2
c
4
(u
3
− u
2
+ 1)
2
c
5
, c
6
, c
10
c
11
(u
2
+ 2)
3
c
8
, c
9
(u + 1)
6
c
12
(u − 1)
6
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
4
(y
3
− y
2
+ 2y −1)
2
c
5
, c
6
, c
10
c
11
(y + 2)
6
c
8
, c
9
, c
12
(y −1)
6
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = 0.520153 + 0.983610I
b = 0.877439 − 0.744862I
−3.55561 + 2.82812I −8.49024 − 2.97945I
u = 1.414210I
a = −0.275030 − 0.506114I
b = 0.877439 + 0.744862I
−3.55561 − 2.82812I −8.49024 + 2.97945I
u = 1.414210I
a = 1.75488 + 1.64382I
b = −0.754878
−7.69319 −15.0195 + 0.I
u = − 1.414210I
a = 0.520153 − 0.983610I
b = 0.877439 + 0.744862I
−3.55561 − 2.82812I −8.49024 + 2.97945I
u = − 1.414210I
a = −0.275030 + 0.506114I
b = 0.877439 − 0.744862I
−3.55561 + 2.82812I −8.49024 − 2.97945I
u = − 1.414210I
a = 1.75488 − 1.64382I
b = −0.754878
−7.69319 −15.0195 + 0.I
11
III. I
u
3
= hb + 1, 3a − 2u − 1, u
2
+ u + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
3
=
2
3
u +
1
3
−1
a
6
=
1
u + 1
a
2
=
2
3
u −
2
3
−1
a
1
=
−1
0
a
4
=
2
3
u +
1
3
−1
a
11
=
−u
u + 1
a
7
=
−u
u + 2
a
8
=
−u
u + 2
a
9
=
−u
u + 1
a
10
=
−2u − 1
u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
20
3
u − 3
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
7
u
2
c
4
(u + 1)
2
c
5
, c
6
, c
10
c
12
u
2
+ u + 1
c
8
, c
9
, c
11
u
2
− u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
2
c
3
, c
7
y
2
c
5
, c
6
, c
8
c
9
, c
10
, c
11
c
12
y
2
+ y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.577350I
b = −1.00000
−1.64493 − 2.02988I −6.33333 + 5.77350I
u = −0.500000 − 0.866025I
a = − 0.577350I
b = −1.00000
−1.64493 + 2.02988I −6.33333 − 5.77350I
15
IV. I
v
1
= ha, −v
2
+ b − 3v + 1, v
3
+ 2v
2
− 3v + 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
v
0
a
3
=
0
v
2
+ 3v − 1
a
6
=
1
0
a
2
=
v
2
+ 3v − 1
v
2
+ 3v − 1
a
1
=
v
2
+ 3v − 1
−v
2
− 2v + 3
a
4
=
−2v
2
− 5v + 4
−2v
2
− 5v + 3
a
11
=
v
0
a
7
=
1
0
a
8
=
−v
2
− 3v + 1
v
2
+ 2v − 3
a
9
=
−v
2
− 2v + 1
v
2
+ 2v − 3
a
10
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8v
2
+ 26v − 26
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
u
3
− u
2
+ 1
c
5
, c
6
, c
10
c
11
u
3
c
7
u
3
+ u
2
+ 2u + 1
c
8
, c
9
(u − 1)
3
c
12
(u + 1)
3
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
3
+ 3y
2
+ 2y − 1
c
2
, c
4
y
3
− y
2
+ 2y − 1
c
5
, c
6
, c
10
c
11
y
3
c
8
, c
9
, c
12
(y − 1)
3
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.539798 + 0.182582I
a = 0
b = 0.877439 + 0.744862I
1.37919 − 2.82812I −9.90089 + 6.32406I
v = 0.539798 − 0.182582I
a = 0
b = 0.877439 − 0.744862I
1.37919 + 2.82812I −9.90089 − 6.32406I
v = −3.07960
a = 0
b = −0.754878
−2.75839 −30.1980
19
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
3
− u
2
+ 2u − 1)
3
(u
29
+ 24u
28
+ ··· − 533u + 81)
c
2
((u − 1)
2
)(u
3
+ u
2
− 1)
3
(u
29
− 6u
28
+ ··· + 5u − 9)
c
3
u
2
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
2
(u
29
+ 2u
28
+ ··· + 36u − 36)
c
4
((u + 1)
2
)(u
3
− u
2
+ 1)
3
(u
29
− 6u
28
+ ··· + 5u − 9)
c
5
, c
6
u
3
(u
2
+ 2)
3
(u
2
+ u + 1)(u
29
+ 2u
28
+ ··· + 24u + 8)
c
7
u
2
(u
3
− u
2
+ 2u − 1)
2
(u
3
+ u
2
+ 2u + 1)(u
29
+ 2u
28
+ ··· + 36u − 36)
c
8
, c
9
((u − 1)
3
)(u + 1)
6
(u
2
− u + 1)(u
29
+ 5u
28
+ ··· + 371u − 49)
c
10
u
3
(u
2
+ 2)
3
(u
2
+ u + 1)(u
29
− 2u
28
+ ··· + 109624u + 17960)
c
11
u
3
(u
2
+ 2)
3
(u
2
− u + 1)(u
29
+ 2u
28
+ ··· + 24u + 8)
c
12
((u − 1)
6
)(u + 1)
3
(u
2
+ u + 1)(u
29
+ 5u
28
+ ··· + 371u − 49)
20
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
2
)(y
3
+ 3y
2
+ 2y − 1)
3
(y
29
− 32y
28
+ ··· + 729751y − 6561)
c
2
, c
4
((y − 1)
2
)(y
3
− y
2
+ 2y − 1)
3
(y
29
− 24y
28
+ ··· − 533y − 81)
c
3
, c
7
y
2
(y
3
+ 3y
2
+ 2y − 1)
3
(y
29
− 6y
28
+ ··· + 7416y − 1296)
c
5
, c
6
, c
11
y
3
(y + 2)
6
(y
2
+ y + 1)(y
29
+ 42y
28
+ ··· + 1472y − 64)
c
8
, c
9
, c
12
((y − 1)
9
)(y
2
+ y + 1)(y
29
− 39y
28
+ ··· + 313551y − 2401)
c
10
y
3
(y + 2)
6
(y
2
+ y + 1)
· (y
29
+ 126y
28
+ ··· + 874175296y − 322561600)
21
