12a
0522
(K12a
0522
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 11 1 2 6 12 5 10 4
Solving Sequence
5,10
11 6 12 9 4 1 7 8 3 2
c
10
c
5
c
11
c
9
c
4
c
12
c
6
c
8
c
3
c
2
c
1
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
86
+ u
85
+ ··· + u − 1i
* 1 irreducible components of dim
C
= 0, with total 86 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
86
+ u
85
+ · · · + 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
2
a
9
=
u
4
− u
2
+ 1
−u
4
a
4
=
u
9
− 2u
7
+ 3u
5
− 2u
3
+ u
−u
9
+ u
7
− u
5
+ u
a
1
=
−u
16
+ 3u
14
− 7u
12
+ 10u
10
− 11u
8
+ 8u
6
− 4u
4
+ 1
u
16
− 2u
14
+ 4u
12
− 4u
10
+ 2u
8
− 2u
4
+ 2u
2
a
7
=
u
35
− 6u
33
+ ··· − u
3
− 2u
−u
35
+ 5u
33
+ ··· − 3u
3
+ u
a
8
=
−u
8
+ u
6
− u
4
+ 1
−u
10
+ 2u
8
− 3u
6
+ 2u
4
− u
2
a
3
=
−u
27
+ 4u
25
+ ··· − u
3
+ 2u
−u
29
+ 5u
27
+ ··· − u
3
+ u
a
2
=
−u
72
+ 11u
70
+ ··· + 2u
2
+ 1
−u
74
+ 12u
72
+ ··· − 8u
4
+ 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
84
+ 52u
82
+ ··· + 8u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
86
+ 45u
85
+ ··· − u + 1
c
2
, c
7
u
86
+ u
85
+ ··· − 3u − 1
c
3
, c
6
u
86
− u
85
+ ··· + 365u − 37
c
4
u
86
+ u
85
+ ··· + 561u − 193
c
5
, c
10
u
86
− u
85
+ ··· − u − 1
c
8
, c
12
u
86
− 7u
85
+ ··· + 313u + 101
c
9
, c
11
u
86
+ 27u
85
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
86
− 7y
85
+ ··· − 29y + 1
c
2
, c
7
y
86
+ 45y
85
+ ··· − y + 1
c
3
, c
6
y
86
− 59y
85
+ ··· + 46891y + 1369
c
4
y
86
+ 17y
85
+ ··· − 460629y + 37249
c
5
, c
10
y
86
− 27y
85
+ ··· − y + 1
c
8
, c
12
y
86
+ 61y
85
+ ··· − 636905y + 10201
c
9
, c
11
y
86
+ 65y
85
+ ··· + 27y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.969092 + 0.230577I
1.222170 − 0.569978I 0
u = 0.969092 − 0.230577I
1.222170 + 0.569978I 0
u = −1.01398
−5.66716 0
u = −0.994526 + 0.214365I
1.02801 + 5.02852I 0
u = −0.994526 − 0.214365I
1.02801 − 5.02852I 0
u = −0.913207 + 0.337928I
−3.63978 − 4.81115I 0
u = −0.913207 − 0.337928I
−3.63978 + 4.81115I 0
u = 1.027160 + 0.012565I
−9.09448 − 4.31679I 0
u = 1.027160 − 0.012565I
−9.09448 + 4.31679I 0
u = −0.956850 + 0.092671I
−3.76254 + 2.30799I −17.1614 − 5.2119I
u = −0.956850 − 0.092671I
−3.76254 − 2.30799I −17.1614 + 5.2119I
u = 1.026270 + 0.167617I
−5.81618 − 2.16784I 0
u = 1.026270 − 0.167617I
−5.81618 + 2.16784I 0
u = −1.025220 + 0.185100I
−1.77300 + 5.86734I 0
u = −1.025220 − 0.185100I
−1.77300 − 5.86734I 0
u = 1.035860 + 0.186249I
−4.69302 − 10.67460I 0
u = 1.035860 − 0.186249I
−4.69302 + 10.67460I 0
u = 0.775009 + 0.716780I
1.56773 + 1.42389I 0
u = 0.775009 − 0.716780I
1.56773 − 1.42389I 0
u = −0.843801 + 0.414336I
−4.40588 + 3.41670I −13.4225 − 4.5615I
u = −0.843801 − 0.414336I
−4.40588 − 3.41670I −13.4225 + 4.5615I
u = 0.878143 + 0.294105I
−0.795053 + 0.238091I −8.00000 + 1.18884I
u = 0.878143 − 0.294105I
−0.795053 − 0.238091I −8.00000 − 1.18884I
u = 0.886214 + 0.621303I
−1.01077 − 2.41495I 0
u = 0.886214 − 0.621303I
−1.01077 + 2.41495I 0
u = −0.713390 + 0.817998I
0.74450 − 1.77637I 0
u = −0.713390 − 0.817998I
0.74450 + 1.77637I 0
u = 0.719042 + 0.826403I
4.93045 + 5.39470I 0
u = 0.719042 − 0.826403I
4.93045 − 5.39470I 0
u = −0.714867 + 0.830441I
2.06695 − 10.28130I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.714867 − 0.830441I
2.06695 + 10.28130I 0
u = −0.839663 + 0.705927I
2.78123 + 2.29980I 0
u = −0.839663 − 0.705927I
2.78123 − 2.29980I 0
u = 0.767562 + 0.787698I
1.78506 + 1.25650I 0
u = 0.767562 − 0.787698I
1.78506 − 1.25650I 0
u = 0.666858 + 0.594632I
−0.969478 + 0.460798I −8.00000 − 0.37110I
u = 0.666858 − 0.594632I
−0.969478 − 0.460798I −8.00000 + 0.37110I
u = 0.738232 + 0.826282I
7.79709 + 4.20556I 0
u = 0.738232 − 0.826282I
7.79709 − 4.20556I 0
u = −0.625946 + 0.633374I
−4.13835 − 4.86582I −10.89777 + 3.77751I
u = −0.625946 − 0.633374I
−4.13835 + 4.86582I −10.89777 − 3.77751I
u = −0.747855 + 0.823375I
7.97492 + 0.47103I 0
u = −0.747855 − 0.823375I
7.97492 − 0.47103I 0
u = −0.767300 + 0.812390I
5.81249 + 1.85290I 0
u = −0.767300 − 0.812390I
5.81249 − 1.85290I 0
u = 0.776497 + 0.815133I
3.17912 − 6.61298I 0
u = 0.776497 − 0.815133I
3.17912 + 6.61298I 0
u = −0.889718 + 0.702646I
2.62802 + 3.10264I 0
u = −0.889718 − 0.702646I
2.62802 − 3.10264I 0
u = −0.970512 + 0.634156I
−5.41959 + 1.29410I 0
u = −0.970512 − 0.634156I
−5.41959 − 1.29410I 0
u = 0.968130 + 0.648442I
−1.82536 − 5.45883I 0
u = 0.968130 − 0.648442I
−1.82536 + 5.45883I 0
u = 0.934330 + 0.712069I
1.09209 − 6.89776I 0
u = 0.934330 − 0.712069I
1.09209 + 6.89776I 0
u = −0.980007 + 0.650482I
−5.11693 + 9.93293I 0
u = −0.980007 − 0.650482I
−5.11693 − 9.93293I 0
u = −0.580139 + 0.542430I
−4.45440 + 3.54027I −11.64854 − 4.01491I
u = −0.580139 − 0.542430I
−4.45440 − 3.54027I −11.64854 + 4.01491I
u = 0.964315 + 0.730403I
1.17862 − 6.98644I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.964315 − 0.730403I
1.17862 + 6.98644I 0
u = 0.966588 + 0.756138I
2.59346 + 0.72174I 0
u = 0.966588 − 0.756138I
2.59346 − 0.72174I 0
u = −0.971753 + 0.750409I
5.18325 + 4.01226I 0
u = −0.971753 − 0.750409I
5.18325 − 4.01226I 0
u = −0.987850 + 0.749439I
7.23739 + 5.42236I 0
u = −0.987850 − 0.749439I
7.23739 − 5.42236I 0
u = −1.003930 + 0.733770I
−0.14253 + 7.60118I 0
u = −1.003930 − 0.733770I
−0.14253 − 7.60118I 0
u = 0.994389 + 0.747284I
7.01063 − 10.09990I 0
u = 0.994389 − 0.747284I
7.01063 + 10.09990I 0
u = 1.004390 + 0.739778I
4.05668 − 11.26340I 0
u = 1.004390 − 0.739778I
4.05668 + 11.26340I 0
u = −1.007950 + 0.740102I
1.1693 + 16.1620I 0
u = −1.007950 − 0.740102I
1.1693 − 16.1620I 0
u = 0.682766
−1.04113 −9.42630
u = −0.090684 + 0.640558I
−1.07418 + 8.04275I −6.21623 − 6.44974I
u = −0.090684 − 0.640558I
−1.07418 − 8.04275I −6.21623 + 6.44974I
u = 0.015782 + 0.629251I
4.23854 − 2.26922I −0.86018 + 3.68549I
u = 0.015782 − 0.629251I
4.23854 + 2.26922I −0.86018 − 3.68549I
u = 0.078093 + 0.624459I
1.75192 − 3.27960I −2.76013 + 3.15493I
u = 0.078093 − 0.624459I
1.75192 + 3.27960I −2.76013 − 3.15493I
u = −0.108748 + 0.599313I
−2.21922 − 0.25000I −7.93893 − 0.34480I
u = −0.108748 − 0.599313I
−2.21922 + 0.25000I −7.93893 + 0.34480I
u = 0.207561 + 0.332577I
−0.520348 − 1.051870I −7.34711 + 6.20714I
u = 0.207561 − 0.332577I
−0.520348 + 1.051870I −7.34711 − 6.20714I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
86
+ 45u
85
+ ··· − u + 1
c
2
, c
7
u
86
+ u
85
+ ··· − 3u − 1
c
3
, c
6
u
86
− u
85
+ ··· + 365u − 37
c
4
u
86
+ u
85
+ ··· + 561u − 193
c
5
, c
10
u
86
− u
85
+ ··· − u − 1
c
8
, c
12
u
86
− 7u
85
+ ··· + 313u + 101
c
9
, c
11
u
86
+ 27u
85
+ ··· + u + 1
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
86
− 7y
85
+ ··· − 29y + 1
c
2
, c
7
y
86
+ 45y
85
+ ··· − y + 1
c
3
, c
6
y
86
− 59y
85
+ ··· + 46891y + 1369
c
4
y
86
+ 17y
85
+ ··· − 460629y + 37249
c
5
, c
10
y
86
− 27y
85
+ ··· − y + 1
c
8
, c
12
y
86
+ 61y
85
+ ··· − 636905y + 10201
c
9
, c
11
y
86
+ 65y
85
+ ··· + 27y + 1
9
