12a
1132
(K12a
1132
)
A knot diagram
1
Linearized knot diagam
4 8 9 10 11 12 3 2 1 5 7 6
Solving Sequence
7,11
12 6 1 5 10 4 2 9 3 8
c
11
c
6
c
12
c
5
c
10
c
4
c
1
c
9
c
3
c
8
c
2
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
65
+ u
64
+ ··· + u − 1i
* 1 irreducible components of dim
C
= 0, with total 65 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
65
+ u
64
+ · · · + u − 1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
6
=
−u
u
3
+ u
a
1
=
u
2
+ 1
−u
4
− 2u
2
a
5
=
−u
3
− 2u
u
3
+ u
a
10
=
−u
6
− 3u
4
− 2u
2
+ 1
u
6
+ 2u
4
+ u
2
a
4
=
u
9
+ 4u
7
+ 5u
5
− 3u
−u
9
− 3u
7
− 3u
5
+ u
a
2
=
u
22
+ 9u
20
+ ··· − 2u
2
+ 1
−u
22
− 8u
20
+ ··· − 6u
4
− u
2
a
9
=
u
12
+ 5u
10
+ 9u
8
+ 4u
6
− 6u
4
− 5u
2
+ 1
−u
14
− 6u
12
− 13u
10
− 10u
8
+ 4u
6
+ 8u
4
+ u
2
a
3
=
u
35
+ 14u
33
+ ··· − 7u
3
− 2u
−u
37
− 15u
35
+ ··· + u
3
+ u
a
8
=
−u
58
− 23u
56
+ ··· − 3u
2
+ 1
u
58
+ 22u
56
+ ··· + 6u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
63
+ 4u
62
+ ··· − 4u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
65
− 13u
64
+ ··· − 8727u + 723
c
2
, c
7
, c
8
u
65
− u
64
+ ··· + u − 1
c
3
u
65
+ u
64
+ ··· − 13u − 5
c
4
, c
5
, c
10
u
65
− u
64
+ ··· + u − 1
c
6
, c
11
, c
12
u
65
+ u
64
+ ··· + u − 1
c
9
u
65
− 7u
64
+ ··· − 871u + 209
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
65
+ 27y
64
+ ··· − 8852703y −522729
c
2
, c
7
, c
8
y
65
+ 59y
64
+ ··· + y −1
c
3
y
65
+ 7y
64
+ ··· − 51y −25
c
4
, c
5
, c
10
y
65
− 65y
64
+ ··· + 33y −1
c
6
, c
11
, c
12
y
65
+ 51y
64
+ ··· + y −1
c
9
y
65
− 9y
64
+ ··· + 359869y −43681
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.132840 + 0.983228I
4.29616 − 4.30197I 6.95722 + 4.03422I
u = −0.132840 − 0.983228I
4.29616 + 4.30197I 6.95722 − 4.03422I
u = 0.066608 + 1.057960I
−1.26726 + 1.59606I 0
u = 0.066608 − 1.057960I
−1.26726 − 1.59606I 0
u = 0.879004 + 0.030229I
14.07260 + 0.14142I 12.00585 + 0.01234I
u = 0.879004 − 0.030229I
14.07260 − 0.14142I 12.00585 − 0.01234I
u = −0.874818 + 0.056154I
12.2815 − 9.6813I 10.05803 + 5.84767I
u = −0.874818 − 0.056154I
12.2815 + 9.6813I 10.05803 − 5.84767I
u = 0.867744 + 0.051686I
6.62538 + 6.16117I 6.00476 − 5.84448I
u = 0.867744 − 0.051686I
6.62538 − 6.16117I 6.00476 + 5.84448I
u = −0.864273 + 0.038009I
7.62346 − 2.20976I 8.35069 − 0.07898I
u = −0.864273 − 0.038009I
7.62346 + 2.20976I 8.35069 + 0.07898I
u = −0.823379 + 0.033650I
6.61850 − 3.24358I 7.07171 + 3.68238I
u = −0.823379 − 0.033650I
6.61850 + 3.24358I 7.07171 − 3.68238I
u = 0.814145
3.01477 2.04740
u = −0.204085 + 1.260030I
2.21606 − 1.37582I 0
u = −0.204085 − 1.260030I
2.21606 + 1.37582I 0
u = −0.421787 + 1.223320I
8.68254 + 5.04083I 0
u = −0.421787 − 1.223320I
8.68254 − 5.04083I 0
u = 0.413210 + 1.226500I
3.00151 − 1.57258I 0
u = 0.413210 − 1.226500I
3.00151 + 1.57258I 0
u = −0.360298 + 1.244800I
2.88088 − 1.01529I 0
u = −0.360298 − 1.244800I
2.88088 + 1.01529I 0
u = 0.144292 + 1.296020I
−3.54772 + 2.65467I 0
u = 0.144292 − 1.296020I
−3.54772 − 2.65467I 0
u = −0.407779 + 1.240170I
3.90894 − 2.34852I 0
u = −0.407779 − 1.240170I
3.90894 + 2.34852I 0
u = −0.076935 + 1.315820I
−6.10693 + 0.13062I 0
u = −0.076935 − 1.315820I
−6.10693 − 0.13062I 0
u = 0.420299 + 1.249580I
10.30050 + 4.50754I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.420299 − 1.249580I
10.30050 − 4.50754I 0
u = 0.117189 + 1.318600I
−3.61647 + 2.96338I 0
u = 0.117189 − 1.318600I
−3.61647 − 2.96338I 0
u = 0.363105 + 1.275950I
−0.95272 + 4.23421I 0
u = 0.363105 − 1.275950I
−0.95272 − 4.23421I 0
u = 0.052090 + 1.327030I
−1.24029 − 3.35891I 0
u = 0.052090 − 1.327030I
−1.24029 + 3.35891I 0
u = −0.165280 + 1.324460I
−5.02180 − 6.10726I 0
u = −0.165280 − 1.324460I
−5.02180 + 6.10726I 0
u = 0.178379 + 1.332110I
0.29566 + 9.54694I 0
u = 0.178379 − 1.332110I
0.29566 − 9.54694I 0
u = −0.371939 + 1.295910I
2.47136 − 7.54612I 0
u = −0.371939 − 1.295910I
2.47136 + 7.54612I 0
u = −0.396138 + 1.302350I
3.44229 − 6.73024I 0
u = −0.396138 − 1.302350I
3.44229 + 6.73024I 0
u = 0.408112 + 1.298850I
9.93098 + 4.75176I 0
u = 0.408112 − 1.298850I
9.93098 − 4.75176I 0
u = 0.396720 + 1.312030I
2.36559 + 10.69650I 0
u = 0.396720 − 1.312030I
2.36559 − 10.69650I 0
u = −0.400544 + 1.316110I
7.9932 − 14.2537I 0
u = −0.400544 − 1.316110I
7.9932 + 14.2537I 0
u = 0.537814 + 0.283525I
5.32003 + 7.05774I 7.82899 − 8.24841I
u = 0.537814 − 0.283525I
5.32003 − 7.05774I 7.82899 + 8.24841I
u = −0.570320 + 0.157975I
6.52518 + 1.38179I 10.75156 + 1.24725I
u = −0.570320 − 0.157975I
6.52518 − 1.38179I 10.75156 − 1.24725I
u = 0.196201 + 0.551150I
4.20028 − 4.05680I 4.64942 + 1.87750I
u = 0.196201 − 0.551150I
4.20028 + 4.05680I 4.64942 − 1.87750I
u = −0.499727 + 0.273958I
−0.07493 − 3.79273I 3.07739 + 8.81677I
u = −0.499727 − 0.273958I
−0.07493 + 3.79273I 3.07739 − 8.81677I
u = 0.368028 + 0.336891I
1.40304 + 1.30266I 2.88088 − 5.27854I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.368028 − 0.336891I
1.40304 − 1.30266I 2.88088 + 5.27854I
u = 0.451706 + 0.174867I
0.967178 + 0.588537I 7.75794 − 2.26949I
u = 0.451706 − 0.174867I
0.967178 − 0.588537I 7.75794 + 2.26949I
u = −0.197430 + 0.427516I
−1.00380 + 1.10655I −1.56812 − 1.52674I
u = −0.197430 − 0.427516I
−1.00380 − 1.10655I −1.56812 + 1.52674I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
65
− 13u
64
+ ··· − 8727u + 723
c
2
, c
7
, c
8
u
65
− u
64
+ ··· + u − 1
c
3
u
65
+ u
64
+ ··· − 13u − 5
c
4
, c
5
, c
10
u
65
− u
64
+ ··· + u − 1
c
6
, c
11
, c
12
u
65
+ u
64
+ ··· + u − 1
c
9
u
65
− 7u
64
+ ··· − 871u + 209
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
65
+ 27y
64
+ ··· − 8852703y −522729
c
2
, c
7
, c
8
y
65
+ 59y
64
+ ··· + y −1
c
3
y
65
+ 7y
64
+ ··· − 51y −25
c
4
, c
5
, c
10
y
65
− 65y
64
+ ··· + 33y −1
c
6
, c
11
, c
12
y
65
+ 51y
64
+ ··· + y −1
c
9
y
65
− 9y
64
+ ··· + 359869y −43681
9
