12a
1030
(K12a
1030
)
A knot diagram
1
Linearized knot diagam
4 7 8 10 11 2 3 1 12 6 5 9
Solving Sequence
5,12
11 6 10 4 9 1 2 8 3 7
c
11
c
5
c
10
c
4
c
9
c
12
c
1
c
8
c
3
c
7
c
2
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
45
+ u
44
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 45 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
45
+ u
44
+ · · · + u + 1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
6
=
u
u
3
+ u
a
10
=
u
2
+ 1
u
4
+ 2u
2
a
4
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
9
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
1
=
u
8
+ 3u
6
+ u
4
− 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
a
2
=
u
20
+ 9u
18
+ ··· − 3u
2
+ 1
u
22
+ 10u
20
+ ··· − 10u
4
+ u
2
a
8
=
−u
12
− 5u
10
− 7u
8
+ 2u
4
− 3u
2
+ 1
u
12
+ 6u
10
+ 12u
8
+ 8u
6
+ u
4
+ 2u
2
a
3
=
−u
31
− 14u
29
+ ··· + 20u
5
− 8u
3
u
31
+ 15u
29
+ ··· − 8u
5
+ u
a
7
=
−u
39
− 18u
37
+ ··· − 22u
5
+ 6u
3
−u
41
− 19u
39
+ ··· + 13u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
43
− 4u
42
+ ··· + 8u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
45
− 15u
44
+ ··· + 9649u − 1519
c
2
, c
3
, c
6
c
7
u
45
− u
44
+ ··· + u + 1
c
4
u
45
− u
44
+ ··· − 77u + 185
c
5
, c
10
, c
11
u
45
+ u
44
+ ··· + u + 1
c
8
, c
9
, c
12
u
45
+ 5u
44
+ ··· − 75u − 11
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
45
− 29y
44
+ ··· + 732811y −2307361
c
2
, c
3
, c
6
c
7
y
45
− 53y
44
+ ··· + 3y −1
c
4
y
45
+ 23y
44
+ ··· − 661921y −34225
c
5
, c
10
, c
11
y
45
+ 43y
44
+ ··· + 3y −1
c
8
, c
9
, c
12
y
45
+ 51y
44
+ ··· − 2229y −121
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.694472 + 0.462147I
−15.5741 − 8.0130I −5.65409 + 5.67100I
u = −0.694472 − 0.462147I
−15.5741 + 8.0130I −5.65409 − 5.67100I
u = −0.653290 + 0.517630I
−15.7763 + 3.5247I −6.18458 + 0.18087I
u = −0.653290 − 0.517630I
−15.7763 − 3.5247I −6.18458 − 0.18087I
u = 0.676367 + 0.461366I
−7.18094 + 5.79158I −3.96237 − 7.08311I
u = 0.676367 − 0.461366I
−7.18094 − 5.79158I −3.96237 + 7.08311I
u = 0.646732 + 0.497182I
−7.31795 − 1.39903I −4.46873 + 0.97736I
u = 0.646732 − 0.497182I
−7.31795 + 1.39903I −4.46873 − 0.97736I
u = −0.652812 + 0.470140I
−4.81518 − 2.15871I −0.09882 + 3.07844I
u = −0.652812 − 0.470140I
−4.81518 + 2.15871I −0.09882 − 3.07844I
u = −0.133945 + 1.220780I
−8.55123 − 2.70934I 0
u = −0.133945 − 1.220780I
−8.55123 + 2.70934I 0
u = 0.042496 + 1.232290I
−2.07584 + 1.44827I 0. − 5.05918I
u = 0.042496 − 1.232290I
−2.07584 − 1.44827I 0. + 5.05918I
u = 0.616614 + 0.253485I
−7.36995 + 4.81091I −1.70501 − 6.62764I
u = 0.616614 − 0.253485I
−7.36995 − 4.81091I −1.70501 + 6.62764I
u = 0.156680 + 1.346240I
−3.63417 + 2.80099I 0
u = 0.156680 − 1.346240I
−3.63417 − 2.80099I 0
u = −0.195571 + 1.364550I
−4.96920 − 5.95062I 0
u = −0.195571 − 1.364550I
−4.96920 + 5.95062I 0
u = 0.314112 + 0.527766I
−8.57820 − 1.58893I −5.96750 − 0.20348I
u = 0.314112 − 0.527766I
−8.57820 + 1.58893I −5.96750 + 0.20348I
u = 0.222603 + 1.378670I
−12.5405 + 7.8575I 0
u = 0.222603 − 1.378670I
−12.5405 − 7.8575I 0
u = −0.102260 + 1.393560I
−6.53884 − 0.76013I 0
u = −0.102260 − 1.393560I
−6.53884 + 0.76013I 0
u = −0.560189 + 0.217034I
0.02712 − 3.19853I 1.49402 + 9.60591I
u = −0.560189 − 0.217034I
0.02712 + 3.19853I 1.49402 − 9.60591I
u = −0.594571
−4.94513 3.01030
u = 0.09606 + 1.43767I
−14.7381 − 0.1515I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.09606 − 1.43767I
−14.7381 + 0.1515I 0
u = 0.493436 + 0.121548I
1.008560 + 0.465711I 7.68686 − 1.44848I
u = 0.493436 − 0.121548I
1.008560 − 0.465711I 7.68686 + 1.44848I
u = −0.23186 + 1.48396I
−11.13820 − 5.38792I 0
u = −0.23186 − 1.48396I
−11.13820 + 5.38792I 0
u = 0.24189 + 1.48537I
−13.4825 + 9.1436I 0
u = 0.24189 − 1.48537I
−13.4825 − 9.1436I 0
u = 0.22338 + 1.49166I
−13.76630 + 1.76687I 0
u = 0.22338 − 1.49166I
−13.76630 − 1.76687I 0
u = −0.24882 + 1.48904I
17.5851 − 11.4561I 0
u = −0.24882 − 1.48904I
17.5851 + 11.4561I 0
u = −0.22026 + 1.50077I
17.1392 + 0.3529I 0
u = −0.22026 − 1.50077I
17.1392 − 0.3529I 0
u = −0.239609 + 0.377539I
−1.077410 + 0.619571I −5.52422 − 1.42738I
u = −0.239609 − 0.377539I
−1.077410 − 0.619571I −5.52422 + 1.42738I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
45
− 15u
44
+ ··· + 9649u − 1519
c
2
, c
3
, c
6
c
7
u
45
− u
44
+ ··· + u + 1
c
4
u
45
− u
44
+ ··· − 77u + 185
c
5
, c
10
, c
11
u
45
+ u
44
+ ··· + u + 1
c
8
, c
9
, c
12
u
45
+ 5u
44
+ ··· − 75u − 11
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
45
− 29y
44
+ ··· + 732811y −2307361
c
2
, c
3
, c
6
c
7
y
45
− 53y
44
+ ··· + 3y −1
c
4
y
45
+ 23y
44
+ ··· − 661921y −34225
c
5
, c
10
, c
11
y
45
+ 43y
44
+ ··· + 3y −1
c
8
, c
9
, c
12
y
45
+ 51y
44
+ ··· − 2229y −121
8
