12a
1165
(K12a
1165
)
A knot diagram
1
Linearized knot diagam
4 9 8 12 1 11 10 3 2 7 6 5
Solving Sequence
1,6
5 12 4 2 11 7 10 8 3 9
c
5
c
12
c
4
c
1
c
11
c
6
c
10
c
7
c
3
c
9
c
2
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
33
+ u
32
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 33 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
33
+ u
32
+ · · · + u + 1i
(i) Arc colorings
a
1
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
12
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
2
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
11
=
−u
3
+ 2u
−u
3
+ u
a
7
=
u
6
− 3u
4
+ 2u
2
+ 1
u
6
− 2u
4
+ u
2
a
10
=
−u
9
+ 4u
7
− 5u
5
+ 3u
−u
9
+ 3u
7
− 3u
5
+ u
a
8
=
u
12
− 5u
10
+ 9u
8
− 4u
6
− 6u
4
+ 5u
2
+ 1
u
12
− 4u
10
+ 6u
8
− 2u
6
− 3u
4
+ 2u
2
a
3
=
−u
28
+ 11u
26
+ ··· + 3u
2
+ 1
−u
28
+ 10u
26
+ ··· + 9u
4
− 2u
2
a
9
=
u
21
− 8u
19
+ ··· − 4u
3
+ 3u
−u
23
+ 9u
21
+ ··· + 4u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
30
− 44u
28
+ 4u
27
+ 216u
26
− 40u
25
− 592u
24
+ 176u
23
+ 892u
22
− 420u
21
−
420u
20
+ 508u
19
− 948u
18
− 52u
17
+ 1812u
16
− 716u
15
− 808u
14
+ 840u
13
− 896u
12
−
64u
11
+ 1080u
10
−520u
9
−56u
8
+ 264u
7
−352u
6
+ 96u
5
+ 64u
4
−64u
3
+ 48u
2
−16u −2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
10
, c
11
u
33
− 3u
32
+ ··· + 9u − 3
c
2
, c
3
, c
8
c
9
u
33
+ u
32
+ ··· + u + 1
c
4
, c
5
, c
12
u
33
+ u
32
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
7
c
10
, c
11
y
33
+ 43y
32
+ ··· − 15y −9
c
2
, c
3
, c
8
c
9
y
33
+ 35y
32
+ ··· − 7y −1
c
4
, c
5
, c
12
y
33
− 25y
32
+ ··· − 7y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.007187 + 0.927489I
13.69600 + 2.31895I 1.75304 − 2.85786I
u = −0.007187 − 0.927489I
13.69600 − 2.31895I 1.75304 + 2.85786I
u = 0.022659 + 0.925236I
7.06487 − 5.65946I −1.58265 + 2.87323I
u = 0.022659 − 0.925236I
7.06487 + 5.65946I −1.58265 − 2.87323I
u = 1.089610 + 0.294783I
−5.38539 + 0.42351I −5.40857 + 0.36274I
u = 1.089610 − 0.294783I
−5.38539 − 0.42351I −5.40857 − 0.36274I
u = −1.14314
−2.30256 −1.78270
u = −1.182680 + 0.290002I
0.43739 + 1.77292I −1.59025 − 0.21543I
u = −1.182680 − 0.290002I
0.43739 − 1.77292I −1.59025 + 0.21543I
u = 1.234350 + 0.088067I
−4.21894 − 1.97469I −11.37360 + 5.72658I
u = 1.234350 − 0.088067I
−4.21894 + 1.97469I −11.37360 − 5.72658I
u = 1.244790 + 0.290367I
−0.08256 − 5.33404I −3.84371 + 7.86352I
u = 1.244790 − 0.290367I
−0.08256 + 5.33404I −3.84371 − 7.86352I
u = 0.124967 + 0.695815I
−2.55035 − 4.09733I −2.17456 + 4.30313I
u = 0.124967 − 0.695815I
−2.55035 + 4.09733I −2.17456 − 4.30313I
u = −1.303370 + 0.091971I
−11.41980 + 2.77587I −12.69893 − 3.54173I
u = −1.303370 − 0.091971I
−11.41980 − 2.77587I −12.69893 + 3.54173I
u = −0.042773 + 0.691881I
3.85716 + 1.79630I 2.14795 − 4.42092I
u = −0.042773 − 0.691881I
3.85716 − 1.79630I 2.14795 + 4.42092I
u = −1.290570 + 0.282135I
−6.93611 + 7.59600I −7.80083 − 6.53721I
u = −1.290570 − 0.282135I
−6.93611 − 7.59600I −7.80083 + 6.53721I
u = 1.271570 + 0.457494I
3.19600 + 0.72997I −4.74001 + 0.15304I
u = 1.271570 − 0.457494I
3.19600 − 0.72997I −4.74001 − 0.15304I
u = −1.285040 + 0.453763I
9.72993 + 2.60735I −1.44806 − 0.13745I
u = −1.285040 − 0.453763I
9.72993 − 2.60735I −1.44806 + 0.13745I
u = 1.296000 + 0.449004I
9.64446 − 7.23064I −1.69264 + 5.79671I
u = 1.296000 − 0.449004I
9.64446 + 7.23064I −1.69264 − 5.79671I
u = −1.306320 + 0.442632I
2.92604 + 10.54330I −5.09643 − 5.66423I
u = −1.306320 − 0.442632I
2.92604 − 10.54330I −5.09643 + 5.66423I
u = 0.391381 + 0.352338I
−6.35493 − 1.38874I −6.74266 + 4.47575I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.391381 − 0.352338I
−6.35493 + 1.38874I −6.74266 − 4.47575I
u = −0.185818 + 0.264071I
−0.115512 + 0.725231I −3.81673 − 9.57308I
u = −0.185818 − 0.264071I
−0.115512 − 0.725231I −3.81673 + 9.57308I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
10
, c
11
u
33
− 3u
32
+ ··· + 9u − 3
c
2
, c
3
, c
8
c
9
u
33
+ u
32
+ ··· + u + 1
c
4
, c
5
, c
12
u
33
+ u
32
+ ··· + u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
7
c
10
, c
11
y
33
+ 43y
32
+ ··· − 15y −9
c
2
, c
3
, c
8
c
9
y
33
+ 35y
32
+ ··· − 7y −1
c
4
, c
5
, c
12
y
33
− 25y
32
+ ··· − 7y −1
8
