12a
0651
(K12a
0651
)
A knot diagram
1
Linearized knot diagam
3 7 10 11 12 8 2 1 6 4 5 9
Solving Sequence
2,8
7 3 1 9 6 10 4 12 5 11
c
7
c
2
c
1
c
8
c
6
c
9
c
3
c
12
c
5
c
11
c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
48
− u
47
+ ··· − 2u
2
− 1i
* 1 irreducible components of dim
C
= 0, with total 48 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
48
− u
47
+ · · · − 2u
2
− 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
9
=
−u
8
− u
6
− u
4
+ 1
−u
10
− 2u
8
− 3u
6
− 2u
4
− u
2
a
6
=
u
2
+ 1
u
2
a
10
=
u
14
+ 3u
12
+ 6u
10
+ 7u
8
+ 6u
6
+ 4u
4
+ 2u
2
+ 1
u
14
+ 2u
12
+ 3u
10
+ 2u
8
− u
2
a
4
=
−u
31
− 6u
29
+ ··· − 18u
5
− 6u
3
−u
31
− 5u
29
+ ··· + 2u
3
+ u
a
12
=
u
13
+ 2u
11
+ 3u
9
+ 2u
7
− u
u
15
+ 3u
13
+ 6u
11
+ 7u
9
+ 6u
7
+ 4u
5
+ 2u
3
+ u
a
5
=
−u
30
− 5u
28
+ ··· + 2u
2
+ 1
−u
32
− 6u
30
+ ··· − 18u
6
− 6u
4
a
11
=
−u
47
− 8u
45
+ ··· + 18u
5
+ 6u
3
−u
47
+ u
46
+ ··· − 2u
2
− 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
46
− 4u
45
+ ··· + 12u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
48
+ 17u
47
+ ··· + 4u + 1
c
2
, c
7
u
48
+ u
47
+ ··· − 2u
2
− 1
c
3
, c
4
, c
5
c
10
, c
11
u
48
− u
47
+ ··· − 2u − 1
c
8
, c
12
u
48
− 5u
47
+ ··· + 100u − 39
c
9
u
48
− 5u
47
+ ··· + 912u + 1305
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
48
+ 29y
47
+ ··· − 16y + 1
c
2
, c
7
y
48
+ 17y
47
+ ··· + 4y + 1
c
3
, c
4
, c
5
c
10
, c
11
y
48
− 63y
47
+ ··· + 4y + 1
c
8
, c
12
y
48
+ 37y
47
+ ··· + 24632y + 1521
c
9
y
48
− 23y
47
+ ··· − 23246424y + 1703025
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.802127 + 0.589214I
−13.2341 − 6.6512I −8.69292 + 2.70499I
u = 0.802127 − 0.589214I
−13.2341 + 6.6512I −8.69292 − 2.70499I
u = −0.780450 + 0.595412I
−3.45383 + 5.14659I −7.86923 − 4.15340I
u = −0.780450 − 0.595412I
−3.45383 − 5.14659I −7.86923 + 4.15340I
u = −0.306787 + 0.928044I
−13.29560 − 2.74578I −13.24399 + 4.02587I
u = −0.306787 − 0.928044I
−13.29560 + 2.74578I −13.24399 − 4.02587I
u = 0.744340 + 0.609755I
0.47988 − 2.41400I −2.77620 + 3.95017I
u = 0.744340 − 0.609755I
0.47988 + 2.41400I −2.77620 − 3.95017I
u = −0.709694 + 0.805377I
1.43993 − 0.10326I −4.11691 − 1.57301I
u = −0.709694 − 0.805377I
1.43993 + 0.10326I −4.11691 + 1.57301I
u = −0.019095 + 1.077630I
−5.06998 − 1.60211I −10.45738 + 4.05120I
u = −0.019095 − 1.077630I
−5.06998 + 1.60211I −10.45738 − 4.05120I
u = 0.750182 + 0.779791I
−7.19201 − 0.77835I −5.36224 + 0.06889I
u = 0.750182 − 0.779791I
−7.19201 + 0.77835I −5.36224 − 0.06889I
u = −0.669363 + 0.604587I
0.001527 − 0.587302I −4.68221 + 4.09309I
u = −0.669363 − 0.604587I
0.001527 + 0.587302I −4.68221 − 4.09309I
u = 0.040819 + 1.103530I
−9.34090 + 4.19623I −14.8023 − 4.2142I
u = 0.040819 − 1.103530I
−9.34090 − 4.19623I −14.8023 + 4.2142I
u = 0.701243 + 0.856750I
3.68589 + 2.68723I 1.90848 − 3.59326I
u = 0.701243 − 0.856750I
3.68589 − 2.68723I 1.90848 + 3.59326I
u = 0.303851 + 0.826787I
−3.75546 + 2.27659I −12.89646 − 5.30128I
u = 0.303851 − 0.826787I
−3.75546 − 2.27659I −12.89646 + 5.30128I
u = −0.050388 + 1.121400I
−19.3092 − 5.5995I −15.3152 + 3.0524I
u = −0.050388 − 1.121400I
−19.3092 + 5.5995I −15.3152 − 3.0524I
u = −0.701027 + 0.900492I
1.15320 − 5.29793I −5.03627 + 7.68449I
u = −0.701027 − 0.900492I
1.15320 + 5.29793I −5.03627 − 7.68449I
u = −0.715058 + 0.438137I
−14.1380 − 3.7995I −9.38326 + 2.79474I
u = −0.715058 − 0.438137I
−14.1380 + 3.7995I −9.38326 − 2.79474I
u = 0.719743 + 0.928582I
−7.64175 + 6.35454I −6.48748 − 5.77861I
u = 0.719743 − 0.928582I
−7.64175 − 6.35454I −6.48748 + 5.77861I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.672923 + 0.473750I
−4.26296 + 2.63953I −9.04168 − 4.04694I
u = 0.672923 − 0.473750I
−4.26296 − 2.63953I −9.04168 + 4.04694I
u = 0.620090 + 1.027290I
−5.75948 + 2.34942I −11.55550 − 1.52820I
u = 0.620090 − 1.027290I
−5.75948 − 2.34942I −11.55550 + 1.52820I
u = −0.648633 + 1.012460I
−1.18407 − 4.57916I −6.64611 + 1.38024I
u = −0.648633 − 1.012460I
−1.18407 + 4.57916I −6.64611 − 1.38024I
u = −0.608868 + 1.044010I
−15.8277 − 1.2103I −12.22073 + 2.35699I
u = −0.608868 − 1.044010I
−15.8277 + 1.2103I −12.22073 − 2.35699I
u = 0.668938 + 1.023950I
−0.74329 + 7.81387I −4.00000 − 8.53366I
u = 0.668938 − 1.023950I
−0.74329 − 7.81387I −4.00000 + 8.53366I
u = −0.676813 + 1.038570I
−4.76998 − 10.66020I −9.85701 + 8.71110I
u = −0.676813 − 1.038570I
−4.76998 + 10.66020I −9.85701 − 8.71110I
u = 0.681817 + 1.047990I
−14.6043 + 12.2368I −10.70547 − 7.24531I
u = 0.681817 − 1.047990I
−14.6043 − 12.2368I −10.70547 + 7.24531I
u = −0.545430
−10.6248 −6.00350
u = −0.257194 + 0.480005I
−0.181190 − 0.868139I −4.26608 + 7.69273I
u = −0.257194 − 0.480005I
−0.181190 + 0.868139I −4.26608 − 7.69273I
u = 0.420030
−1.58694 −4.88980
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
48
+ 17u
47
+ ··· + 4u + 1
c
2
, c
7
u
48
+ u
47
+ ··· − 2u
2
− 1
c
3
, c
4
, c
5
c
10
, c
11
u
48
− u
47
+ ··· − 2u − 1
c
8
, c
12
u
48
− 5u
47
+ ··· + 100u − 39
c
9
u
48
− 5u
47
+ ··· + 912u + 1305
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
48
+ 29y
47
+ ··· − 16y + 1
c
2
, c
7
y
48
+ 17y
47
+ ··· + 4y + 1
c
3
, c
4
, c
5
c
10
, c
11
y
48
− 63y
47
+ ··· + 4y + 1
c
8
, c
12
y
48
+ 37y
47
+ ··· + 24632y + 1521
c
9
y
48
− 23y
47
+ ··· − 23246424y + 1703025
8
