12a
0501
(K12a
0501
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 10 11 2 1 12 6 5 4
Solving Sequence
2,8
7 3 4 1 9 5 12 10 11 6
c
7
c
2
c
3
c
1
c
8
c
4
c
12
c
9
c
11
c
6
c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
99
+ u
98
+ ··· + 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 99 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
99
+ u
98
+ · · · + 2u + 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
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
5
=
u
21
+ 4u
19
+ 9u
17
+ 12u
15
+ 12u
13
+ 10u
11
+ 9u
9
+ 6u
7
+ 3u
5
+ u
u
23
+ 5u
21
+ ··· + 2u
3
+ u
a
12
=
−u
11
− 2u
9
− 2u
7
+ u
3
u
11
+ 3u
9
+ 4u
7
+ 3u
5
+ u
3
+ u
a
10
=
u
32
+ 7u
30
+ ··· + 2u
12
+ 1
−u
32
− 8u
30
+ ··· − 12u
8
− 4u
6
a
11
=
u
55
+ 12u
53
+ ··· + 5u
7
+ 2u
3
u
57
+ 13u
55
+ ··· + 2u
3
+ u
a
6
=
−u
87
− 20u
85
+ ··· − 5u
7
− 2u
3
u
87
+ 21u
85
+ ··· + 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
97
− 4u
96
+ ··· − 12u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
99
+ 47u
98
+ ··· − 2u − 1
c
2
, c
7
u
99
+ u
98
+ ··· + 2u + 1
c
3
u
99
− u
98
+ ··· − 2396u + 457
c
4
u
99
+ u
98
+ ··· − 1366u + 521
c
5
, c
6
, c
10
u
99
− u
98
+ ··· + 2u + 1
c
8
u
99
+ 5u
98
+ ··· + 1102u + 57
c
9
u
99
+ 21u
98
+ ··· + 218716u + 11327
c
11
u
99
+ 3u
98
+ ··· − 14u − 3
c
12
u
99
+ 11u
98
+ ··· + 14402u + 701
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
99
+ 11y
98
+ ··· + 2y −1
c
2
, c
7
y
99
+ 47y
98
+ ··· − 2y −1
c
3
y
99
− 25y
98
+ ··· + 8147378y −208849
c
4
y
99
− 17y
98
+ ··· + 17086450y −271441
c
5
, c
6
, c
10
y
99
− 89y
98
+ ··· − 2y −1
c
8
y
99
+ 19y
98
+ ··· + 191938y −3249
c
9
y
99
+ 31y
98
+ ··· − 2952423990y −128300929
c
11
y
99
− 5y
98
+ ··· − 218y −9
c
12
y
99
+ 23y
98
+ ··· − 14304490y −491401
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.469814 + 0.889386I
−5.15974 − 3.45007I 0
u = −0.469814 − 0.889386I
−5.15974 + 3.45007I 0
u = −0.148767 + 0.934892I
−5.20598 − 3.73864I 0
u = −0.148767 − 0.934892I
−5.20598 + 3.73864I 0
u = 0.242603 + 1.031670I
−0.575080 + 0.871667I 0
u = 0.242603 − 1.031670I
−0.575080 − 0.871667I 0
u = 0.650159 + 0.633663I
−2.28389 + 9.47082I 0. − 7.96667I
u = 0.650159 − 0.633663I
−2.28389 − 9.47082I 0. + 7.96667I
u = 0.567446 + 0.934324I
−3.16890 − 4.70879I 0
u = 0.567446 − 0.934324I
−3.16890 + 4.70879I 0
u = −0.561044 + 0.947080I
2.13253 + 1.20620I 0
u = −0.561044 − 0.947080I
2.13253 − 1.20620I 0
u = −0.645418 + 0.621535I
3.08946 − 5.93342I 2.82989 + 7.73749I
u = −0.645418 − 0.621535I
3.08946 + 5.93342I 2.82989 − 7.73749I
u = −0.226159 + 1.083640I
−3.58165 + 2.19221I 0
u = −0.226159 − 1.083640I
−3.58165 − 2.19221I 0
u = 0.542662 + 0.972451I
0.53423 + 2.32067I 0
u = 0.542662 − 0.972451I
0.53423 − 2.32067I 0
u = −0.406038 + 1.044390I
−4.93260 − 3.36503I 0
u = −0.406038 − 1.044390I
−4.93260 + 3.36503I 0
u = −0.591230 + 0.646260I
−4.43604 − 0.89349I −4.62087 + 3.00648I
u = −0.591230 − 0.646260I
−4.43604 + 0.89349I −4.62087 − 3.00648I
u = 0.624098 + 0.600705I
1.62616 + 2.28184I 0. − 2.63017I
u = 0.624098 − 0.600705I
1.62616 − 2.28184I 0. + 2.63017I
u = 0.559694 + 0.987397I
0.64836 + 2.17091I 0
u = 0.559694 − 0.987397I
0.64836 − 2.17091I 0
u = 0.646091 + 0.572926I
1.86865 + 2.54840I 1.88929 − 4.22472I
u = 0.646091 − 0.572926I
1.86865 − 2.54840I 1.88929 + 4.22472I
u = −0.244895 + 1.115700I
−4.07787 + 1.55190I 0
u = −0.244895 − 1.115700I
−4.07787 − 1.55190I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.232455 + 1.127000I
−2.86423 − 5.33511I 0
u = 0.232455 − 1.127000I
−2.86423 + 5.33511I 0
u = −0.653529 + 0.536527I
4.41016 + 0.73901I 5.92100 − 1.06674I
u = −0.653529 − 0.536527I
4.41016 − 0.73901I 5.92100 + 1.06674I
u = 0.668382 + 0.516240I
−0.40853 − 4.10398I 0.48519 + 2.62326I
u = 0.668382 − 0.516240I
−0.40853 + 4.10398I 0.48519 − 2.62326I
u = −0.231557 + 1.135340I
−8.36784 + 8.86222I 0
u = −0.231557 − 1.135340I
−8.36784 − 8.86222I 0
u = −0.564773 + 1.011980I
3.01104 − 5.49491I 0
u = −0.564773 − 1.011980I
3.01104 + 5.49491I 0
u = 0.259545 + 1.131170I
−10.36610 + 0.21333I 0
u = 0.259545 − 1.131170I
−10.36610 − 0.21333I 0
u = −0.333189 + 1.112900I
−4.98807 − 1.63643I 0
u = −0.333189 − 1.112900I
−4.98807 + 1.63643I 0
u = −0.768061 + 0.334118I
−3.77803 + 11.62790I −3.49560 − 7.24187I
u = −0.768061 − 0.334118I
−3.77803 − 11.62790I −3.49560 + 7.24187I
u = 0.761147 + 0.337791I
1.68726 − 8.05078I 1.00959 + 7.12608I
u = 0.761147 − 0.337791I
1.68726 + 8.05078I 1.00959 − 7.12608I
u = 0.570821 + 1.024070I
−1.90077 + 8.91802I 0
u = 0.570821 − 1.024070I
−1.90077 − 8.91802I 0
u = 0.353113 + 1.121300I
−4.15696 + 5.26132I 0
u = 0.353113 − 1.121300I
−4.15696 − 5.26132I 0
u = 0.323859 + 1.131150I
−11.06550 − 0.52973I 0
u = 0.323859 − 1.131150I
−11.06550 + 0.52973I 0
u = −0.736585 + 0.362308I
0.85605 + 4.62614I 0.34575 − 4.53704I
u = −0.736585 − 0.362308I
0.85605 − 4.62614I 0.34575 + 4.53704I
u = −0.745397 + 0.336513I
0.35085 + 4.23448I −1.71767 − 1.98109I
u = −0.745397 − 0.336513I
0.35085 − 4.23448I −1.71767 + 1.98109I
u = −0.705352 + 0.406363I
−0.90793 − 1.98651I −0.17740 + 1.94504I
u = −0.705352 − 0.406363I
−0.90793 + 1.98651I −0.17740 − 1.94504I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.355088 + 1.132520I
−9.73220 − 8.58110I 0
u = −0.355088 − 1.132520I
−9.73220 + 8.58110I 0
u = 0.715758 + 0.381198I
3.68933 − 1.31194I 5.02327 − 0.03733I
u = 0.715758 − 0.381198I
3.68933 + 1.31194I 5.02327 + 0.03733I
u = 0.746606 + 0.312147I
−5.98648 − 2.63880I −6.16930 + 2.15328I
u = 0.746606 − 0.312147I
−5.98648 + 2.63880I −6.16930 − 2.15328I
u = 0.500633 + 1.113340I
−3.16752 + 2.36428I 0
u = 0.500633 − 1.113340I
−3.16752 − 2.36428I 0
u = −0.564626 + 1.086520I
−2.90289 − 2.89174I 0
u = −0.564626 − 1.086520I
−2.90289 + 2.89174I 0
u = −0.496006 + 1.123710I
−8.78413 + 0.80483I 0
u = −0.496006 − 1.123710I
−8.78413 − 0.80483I 0
u = −0.517957 + 1.114130I
−3.73484 − 5.93656I 0
u = −0.517957 − 1.114130I
−3.73484 + 5.93656I 0
u = 0.564691 + 1.098850I
1.58780 + 6.21411I 0
u = 0.564691 − 1.098850I
1.58780 − 6.21411I 0
u = 0.520518 + 1.126860I
−9.73594 + 8.31531I 0
u = 0.520518 − 1.126860I
−9.73594 − 8.31531I 0
u = −0.567856 + 1.109820I
−1.33445 − 9.58664I 0
u = −0.567856 − 1.109820I
−1.33445 + 9.58664I 0
u = −0.564234 + 1.120740I
−1.94479 − 9.19767I 0
u = −0.564234 − 1.120740I
−1.94479 + 9.19767I 0
u = 0.557641 + 1.127410I
−8.36659 + 7.57130I 0
u = 0.557641 − 1.127410I
−8.36659 − 7.57130I 0
u = 0.569152 + 1.124680I
−0.62462 + 13.07100I 0
u = 0.569152 − 1.124680I
−0.62462 − 13.07100I 0
u = −0.570149 + 1.127840I
−6.1128 − 16.6680I 0
u = −0.570149 − 1.127840I
−6.1128 + 16.6680I 0
u = 0.690221 + 0.227322I
−7.18528 − 3.70755I −7.70867 + 3.15852I
u = 0.690221 − 0.227322I
−7.18528 + 3.70755I −7.70867 − 3.15852I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.237632 + 0.651195I
−0.227540 + 1.212660I −2.71740 − 5.80081I
u = 0.237632 − 0.651195I
−0.227540 − 1.212660I −2.71740 + 5.80081I
u = −0.645466 + 0.239263I
−1.29221 + 1.42569I −4.26718 − 3.80181I
u = −0.645466 − 0.239263I
−1.29221 − 1.42569I −4.26718 + 3.80181I
u = −0.663803 + 0.156320I
−6.10535 − 5.18308I −6.43617 + 3.54727I
u = −0.663803 − 0.156320I
−6.10535 + 5.18308I −6.43617 − 3.54727I
u = 0.630812 + 0.169069I
−0.60523 + 1.97398I −2.11200 − 3.87352I
u = 0.630812 − 0.169069I
−0.60523 − 1.97398I −2.11200 + 3.87352I
u = −0.517496
−2.26066 −3.53670
8
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
99
+ 47u
98
+ ··· − 2u − 1
c
2
, c
7
u
99
+ u
98
+ ··· + 2u + 1
c
3
u
99
− u
98
+ ··· − 2396u + 457
c
4
u
99
+ u
98
+ ··· − 1366u + 521
c
5
, c
6
, c
10
u
99
− u
98
+ ··· + 2u + 1
c
8
u
99
+ 5u
98
+ ··· + 1102u + 57
c
9
u
99
+ 21u
98
+ ··· + 218716u + 11327
c
11
u
99
+ 3u
98
+ ··· − 14u − 3
c
12
u
99
+ 11u
98
+ ··· + 14402u + 701
9
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
99
+ 11y
98
+ ··· + 2y −1
c
2
, c
7
y
99
+ 47y
98
+ ··· − 2y −1
c
3
y
99
− 25y
98
+ ··· + 8147378y −208849
c
4
y
99
− 17y
98
+ ··· + 17086450y −271441
c
5
, c
6
, c
10
y
99
− 89y
98
+ ··· − 2y −1
c
8
y
99
+ 19y
98
+ ··· + 191938y −3249
c
9
y
99
+ 31y
98
+ ··· − 2952423990y −128300929
c
11
y
99
− 5y
98
+ ··· − 218y −9
c
12
y
99
+ 23y
98
+ ··· − 14304490y −491401
10
