12a
0761
(K12a
0761
)
A knot diagram
1
Linearized knot diagam
3 8 10 11 12 9 2 7 1 6 5 4
Solving Sequence
6,12
5 11 4 1 10 3 2 9 7 8
c
5
c
11
c
4
c
12
c
10
c
3
c
1
c
9
c
6
c
8
c
2
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
69
+ u
68
+ ··· − u + 1i
* 1 irreducible components of dim
C
= 0, with total 69 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
69
+ u
68
+ · · · − u + 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
5
=
1
u
2
a
11
=
−u
−u
3
+ u
a
4
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
10
=
u
3
− 2u
−u
3
+ u
a
3
=
u
10
− 5u
8
+ 8u
6
− 3u
4
− 3u
2
+ 1
−u
10
+ 4u
8
− 5u
6
+ 3u
2
a
2
=
−u
27
+ 12u
25
+ ··· − 2u
5
+ 5u
3
u
27
− 11u
25
+ ··· − u
3
+ u
a
9
=
u
15
− 6u
13
+ 14u
11
− 14u
9
+ 2u
7
+ 6u
5
− 2u
3
− 2u
u
17
− 7u
15
+ 19u
13
− 22u
11
+ 3u
9
+ 14u
7
− 6u
5
− 4u
3
+ u
a
7
=
u
32
− 13u
30
+ ··· − 2u
2
+ 1
u
34
− 14u
32
+ ··· − 8u
4
+ u
2
a
8
=
u
49
− 20u
47
+ ··· − 8u
3
− u
u
51
− 21u
49
+ ··· − 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
66
+ 108u
64
+ ··· − 12u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
u
69
+ 17u
68
+ ··· + 3u + 1
c
2
, c
7
u
69
+ u
68
+ ··· + u − 1
c
3
u
69
+ u
68
+ ··· − 129u − 137
c
4
, c
5
, c
11
u
69
− u
68
+ ··· − u − 1
c
9
u
69
− 7u
68
+ ··· − u + 1
c
10
, c
12
u
69
+ 3u
68
+ ··· + 137u + 39
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
8
y
69
+ 71y
68
+ ··· − 29y −1
c
2
, c
7
y
69
− 17y
68
+ ··· + 3y −1
c
3
y
69
− 13y
68
+ ··· + 104047y −18769
c
4
, c
5
, c
11
y
69
− 57y
68
+ ··· + 3y −1
c
9
y
69
− y
68
+ ··· − 237y −1
c
10
, c
12
y
69
+ 43y
68
+ ··· + 12139y −1521
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.092180 + 0.321855I
5.91460 + 0.32154I 0
u = −1.092180 − 0.321855I
5.91460 − 0.32154I 0
u = 1.096740 + 0.333708I
5.47967 − 6.53917I 0
u = 1.096740 − 0.333708I
5.47967 + 6.53917I 0
u = 0.138165 + 0.798793I
2.56851 + 10.69340I 1.65374 − 7.70378I
u = 0.138165 − 0.798793I
2.56851 − 10.69340I 1.65374 + 7.70378I
u = 1.145410 + 0.328636I
−1.73469 − 2.50512I 0
u = 1.145410 − 0.328636I
−1.73469 + 2.50512I 0
u = −0.140078 + 0.792908I
3.02805 − 4.42671I 2.55261 + 2.89150I
u = −0.140078 − 0.792908I
3.02805 + 4.42671I 2.55261 − 2.89150I
u = 0.110756 + 0.793388I
−4.87332 + 6.59799I −3.56404 − 7.84229I
u = 0.110756 − 0.793388I
−4.87332 − 6.59799I −3.56404 + 7.84229I
u = −1.166290 + 0.294481I
0.672378 − 0.761865I 0
u = −1.166290 − 0.294481I
0.672378 + 0.761865I 0
u = 0.012224 + 0.791415I
−0.94544 − 2.84281I −1.00503 + 2.82836I
u = 0.012224 − 0.791415I
−0.94544 + 2.84281I −1.00503 − 2.82836I
u = 0.074603 + 0.785868I
−5.96794 + 1.10890I −6.58754 − 0.13737I
u = 0.074603 − 0.785868I
−5.96794 − 1.10890I −6.58754 + 0.13737I
u = −0.106193 + 0.769108I
−2.51716 − 3.12629I 2.15915 + 3.27567I
u = −0.106193 − 0.769108I
−2.51716 + 3.12629I 2.15915 − 3.27567I
u = 1.193520 + 0.331076I
−2.55117 + 2.93757I 0
u = 1.193520 − 0.331076I
−2.55117 − 2.93757I 0
u = 1.245240 + 0.345004I
2.86320 + 6.94117I 0
u = 1.245240 − 0.345004I
2.86320 − 6.94117I 0
u = −1.30108
2.90585 0
u = −1.277260 + 0.264440I
2.55105 − 1.50715I 0
u = −1.277260 − 0.264440I
2.55105 + 1.50715I 0
u = −0.070446 + 0.690883I
−1.19123 − 1.83777I 2.28274 + 4.57123I
u = −0.070446 − 0.690883I
−1.19123 + 1.83777I 2.28274 − 4.57123I
u = −1.264530 + 0.340025I
3.01410 − 1.23373I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.264530 − 0.340025I
3.01410 + 1.23373I 0
u = −0.603470 + 0.301354I
6.73153 − 0.61716I 7.13438 + 2.10966I
u = −0.603470 − 0.301354I
6.73153 + 0.61716I 7.13438 − 2.10966I
u = 0.589520 + 0.321708I
6.41855 + 6.84674I 6.30902 − 7.28330I
u = 0.589520 − 0.321708I
6.41855 − 6.84674I 6.30902 + 7.28330I
u = 1.318830 + 0.298622I
3.18430 + 5.45567I 0
u = 1.318830 − 0.298622I
3.18430 − 5.45567I 0
u = −1.315810 + 0.338996I
−1.61288 − 5.16596I 0
u = −1.315810 − 0.338996I
−1.61288 + 5.16596I 0
u = −1.362700 + 0.054216I
4.88257 − 4.45827I 0
u = −1.362700 − 0.054216I
4.88257 + 4.45827I 0
u = −0.215382 + 0.597701I
5.40705 − 2.59249I 4.08361 + 4.36083I
u = −0.215382 − 0.597701I
5.40705 + 2.59249I 4.08361 − 4.36083I
u = 1.365400 + 0.023049I
6.60295 + 0.80819I 0
u = 1.365400 − 0.023049I
6.60295 − 0.80819I 0
u = −1.346740 + 0.250330I
10.10940 + 0.56737I 0
u = −1.346740 − 0.250330I
10.10940 − 0.56737I 0
u = 1.348030 + 0.257995I
10.26320 + 5.75336I 0
u = 1.348030 − 0.257995I
10.26320 − 5.75336I 0
u = 1.333890 + 0.330249I
2.00995 + 7.10245I 0
u = 1.333890 − 0.330249I
2.00995 − 7.10245I 0
u = 0.231821 + 0.578390I
5.22939 − 3.62581I 3.68752 + 0.72835I
u = 0.231821 − 0.578390I
5.22939 + 3.62581I 3.68752 − 0.72835I
u = −1.337180 + 0.342771I
−0.32289 − 10.69870I 0
u = −1.337180 − 0.342771I
−0.32289 + 10.69870I 0
u = 1.352750 + 0.339947I
7.73069 + 8.51857I 0
u = 1.352750 − 0.339947I
7.73069 − 8.51857I 0
u = −1.352500 + 0.343185I
7.2637 − 14.8161I 0
u = −1.352500 − 0.343185I
7.2637 + 14.8161I 0
u = −1.398340 + 0.054036I
12.5949 − 7.8659I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.398340 − 0.054036I
12.5949 + 7.8659I 0
u = 1.398680 + 0.048186I
12.92990 + 1.53899I 0
u = 1.398680 − 0.048186I
12.92990 − 1.53899I 0
u = 0.462955 + 0.294667I
−0.73130 + 3.44818I 1.19909 − 9.10721I
u = 0.462955 − 0.294667I
−0.73130 − 3.44818I 1.19909 + 9.10721I
u = −0.465435 + 0.129552I
0.992427 − 0.375285I 9.31448 + 1.85856I
u = −0.465435 − 0.129552I
0.992427 + 0.375285I 9.31448 − 1.85856I
u = 0.246534 + 0.364424I
−1.34874 − 0.90520I −2.53630 + 0.15595I
u = 0.246534 − 0.364424I
−1.34874 + 0.90520I −2.53630 − 0.15595I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
u
69
+ 17u
68
+ ··· + 3u + 1
c
2
, c
7
u
69
+ u
68
+ ··· + u − 1
c
3
u
69
+ u
68
+ ··· − 129u − 137
c
4
, c
5
, c
11
u
69
− u
68
+ ··· − u − 1
c
9
u
69
− 7u
68
+ ··· − u + 1
c
10
, c
12
u
69
+ 3u
68
+ ··· + 137u + 39
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
8
y
69
+ 71y
68
+ ··· − 29y −1
c
2
, c
7
y
69
− 17y
68
+ ··· + 3y −1
c
3
y
69
− 13y
68
+ ··· + 104047y −18769
c
4
, c
5
, c
11
y
69
− 57y
68
+ ··· + 3y −1
c
9
y
69
− y
68
+ ··· − 237y −1
c
10
, c
12
y
69
+ 43y
68
+ ··· + 12139y −1521
9
