12a
0652
(K12a
0652
)
A knot diagram
1
Linearized knot diagam
3 7 10 11 12 8 2 1 6 5 4 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
77
− u
76
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 77 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
77
− u
76
+ · · · − u − 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
76
+ 13u
74
+ ··· + 3u
2
+ 1
u
76
− u
75
+ ··· + 2u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
75
− 4u
74
+ ··· + 12u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
77
+ 27u
76
+ ··· − 5u − 1
c
2
, c
7
u
77
+ u
76
+ ··· − u + 1
c
3
, c
5
u
77
− u
76
+ ··· + 125u + 37
c
4
, c
10
, c
11
u
77
+ u
76
+ ··· + 3u + 1
c
8
, c
12
u
77
− 5u
76
+ ··· − 1000u + 112
c
9
u
77
− 7u
76
+ ··· + 707u − 55
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
77
+ 47y
76
+ ··· − y −1
c
2
, c
7
y
77
+ 27y
76
+ ··· − 5y −1
c
3
, c
5
y
77
− 53y
76
+ ··· − 24557y −1369
c
4
, c
10
, c
11
y
77
+ 63y
76
+ ··· − 5y −1
c
8
, c
12
y
77
+ 55y
76
+ ··· − 254176y −12544
c
9
y
77
− 13y
76
+ ··· + 127499y −3025
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.767529 + 0.640028I
6.28167 + 3.64431I 0
u = −0.767529 − 0.640028I
6.28167 − 3.64431I 0
u = 0.796599 + 0.602734I
0.58640 − 9.94909I 0
u = 0.796599 − 0.602734I
0.58640 + 9.94909I 0
u = −0.790354 + 0.596356I
−3.97378 + 5.75046I 0
u = −0.790354 − 0.596356I
−3.97378 − 5.75046I 0
u = 0.714241 + 0.723377I
4.65576 + 2.80831I 0
u = 0.714241 − 0.723377I
4.65576 − 2.80831I 0
u = 0.779593 + 0.587691I
−0.83188 − 1.51444I −4.00000 + 0.I
u = 0.779593 − 0.587691I
−0.83188 + 1.51444I −4.00000 + 0.I
u = 0.739590 + 0.614293I
0.54882 − 2.32085I −4.00000 + 4.35719I
u = 0.739590 − 0.614293I
0.54882 + 2.32085I −4.00000 − 4.35719I
u = −0.355189 + 0.885687I
−0.13092 − 6.42409I −6.49563 + 7.55459I
u = −0.355189 − 0.885687I
−0.13092 + 6.42409I −6.49563 − 7.55459I
u = 0.053490 + 1.054100I
0.50982 + 3.18183I 0
u = 0.053490 − 1.054100I
0.50982 − 3.18183I 0
u = −0.018030 + 1.072430I
−4.95935 − 1.55132I 0
u = −0.018030 − 1.072430I
−4.95935 + 1.55132I 0
u = 0.309910 + 0.869885I
−4.29728 + 2.46833I −11.58640 − 4.77585I
u = 0.309910 − 0.869885I
−4.29728 − 2.46833I −11.58640 + 4.77585I
u = −0.722298 + 0.799569I
1.242630 + 0.172666I 0
u = −0.722298 − 0.799569I
1.242630 − 0.172666I 0
u = −0.667595 + 0.617931I
0.079449 − 0.606625I −4.37867 + 4.13336I
u = −0.667595 − 0.617931I
0.079449 + 0.606625I −4.37867 − 4.13336I
u = −0.244459 + 0.872287I
−0.63700 + 1.40817I −7.77578 + 0.80099I
u = −0.244459 − 0.872287I
−0.63700 − 1.40817I −7.77578 − 0.80099I
u = 0.742292 + 0.808838I
5.79449 − 3.80795I 0
u = 0.742292 − 0.808838I
5.79449 + 3.80795I 0
u = 0.695161 + 0.854828I
3.60047 + 2.66787I 0
u = 0.695161 − 0.854828I
3.60047 − 2.66787I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.635891 + 0.903812I
3.88187 + 2.39954I 0
u = 0.635891 − 0.903812I
3.88187 − 2.39954I 0
u = −0.036950 + 1.108930I
−6.70754 − 0.49420I 0
u = −0.036950 − 1.108930I
−6.70754 + 0.49420I 0
u = 0.047933 + 1.109520I
−9.95665 + 4.78977I 0
u = 0.047933 − 1.109520I
−9.95665 − 4.78977I 0
u = −0.056065 + 1.109190I
−5.46749 − 9.03732I 0
u = −0.056065 − 1.109190I
−5.46749 + 9.03732I 0
u = −0.733136 + 0.860855I
9.52540 − 2.78409I 0
u = −0.733136 − 0.860855I
9.52540 + 2.78409I 0
u = −0.708955 + 0.907491I
0.91799 − 5.63546I 0
u = −0.708955 − 0.907491I
0.91799 + 5.63546I 0
u = −0.696328 + 0.480021I
−1.53055 + 1.07598I −4.35115 − 0.38666I
u = −0.696328 − 0.480021I
−1.53055 − 1.07598I −4.35115 + 0.38666I
u = 0.724452 + 0.906811I
5.49817 + 9.37701I 0
u = 0.724452 − 0.906811I
5.49817 − 9.37701I 0
u = 0.659555 + 0.964128I
3.92779 + 2.48033I 0
u = 0.659555 − 0.964128I
3.92779 − 2.48033I 0
u = 0.686146 + 0.450824I
−4.87661 + 3.11233I −7.53324 − 3.62541I
u = 0.686146 − 0.450824I
−4.87661 − 3.11233I −7.53324 + 3.62541I
u = −0.604287 + 1.031010I
−2.08704 + 2.38689I 0
u = −0.604287 − 1.031010I
−2.08704 − 2.38689I 0
u = −0.681244 + 0.427432I
−0.45981 − 7.28130I −2.78236 + 6.05298I
u = −0.681244 − 0.427432I
−0.45981 + 7.28130I −2.78236 − 6.05298I
u = −0.650396 + 1.008820I
−1.06542 − 4.56285I 0
u = −0.650396 − 1.008820I
−1.06542 + 4.56285I 0
u = 0.612519 + 1.032810I
−6.46139 + 1.85421I 0
u = 0.612519 − 1.032810I
−6.46139 − 1.85421I 0
u = −0.622370 + 1.034490I
−3.06619 − 6.13166I 0
u = −0.622370 − 1.034490I
−3.06619 + 6.13166I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.668586 + 1.021010I
−0.65211 + 7.70825I 0
u = 0.668586 − 1.021010I
−0.65211 − 7.70825I 0
u = −0.684993 + 1.018520I
5.14995 − 9.16004I 0
u = −0.684993 − 1.018520I
5.14995 + 9.16004I 0
u = 0.674345 + 1.040570I
−2.17378 + 7.01516I 0
u = 0.674345 − 1.040570I
−2.17378 − 7.01516I 0
u = −0.680506 + 1.041540I
−5.29992 − 11.30270I 0
u = −0.680506 − 1.041540I
−5.29992 + 11.30270I 0
u = 0.684731 + 1.041550I
−0.7247 + 15.5336I 0
u = 0.684731 − 1.041550I
−0.7247 − 15.5336I 0
u = 0.513241 + 0.334360I
4.82076 + 1.75633I 2.56531 − 3.98388I
u = 0.513241 − 0.334360I
4.82076 − 1.75633I 2.56531 + 3.98388I
u = −0.255361 + 0.463798I
−0.166525 − 0.855075I −3.98465 + 7.89301I
u = −0.255361 − 0.463798I
−0.166525 + 0.855075I −3.98465 − 7.89301I
u = −0.495154 + 0.073528I
2.07428 + 3.61210I 0.95126 − 2.73924I
u = −0.495154 − 0.073528I
2.07428 − 3.61210I 0.95126 + 2.73924I
u = 0.465846
−1.94396 −3.97790
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
77
+ 27u
76
+ ··· − 5u − 1
c
2
, c
7
u
77
+ u
76
+ ··· − u + 1
c
3
, c
5
u
77
− u
76
+ ··· + 125u + 37
c
4
, c
10
, c
11
u
77
+ u
76
+ ··· + 3u + 1
c
8
, c
12
u
77
− 5u
76
+ ··· − 1000u + 112
c
9
u
77
− 7u
76
+ ··· + 707u − 55
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
77
+ 47y
76
+ ··· − y −1
c
2
, c
7
y
77
+ 27y
76
+ ··· − 5y −1
c
3
, c
5
y
77
− 53y
76
+ ··· − 24557y −1369
c
4
, c
10
, c
11
y
77
+ 63y
76
+ ··· − 5y −1
c
8
, c
12
y
77
+ 55y
76
+ ··· − 254176y −12544
c
9
y
77
− 13y
76
+ ··· + 127499y −3025
9
