12a
0684
(K12a
0684
)
A knot diagram
1
Linearized knot diagam
3 7 11 12 10 8 2 1 6 5 4 9
Solving Sequence
2,8
7 3 1 9 6 10 5 11 12 4
c
7
c
2
c
1
c
8
c
6
c
9
c
5
c
10
c
12
c
4
c
3
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
67
+ u
66
+ ··· + 3u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 67 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
67
+ u
66
+ · · · + 3u
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
5
=
u
26
+ 5u
24
+ ··· + 3u
2
+ 1
u
26
+ 4u
24
+ ··· − 2u
4
+ u
2
a
11
=
u
38
+ 7u
36
+ ··· + 4u
2
+ 1
u
38
+ 6u
36
+ ··· + 2u
4
− u
2
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
4
=
−u
54
− 9u
52
+ ··· + 4u
2
+ 1
−u
56
− 10u
54
+ ··· − 34u
6
− 10u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
65
− 4u
64
+ ··· − 16u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
67
+ 23u
66
+ ··· − 6u − 1
c
2
, c
7
u
67
+ u
66
+ ··· + 3u
2
+ 1
c
3
, c
4
, c
11
u
67
+ u
66
+ ··· + 2u + 1
c
5
, c
9
, c
10
u
67
− 3u
66
+ ··· + 11u − 16
c
8
, c
12
u
67
− 5u
66
+ ··· − 32u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
67
+ 43y
66
+ ··· − 14y −1
c
2
, c
7
y
67
+ 23y
66
+ ··· − 6y −1
c
3
, c
4
, c
11
y
67
− 53y
66
+ ··· − 6y −1
c
5
, c
9
, c
10
y
67
+ 63y
66
+ ··· − 1383y −256
c
8
, c
12
y
67
+ 35y
66
+ ··· − 12512y −256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.803360 + 0.638492I
2.78379 + 9.20045I −4.00000 − 5.04305I
u = −0.803360 − 0.638492I
2.78379 − 9.20045I −4.00000 + 5.04305I
u = 0.800124 + 0.647068I
7.09459 − 4.72698I 0. + 2.48714I
u = 0.800124 − 0.647068I
7.09459 + 4.72698I 0. − 2.48714I
u = −0.794421 + 0.657199I
3.54889 + 0.19967I 0
u = −0.794421 − 0.657199I
3.54889 − 0.19967I 0
u = −0.729773 + 0.636528I
0.83498 + 2.07700I −1.30731 − 4.65040I
u = −0.729773 − 0.636528I
0.83498 − 2.07700I −1.30731 + 4.65040I
u = 0.701441 + 0.764368I
0.332471 − 0.137935I −4.00000 + 0.I
u = 0.701441 − 0.764368I
0.332471 + 0.137935I −4.00000 + 0.I
u = 0.751806 + 0.599939I
−4.30064 − 4.22428I −7.11593 + 3.82963I
u = 0.751806 − 0.599939I
−4.30064 + 4.22428I −7.11593 − 3.82963I
u = 0.022057 + 1.053290I
−4.58704 + 1.51218I −9.45944 − 4.55261I
u = 0.022057 − 1.053290I
−4.58704 − 1.51218I −9.45944 + 4.55261I
u = 0.096493 + 1.057100I
−2.57943 − 0.08281I −8.50549 + 0.I
u = 0.096493 − 1.057100I
−2.57943 + 0.08281I −8.50549 + 0.I
u = −0.669102 + 0.844952I
3.28932 − 2.58275I 0
u = −0.669102 − 0.844952I
3.28932 + 2.58275I 0
u = 0.529127 + 0.939240I
−0.06741 + 5.98627I 0
u = 0.529127 − 0.939240I
−0.06741 − 5.98627I 0
u = 0.647786 + 0.655651I
0.241433 + 0.748431I −4.13794 − 3.90803I
u = 0.647786 − 0.655651I
0.241433 − 0.748431I −4.13794 + 3.90803I
u = −0.092376 + 1.074670I
0.91363 − 4.29574I 0
u = −0.092376 − 1.074670I
0.91363 + 4.29574I 0
u = −0.028914 + 1.086230I
−9.95694 − 3.35433I −14.2561 + 0.I
u = −0.028914 − 1.086230I
−9.95694 + 3.35433I −14.2561 + 0.I
u = 0.087961 + 1.086010I
−3.41796 + 8.65689I 0
u = 0.087961 − 1.086010I
−3.41796 − 8.65689I 0
u = −0.558836 + 0.972282I
3.64416 − 1.88415I 0
u = −0.558836 − 0.972282I
3.64416 + 1.88415I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.567085 + 0.994839I
−0.56916 − 2.29584I 0
u = 0.567085 − 0.994839I
−0.56916 + 2.29584I 0
u = 0.672545 + 0.927735I
−0.16758 + 5.42739I 0
u = 0.672545 − 0.927735I
−0.16758 − 5.42739I 0
u = −0.762268 + 0.857726I
6.75974 + 1.69859I 0
u = −0.762268 − 0.857726I
6.75974 − 1.69859I 0
u = 0.760734 + 0.867270I
10.68380 + 2.86836I 0
u = 0.760734 − 0.867270I
10.68380 − 2.86836I 0
u = −0.757930 + 0.876228I
6.70343 − 7.43134I 0
u = −0.757930 − 0.876228I
6.70343 + 7.43134I 0
u = −0.650192 + 0.524941I
−4.92057 − 2.05889I −8.44124 + 3.45168I
u = −0.650192 − 0.524941I
−4.92057 + 2.05889I −8.44124 − 3.45168I
u = −0.271313 + 0.769915I
−4.53163 − 2.07205I −11.22172 + 5.13585I
u = −0.271313 − 0.769915I
−4.53163 + 2.07205I −11.22172 − 5.13585I
u = 0.649976 + 0.994312I
−0.77232 + 4.37126I 0
u = 0.649976 − 0.994312I
−0.77232 − 4.37126I 0
u = −0.631035 + 1.015860I
−6.25413 − 2.96400I 0
u = −0.631035 − 1.015860I
−6.25413 + 2.96400I 0
u = −0.671448 + 1.010100I
−0.27092 − 7.45199I 0
u = −0.671448 − 1.010100I
−0.27092 + 7.45199I 0
u = 0.669526 + 1.027320I
−5.55831 + 9.64000I 0
u = 0.669526 − 1.027320I
−5.55831 − 9.64000I 0
u = −0.701809 + 1.019670I
2.45618 − 5.84517I 0
u = −0.701809 − 1.019670I
2.45618 + 5.84517I 0
u = 0.701023 + 1.026000I
5.95293 + 10.38420I 0
u = 0.701023 − 1.026000I
5.95293 − 10.38420I 0
u = −0.699473 + 1.030620I
1.6032 − 14.8599I 0
u = −0.699473 − 1.030620I
1.6032 + 14.8599I 0
u = 0.634928 + 0.324518I
1.12766 + 6.71660I −2.59886 − 5.83457I
u = 0.634928 − 0.324518I
1.12766 − 6.71660I −2.59886 + 5.83457I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.616892 + 0.299152I
5.31573 − 2.35989I 1.86076 + 3.06293I
u = −0.616892 − 0.299152I
5.31573 + 2.35989I 1.86076 − 3.06293I
u = 0.597047 + 0.266295I
1.62809 − 2.00771I −1.45361 + 0.46558I
u = 0.597047 − 0.266295I
1.62809 + 2.00771I −1.45361 − 0.46558I
u = 0.255920 + 0.412745I
−0.118014 + 0.819285I −3.06015 − 8.28989I
u = 0.255920 − 0.412745I
−0.118014 − 0.819285I −3.06015 + 8.28989I
u = −0.412874
−2.43012 −1.69860
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
67
+ 23u
66
+ ··· − 6u − 1
c
2
, c
7
u
67
+ u
66
+ ··· + 3u
2
+ 1
c
3
, c
4
, c
11
u
67
+ u
66
+ ··· + 2u + 1
c
5
, c
9
, c
10
u
67
− 3u
66
+ ··· + 11u − 16
c
8
, c
12
u
67
− 5u
66
+ ··· − 32u + 16
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
67
+ 43y
66
+ ··· − 14y −1
c
2
, c
7
y
67
+ 23y
66
+ ··· − 6y −1
c
3
, c
4
, c
11
y
67
− 53y
66
+ ··· − 6y −1
c
5
, c
9
, c
10
y
67
+ 63y
66
+ ··· − 1383y −256
c
8
, c
12
y
67
+ 35y
66
+ ··· − 12512y −256
9
