11a
121
(K11a
121
)
A knot diagram
1
Linearized knot diagam
6 1 10 8 2 5 3 11 4 9 7
Solving Sequence
2,6
1 3 5 7 8 4 11 9 10
c
1
c
2
c
5
c
6
c
7
c
4
c
11
c
8
c
10
c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
11
+ 2u
9
+ 4u
7
+ 4u
5
− u
4
+ 3u
3
− u
2
+ 2u − 1i
I
u
2
= hu
48
− u
47
+ ··· + 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 59 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
11
+ 2u
9
+ 4u
7
+ 4u
5
− u
4
+ 3u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
5
=
−u
u
a
7
=
−u
3
u
3
+ u
a
8
=
u
9
+ 2u
7
+ 3u
5
+ 2u
3
+ u
−u
9
− 2u
7
− 3u
5
+ u
4
− 2u
3
+ u
2
− u + 1
a
4
=
u
8
− u
7
+ u
6
− 2u
5
+ 2u
4
− 2u
3
+ u
2
− 2u
−u
9
− u
8
− u
7
− u
6
− u
5
− 2u
4
− u
2
+ u
a
11
=
−u
8
− u
6
− u
4
+ 1
u
8
+ 2u
6
+ 2u
4
+ 2u
2
a
9
=
u
10
+ u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ 2u
3
− u
2
+ u
−u
10
− u
9
− 2u
8
− 2u
7
− 2u
6
− 3u
5
− u
4
− 2u
3
+ u
2
− u + 1
a
10
=
u
10
+ 2u
8
+ u
7
+ 3u
6
+ u
5
+ 2u
4
+ u
3
+ u
2
+ u
−u
8
− u
7
− u
6
− u
5
− u
4
− u
3
− u + 1
a
10
=
u
10
+ 2u
8
+ u
7
+ 3u
6
+ u
5
+ 2u
4
+ u
3
+ u
2
+ u
−u
8
− u
7
− u
6
− u
5
− u
4
− u
3
− u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
10
+ 4u
9
+ 4u
8
+ 8u
7
+ 12u
6
+ 16u
5
+ 8u
4
+ 8u
3
+ 4u
2
+ 8u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
9
u
11
+ 2u
9
+ 4u
7
+ 4u
5
− u
4
+ 3u
3
− u
2
+ 2u − 1
c
2
, c
6
, c
8
c
10
u
11
+ 4u
10
+ ··· + 2u − 1
c
4
, c
11
u
11
+ 2u
9
− 2u
8
+ 10u
7
+ 12u
5
− 3u
4
+ 5u
3
− u
2
− 1
c
7
u
11
− 7u
10
+ ··· + 28u − 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
9
y
11
+ 4y
10
+ ··· + 2y −1
c
2
, c
6
, c
8
c
10
y
11
+ 8y
10
+ ··· + 22y −1
c
4
, c
11
y
11
+ 4y
10
+ ··· − 2y −1
c
7
y
11
− 3y
10
+ ··· + 48y −64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.111009 + 1.030810I
−5.93919 − 3.55367I −6.35449 + 4.86751I
u = −0.111009 − 1.030810I
−5.93919 + 3.55367I −6.35449 − 4.86751I
u = 0.594105 + 0.723647I
1.48764 + 1.96750I 4.49213 − 3.23948I
u = 0.594105 − 0.723647I
1.48764 − 1.96750I 4.49213 + 3.23948I
u = −0.817015 + 0.707633I
6.68078 + 3.13136I 8.76083 − 0.56604I
u = −0.817015 − 0.707633I
6.68078 − 3.13136I 8.76083 + 0.56604I
u = −0.617277 + 0.966546I
−0.07920 − 7.68222I 0.97285 + 8.49443I
u = −0.617277 − 0.966546I
−0.07920 + 7.68222I 0.97285 − 8.49443I
u = 0.729012 + 1.011350I
4.8176 + 14.7555I 5.24582 − 10.31160I
u = 0.729012 − 1.011350I
4.8176 − 14.7555I 5.24582 + 10.31160I
u = 0.444369
0.869046 11.7660
5
II. I
u
2
= hu
48
− u
47
+ · · · + 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
5
=
−u
u
a
7
=
−u
3
u
3
+ u
a
8
=
u
9
+ 2u
7
+ 3u
5
+ 2u
3
+ u
u
11
+ u
9
+ 2u
7
+ u
5
+ u
3
+ u
a
4
=
−u
21
− 4u
19
+ ··· − 2u
3
− u
−u
23
− 3u
21
+ ··· − 2u
3
+ u
a
11
=
−u
8
− u
6
− u
4
+ 1
u
8
+ 2u
6
+ 2u
4
+ 2u
2
a
9
=
−u
27
− 4u
25
+ ··· + 10u
5
+ 3u
3
u
27
+ 5u
25
+ ··· − u
3
+ u
a
10
=
−u
46
− 7u
44
+ ··· − 4u
4
+ 1
u
46
+ 8u
44
+ ··· + 4u
4
+ u
2
a
10
=
−u
46
− 7u
44
+ ··· − 4u
4
+ 1
u
46
+ 8u
44
+ ··· + 4u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
45
+ 28u
43
+ 132u
41
+ 448u
39
+ 1224u
37
+ 2772u
35
+ 5348u
33
+
8916u
31
+ 12948u
29
−4u
28
+ 16456u
27
−20u
26
+ 18292u
25
−68u
24
+ 17704u
23
−164u
22
+
14776u
21
− 308u
20
+ 10428u
19
− 468u
18
+ 6020u
17
− 576u
16
+ 2644u
15
− 580u
14
+
720u
13
−468u
12
−288u
10
−88u
9
−124u
8
−4u
7
−24u
6
+ 36u
5
+ 8u
4
+ 24u
3
+ 4u
2
+ 4u + 2
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
9
u
48
− u
47
+ ··· + 2u + 1
c
2
, c
6
, c
8
c
10
u
48
+ 15u
47
+ ··· + 8u
3
+ 1
c
4
, c
11
u
48
+ 5u
47
+ ··· + 12u + 1
c
7
(u
24
+ 3u
23
+ ··· + 18u + 7)
2
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
9
y
48
+ 15y
47
+ ··· + 8y
3
+ 1
c
2
, c
6
, c
8
c
10
y
48
+ 35y
47
+ ··· + 88y
2
+ 1
c
4
, c
11
y
48
− 5y
47
+ ··· − 24y + 1
c
7
(y
24
− 9y
23
+ ··· − 212y + 49)
2
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.447030 + 0.894068I
0.85406 + 3.28062I 1.88284 − 1.76353I
u = −0.447030 − 0.894068I
0.85406 − 3.28062I 1.88284 + 1.76353I
u = −0.037970 + 1.018320I
−3.47428 + 2.08425I −3.81787 − 2.59078I
u = −0.037970 − 1.018320I
−3.47428 − 2.08425I −3.81787 + 2.59078I
u = 0.103335 + 0.964930I
−2.07060 + 1.71275I 0.95839 − 4.38827I
u = 0.103335 − 0.964930I
−2.07060 − 1.71275I 0.95839 + 4.38827I
u = 0.709249 + 0.753994I
1.54659 + 2.07802I 3.74247 − 4.14356I
u = 0.709249 − 0.753994I
1.54659 − 2.07802I 3.74247 + 4.14356I
u = 0.161802 + 1.028080I
0.15229 + 3.45771I 1.61918 − 3.33537I
u = 0.161802 − 1.028080I
0.15229 − 3.45771I 1.61918 + 3.33537I
u = 0.786969 + 0.691947I
0.15229 − 3.45771I 1.61918 + 3.33537I
u = 0.786969 − 0.691947I
0.15229 + 3.45771I 1.61918 − 3.33537I
u = −0.156596 + 1.043700I
−0.78809 − 9.12338I −0.18249 + 8.13527I
u = −0.156596 − 1.043700I
−0.78809 + 9.12338I −0.18249 − 8.13527I
u = −0.779513 + 0.728650I
3.78730 + 1.05884I 9.33375 − 1.03697I
u = −0.779513 − 0.728650I
3.78730 − 1.05884I 9.33375 + 1.03697I
u = 0.820160 + 0.698926I
5.77023 − 8.94227I 7.03302 + 5.48937I
u = 0.820160 − 0.698926I
5.77023 + 8.94227I 7.03302 − 5.48937I
u = −0.559504 + 0.928720I
−3.47428 − 2.08425I −3.81787 + 2.59078I
u = −0.559504 − 0.928720I
−3.47428 + 2.08425I −3.81787 − 2.59078I
u = 0.357761 + 0.828361I
1.54659 + 2.07802I 3.74247 − 4.14356I
u = 0.357761 − 0.828361I
1.54659 − 2.07802I 3.74247 + 4.14356I
u = −0.798379 + 0.782289I
7.98533 10.04300 + 0.I
u = −0.798379 − 0.782289I
7.98533 10.04300 + 0.I
u = 0.795531 + 0.794799I
7.45278 + 5.81585I 8.97012 − 5.48927I
u = 0.795531 − 0.794799I
7.45278 − 5.81585I 8.97012 + 5.48927I
u = 0.644764 + 0.924836I
0.94545 + 3.01303I 3.90717 − 2.47987I
u = 0.644764 − 0.924836I
0.94545 − 3.01303I 3.90717 + 2.47987I
u = 0.684868 + 0.970999I
0.85406 + 3.28062I 1.88284 − 1.76353I
u = 0.684868 − 0.970999I
0.85406 − 3.28062I 1.88284 + 1.76353I
9
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.750786 + 0.945298I
6.98909 8.15485 + 0.I
u = 0.750786 − 0.945298I
6.98909 8.15485 + 0.I
u = −0.748039 + 0.955471I
7.45278 − 5.81585I 8.97012 + 5.48927I
u = −0.748039 − 0.955471I
7.45278 + 5.81585I 8.97012 − 5.48927I
u = −0.718495 + 0.983429I
3.01107 − 6.72706I 7.45449 + 6.34172I
u = −0.718495 − 0.983429I
3.01107 + 6.72706I 7.45449 − 6.34172I
u = 0.712082 + 1.003140I
−0.78809 + 9.12338I 0. − 8.13527I
u = 0.712082 − 1.003140I
−0.78809 − 9.12338I 0. + 8.13527I
u = −0.730704 + 1.006040I
5.77023 − 8.94227I 7.03302 + 5.48937I
u = −0.730704 − 1.006040I
5.77023 + 8.94227I 7.03302 − 5.48937I
u = −0.520871 + 0.529700I
0.94545 + 3.01303I 3.90717 − 2.47987I
u = −0.520871 − 0.529700I
0.94545 − 3.01303I 3.90717 + 2.47987I
u = −0.619099 + 0.144052I
3.01107 − 6.72706I 7.45449 + 6.34172I
u = −0.619099 − 0.144052I
3.01107 + 6.72706I 7.45449 − 6.34172I
u = 0.605322 + 0.114770I
3.78730 + 1.05884I 9.33375 − 1.03697I
u = 0.605322 − 0.114770I
3.78730 − 1.05884I 9.33375 + 1.03697I
u = −0.516429 + 0.228211I
−2.07060 − 1.71275I 0.95839 + 4.38827I
u = −0.516429 − 0.228211I
−2.07060 + 1.71275I 0.95839 − 4.38827I
10
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
9
(u
11
+ 2u
9
+ ··· + 2u − 1)(u
48
− u
47
+ ··· + 2u + 1)
c
2
, c
6
, c
8
c
10
(u
11
+ 4u
10
+ ··· + 2u − 1)(u
48
+ 15u
47
+ ··· + 8u
3
+ 1)
c
4
, c
11
(u
11
+ 2u
9
− 2u
8
+ 10u
7
+ 12u
5
− 3u
4
+ 5u
3
− u
2
− 1)
· (u
48
+ 5u
47
+ ··· + 12u + 1)
c
7
(u
11
− 7u
10
+ ··· + 28u − 8)(u
24
+ 3u
23
+ ··· + 18u + 7)
2
11
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
9
(y
11
+ 4y
10
+ ··· + 2y −1)(y
48
+ 15y
47
+ ··· + 8y
3
+ 1)
c
2
, c
6
, c
8
c
10
(y
11
+ 8y
10
+ ··· + 22y −1)(y
48
+ 35y
47
+ ··· + 88y
2
+ 1)
c
4
, c
11
(y
11
+ 4y
10
+ ··· − 2y −1)(y
48
− 5y
47
+ ··· − 24y + 1)
c
7
(y
11
− 3y
10
+ ··· + 48y −64)(y
24
− 9y
23
+ ··· − 212y + 49)
2
12
