11a
221
(K11a
221
)
A knot diagram
1
Linearized knot diagam
7 1 10 11 8 2 5 6 3 4 9
Solving Sequence
2,6
7 1
3,9
10 8 5 11 4
c
6
c
1
c
2
c
9
c
8
c
5
c
11
c
4
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h2.58574 × 10
22
u
40
+ 1.94775 × 10
22
u
39
+ ··· + 4.92580 × 10
22
b + 1.64635 × 10
22
,
− 8.09547 × 10
21
u
40
+ 5.99125 × 10
21
u
39
+ ··· + 1.97032 × 10
23
a + 1.41113 × 10
23
, u
41
+ u
40
+ ··· − u
2
+ 4i
I
v
1
= ha, b − 1, v
2
+ v −1i
* 2 irreducible components of dim
C
= 0, with total 43 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
= h2.59×10
22
u
40
+1.95×10
22
u
39
+· · ·+4.93×10
22
b+1.65×10
22
, −8.10×
10
21
u
40
+5.99×10
21
u
39
+· · ·+1.97×10
23
a+1.41×10
23
, u
41
+u
40
+· · ·−u
2
+4i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
9
=
0.0410870u
40
− 0.0304075u
39
+ ··· + 2.81027u − 0.716193
−0.524938u
40
− 0.395417u
39
+ ··· − 2.01455u − 0.334229
a
10
=
−0.467248u
40
− 0.157588u
39
+ ··· + 1.16973u − 0.888909
−0.369945u
40
− 0.267670u
39
+ ··· − 1.30888u − 0.201698
a
8
=
−0.483851u
40
− 0.425824u
39
+ ··· + 0.795719u − 1.05042
−0.524938u
40
− 0.395417u
39
+ ··· − 2.01455u − 0.334229
a
5
=
−0.483851u
40
− 0.425824u
39
+ ··· + 0.795719u − 1.05042
0.0665166u
40
+ 0.364543u
39
+ ··· + 0.0791500u + 0.566335
a
11
=
−0.526272u
40
− 0.615949u
39
+ ··· − 0.847432u − 2.92163
−0.400524u
40
+ 0.0414901u
39
+ ··· − 0.0904238u − 0.792124
a
4
=
0.405800u
40
+ 0.723766u
39
+ ··· − 0.573295u + 3.61744
0.260796u
40
+ 0.239160u
39
+ ··· + 0.874019u + 0.565373
a
4
=
0.405800u
40
+ 0.723766u
39
+ ··· − 0.573295u + 3.61744
0.260796u
40
+ 0.239160u
39
+ ··· + 0.874019u + 0.565373
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
3657064353645414395094
24629024686271213113517
u
40
−
45534143106179376249815
24629024686271213113517
u
39
+ ··· +
159536480684658033188744
24629024686271213113517
u −
110862013990068277848729
24629024686271213113517
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
41
+ u
40
+ ··· − u
2
+ 4
c
2
u
41
+ 15u
40
+ ··· + 8u − 16
c
3
, c
4
, c
9
c
10
u
41
− 2u
40
+ ··· − u − 1
c
5
, c
7
, c
8
u
41
− 3u
40
+ ··· − 6u + 1
c
11
u
41
+ 12u
40
+ ··· − 503u − 73
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
41
+ 15y
40
+ ··· + 8y −16
c
2
y
41
+ 19y
40
+ ··· + 16416y −256
c
3
, c
4
, c
9
c
10
y
41
− 48y
40
+ ··· + 3y −1
c
5
, c
7
, c
8
y
41
− 35y
40
+ ··· + 62y −1
c
11
y
41
− 12y
40
+ ··· + 23351y −5329
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.122270 + 1.001390I
a = −0.003929 − 0.811821I
b = 0.562217 + 0.598084I
4.86048 − 2.17709I 3.44971 + 3.79306I
u = −0.122270 − 1.001390I
a = −0.003929 + 0.811821I
b = 0.562217 − 0.598084I
4.86048 + 2.17709I 3.44971 − 3.79306I
u = 0.551581 + 0.859891I
a = 0.449439 + 1.057630I
b = 0.181877 − 0.689383I
0.32453 + 2.20665I 2.42130 − 3.15065I
u = 0.551581 − 0.859891I
a = 0.449439 − 1.057630I
b = 0.181877 + 0.689383I
0.32453 − 2.20665I 2.42130 + 3.15065I
u = 1.02478
a = −0.908342
b = 1.33636
2.95183 3.34750
u = −0.679117 + 0.681890I
a = 0.700414 − 1.106750I
b = 0.001662 + 0.650682I
2.92066 + 0.49867I 9.33255 − 1.40381I
u = −0.679117 − 0.681890I
a = 0.700414 + 1.106750I
b = 0.001662 − 0.650682I
2.92066 − 0.49867I 9.33255 + 1.40381I
u = −0.545090 + 0.785733I
a = −0.69091 + 2.59079I
b = −1.209880 − 0.257619I
7.70281 − 1.46253I 4.97551 + 4.38414I
u = −0.545090 − 0.785733I
a = −0.69091 − 2.59079I
b = −1.209880 + 0.257619I
7.70281 + 1.46253I 4.97551 − 4.38414I
u = 0.815378 + 0.666881I
a = 0.75804 + 1.25639I
b = −0.085807 − 0.724003I
11.08220 − 2.09439I 10.58118 + 0.49911I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.815378 − 0.666881I
a = 0.75804 − 1.25639I
b = −0.085807 + 0.724003I
11.08220 + 2.09439I 10.58118 − 0.49911I
u = 0.925345 + 0.534295I
a = −0.848621 − 0.304695I
b = 1.281480 + 0.256105I
−1.06929 − 3.78517I 3.33312 + 5.32313I
u = 0.925345 − 0.534295I
a = −0.848621 + 0.304695I
b = 1.281480 − 0.256105I
−1.06929 + 3.78517I 3.33312 − 5.32313I
u = 0.512185 + 0.958100I
a = −0.69987 − 1.88985I
b = −1.298390 + 0.245537I
−1.14433 + 2.71303I 3.06796 − 2.16565I
u = 0.512185 − 0.958100I
a = −0.69987 + 1.88985I
b = −1.298390 − 0.245537I
−1.14433 − 2.71303I 3.06796 + 2.16565I
u = 0.471678 + 0.778273I
a = −0.539722 − 0.459733I
b = 1.018830 + 0.371555I
−0.495471 + 1.323540I 2.90171 − 5.22285I
u = 0.471678 − 0.778273I
a = −0.539722 + 0.459733I
b = 1.018830 − 0.371555I
−0.495471 − 1.323540I 2.90171 + 5.22285I
u = −0.579330 + 0.928710I
a = −0.625557 + 0.571406I
b = 1.082590 − 0.468575I
7.20747 − 3.04463I 5.27357 + 2.39823I
u = −0.579330 − 0.928710I
a = −0.625557 − 0.571406I
b = 1.082590 + 0.468575I
7.20747 + 3.04463I 5.27357 − 2.39823I
u = −0.790308 + 0.341056I
a = −0.772495 + 0.188053I
b = 1.220600 − 0.156477I
−2.45808 + 0.68070I −0.75996 + 1.22832I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.790308 − 0.341056I
a = −0.772495 − 0.188053I
b = 1.220600 + 0.156477I
−2.45808 − 0.68070I −0.75996 − 1.22832I
u = −0.637944 + 0.967189I
a = 0.396872 − 1.193270I
b = 0.182840 + 0.800800I
2.06145 − 5.60392I 6.28993 + 7.67426I
u = −0.637944 − 0.967189I
a = 0.396872 + 1.193270I
b = 0.182840 − 0.800800I
2.06145 + 5.60392I 6.28993 − 7.67426I
u = −1.003890 + 0.629446I
a = −0.896695 + 0.361308I
b = 1.320330 − 0.305527I
6.66704 + 5.82869I 5.58070 − 3.39540I
u = −1.003890 − 0.629446I
a = −0.896695 − 0.361308I
b = 1.320330 + 0.305527I
6.66704 − 5.82869I 5.58070 + 3.39540I
u = −0.070929 + 1.209930I
a = −0.919362 + 0.220397I
b = −1.42404 − 0.03377I
−7.93550 − 1.94462I −3.70499 + 3.68184I
u = −0.070929 − 1.209930I
a = −0.919362 − 0.220397I
b = −1.42404 + 0.03377I
−7.93550 + 1.94462I −3.70499 − 3.68184I
u = −0.028788 + 0.761611I
a = −0.057057 + 0.439082I
b = 0.642973 − 0.323659I
−1.37623 + 1.10536I −2.43864 − 5.69625I
u = −0.028788 − 0.761611I
a = −0.057057 − 0.439082I
b = 0.642973 + 0.323659I
−1.37623 − 1.10536I −2.43864 + 5.69625I
u = 0.703874 + 1.021500I
a = 0.382110 + 1.273810I
b = 0.170327 − 0.865341I
9.99184 + 7.80021I 8.36490 − 5.64860I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.703874 − 1.021500I
a = 0.382110 − 1.273810I
b = 0.170327 + 0.865341I
9.99184 − 7.80021I 8.36490 + 5.64860I
u = −0.601596 + 1.090350I
a = −0.30873 + 1.63089I
b = −1.364280 − 0.291615I
−4.56137 − 5.79983I −1.81042 + 3.80578I
u = −0.601596 − 1.090350I
a = −0.30873 − 1.63089I
b = −1.364280 + 0.291615I
−4.56137 + 5.79983I −1.81042 − 3.80578I
u = 0.241330 + 1.238970I
a = −0.698673 − 0.677867I
b = −1.43772 + 0.11527I
−1.67461 + 4.38863I 0.33432 − 3.52334I
u = 0.241330 − 1.238970I
a = −0.698673 + 0.677867I
b = −1.43772 − 0.11527I
−1.67461 − 4.38863I 0.33432 + 3.52334I
u = 0.689794 + 1.111280I
a = −0.10318 − 1.66094I
b = −1.37517 + 0.33619I
−2.86444 + 9.70772I 1.83000 − 8.47841I
u = 0.689794 − 1.111280I
a = −0.10318 + 1.66094I
b = −1.37517 − 0.33619I
−2.86444 − 9.70772I 1.83000 + 8.47841I
u = −0.758005 + 1.117850I
a = 0.03150 + 1.68920I
b = −1.37919 − 0.37091I
5.09814 − 12.24280I 4.42370 + 7.04565I
u = −0.758005 − 1.117850I
a = 0.03150 − 1.68920I
b = −1.37919 + 0.37091I
5.09814 + 12.24280I 4.42370 − 7.04565I
u = −0.573323
a = 2.01606
b = −0.386383
8.19168 12.7990
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.360746
a = 1.28515
b = −0.132462
0.783707 12.9610
9
II. I
v
1
= ha, b − 1, v
2
+ v − 1i
(i) Arc colorings
a
2
=
v
0
a
6
=
1
0
a
7
=
1
0
a
1
=
v
0
a
3
=
v
0
a
9
=
0
1
a
10
=
−v + 1
1
a
8
=
1
1
a
5
=
0
−1
a
11
=
v
v
a
4
=
−v + 1
−v
a
4
=
−v + 1
−v
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
2
c
3
, c
4
, c
11
u
2
+ u − 1
c
5
(u − 1)
2
c
7
, c
8
(u + 1)
2
c
9
, c
10
u
2
− u − 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
2
c
3
, c
4
, c
9
c
10
, c
11
y
2
− 3y + 1
c
5
, c
7
, c
8
(y − 1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.618034
a = 0
b = 1.00000
−0.657974 3.00000
v = −1.61803
a = 0
b = 1.00000
7.23771 3.00000
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
2
(u
41
+ u
40
+ ··· − u
2
+ 4)
c
2
u
2
(u
41
+ 15u
40
+ ··· + 8u − 16)
c
3
, c
4
(u
2
+ u − 1)(u
41
− 2u
40
+ ··· − u − 1)
c
5
((u − 1)
2
)(u
41
− 3u
40
+ ··· − 6u + 1)
c
7
, c
8
((u + 1)
2
)(u
41
− 3u
40
+ ··· − 6u + 1)
c
9
, c
10
(u
2
− u − 1)(u
41
− 2u
40
+ ··· − u − 1)
c
11
(u
2
+ u − 1)(u
41
+ 12u
40
+ ··· − 503u − 73)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
2
(y
41
+ 15y
40
+ ··· + 8y − 16)
c
2
y
2
(y
41
+ 19y
40
+ ··· + 16416y − 256)
c
3
, c
4
, c
9
c
10
(y
2
− 3y + 1)(y
41
− 48y
40
+ ··· + 3y − 1)
c
5
, c
7
, c
8
((y − 1)
2
)(y
41
− 35y
40
+ ··· + 62y − 1)
c
11
(y
2
− 3y + 1)(y
41
− 12y
40
+ ··· + 23351y − 5329)
15
