11a
81
(K11a
81
)
A knot diagram
1
Linearized knot diagam
6 1 10 9 2 3 4 11 7 8 5
Solving Sequence
2,6
1 3
7,9
10 5 4 11 8
c
1
c
2
c
6
c
9
c
5
c
4
c
11
c
8
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.12437 × 10
21
u
64
+ 2.08104 × 10
21
u
63
+ ··· + 3.92161 × 10
20
b − 9.56908 × 10
20
,
6.77960 × 10
19
u
64
− 7.94718 × 10
20
u
63
+ ··· + 3.92161 × 10
20
a + 1.89541 × 10
21
, u
65
+ 2u
64
+ ··· + u − 1i
I
u
2
= hb + u, a − u − 1, u
2
+ u + 1i
* 2 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
= h1.12 × 10
21
u
64
+ 2.08 × 10
21
u
63
+ · · · + 3.92 × 10
20
b − 9.57 × 10
20
, 6.78 ×
10
19
u
64
−7.95×10
20
u
63
+· · ·+3.92×10
20
a+1.90×10
21
, u
65
+2u
64
+· · ·+u−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
7
=
−u
5
− 2u
3
− u
−u
7
− u
5
+ u
a
9
=
−0.172878u
64
+ 2.02651u
63
+ ··· + 2.31811u − 4.83325
−2.86712u
64
− 5.30659u
63
+ ··· + 1.95308u + 2.44009
a
10
=
−0.142247u
64
+ 2.05786u
63
+ ··· + 1.94975u − 4.74893
−2.69775u
64
− 4.93896u
63
+ ··· + 2.26672u + 2.24110
a
5
=
−u
u
a
4
=
5.04000u
64
+ 5.88259u
63
+ ··· − 11.8961u + 0.0715256
0.371835u
64
+ 4.36917u
63
+ ··· + 11.7089u − 4.79741
a
11
=
u
4
+ u
2
+ 1
−u
4
a
8
=
−0.206126u
64
+ 1.99373u
63
+ ··· + 3.07367u − 4.01687
−3.03387u
64
− 5.47353u
63
+ ··· + 2.13727u + 2.43980
a
8
=
−0.206126u
64
+ 1.99373u
63
+ ··· + 3.07367u − 4.01687
−3.03387u
64
− 5.47353u
63
+ ··· + 2.13727u + 2.43980
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
3365010802379045894269
392161237007130374129
u
64
−
314262698830792944879
392161237007130374129
u
63
+ ··· +
15377811800569051171877
392161237007130374129
u −
7348835260697976503736
392161237007130374129
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
65
− 2u
64
+ ··· + u + 1
c
2
u
65
+ 36u
64
+ ··· − 5u − 1
c
3
u
65
+ 2u
64
+ ··· − 77u − 209
c
4
u
65
− 14u
63
+ ··· − 51079u − 9713
c
6
, c
11
u
65
+ 2u
64
+ ··· − 27u + 17
c
7
u
65
− 2u
64
+ ··· + u − 1
c
8
, c
10
u
65
− 3u
64
+ ··· − 6u + 1
c
9
u
65
+ 11u
64
+ ··· − 12u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
65
+ 36y
64
+ ··· − 5y −1
c
2
y
65
− 12y
64
+ ··· − 97y −1
c
3
y
65
− 80y
64
+ ··· + 680999y −43681
c
4
y
65
− 28y
64
+ ··· − 2283276729y −94342369
c
6
, c
11
y
65
− 60y
64
+ ··· − 15013y −289
c
7
y
65
+ 12y
64
+ ··· − 5y −1
c
8
, c
10
y
65
− 51y
64
+ ··· − 94y −1
c
9
y
65
+ 15y
64
+ ··· − 152y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.255209 + 0.948908I
a = −0.99928 + 1.01479I
b = 2.04192 − 0.64047I
−4.38791 + 0.83519I −11.90532 − 1.80779I
u = 0.255209 − 0.948908I
a = −0.99928 − 1.01479I
b = 2.04192 + 0.64047I
−4.38791 − 0.83519I −11.90532 + 1.80779I
u = 0.379172 + 0.954880I
a = 0.44986 + 1.99487I
b = −0.95093 − 2.01516I
−3.54308 + 4.03035I −8.72949 − 8.88482I
u = 0.379172 − 0.954880I
a = 0.44986 − 1.99487I
b = −0.95093 + 2.01516I
−3.54308 − 4.03035I −8.72949 + 8.88482I
u = 0.484262 + 0.914397I
a = 1.118230 + 0.362011I
b = −2.04011 − 0.02854I
0.85073 + 5.73380I 0. − 9.30698I
u = 0.484262 − 0.914397I
a = 1.118230 − 0.362011I
b = −2.04011 + 0.02854I
0.85073 − 5.73380I 0. + 9.30698I
u = −0.350482 + 0.867729I
a = 0.86949 − 2.41938I
b = −2.39364 − 0.40176I
−2.05273 − 1.79214I −3.9608 − 27.3479I
u = −0.350482 − 0.867729I
a = 0.86949 + 2.41938I
b = −2.39364 + 0.40176I
−2.05273 + 1.79214I −3.9608 + 27.3479I
u = −0.416907 + 0.814224I
a = −0.0826608 − 0.0580767I
b = −0.394803 + 0.423441I
−0.06086 − 1.78141I 0.16593 + 3.65886I
u = −0.416907 − 0.814224I
a = −0.0826608 + 0.0580767I
b = −0.394803 − 0.423441I
−0.06086 + 1.78141I 0.16593 − 3.65886I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.688274 + 0.597046I
a = 0.937870 + 0.013321I
b = −0.177796 − 0.445216I
−1.20524 − 3.66120I −3.96415 + 8.51812I
u = −0.688274 − 0.597046I
a = 0.937870 − 0.013321I
b = −0.177796 + 0.445216I
−1.20524 + 3.66120I −3.96415 − 8.51812I
u = 0.895488 + 0.125785I
a = −0.09492 + 1.43200I
b = −0.376735 − 0.287159I
−7.23534 − 2.53854I −7.87268 + 2.81634I
u = 0.895488 − 0.125785I
a = −0.09492 − 1.43200I
b = −0.376735 + 0.287159I
−7.23534 + 2.53854I −7.87268 − 2.81634I
u = 0.042517 + 0.896108I
a = −1.233970 − 0.489969I
b = 1.50275 + 1.00485I
−1.88737 − 1.49983I −7.09909 + 4.37897I
u = 0.042517 − 0.896108I
a = −1.233970 + 0.489969I
b = 1.50275 − 1.00485I
−1.88737 + 1.49983I −7.09909 − 4.37897I
u = −0.873776 + 0.112840I
a = −0.53746 − 2.51675I
b = −0.325555 + 0.658517I
−7.98517 + 11.01330I −4.27925 − 5.99396I
u = −0.873776 − 0.112840I
a = −0.53746 + 2.51675I
b = −0.325555 − 0.658517I
−7.98517 − 11.01330I −4.27925 + 5.99396I
u = −0.457366 + 1.034950I
a = −0.505700 + 0.060882I
b = 0.747461 + 0.669285I
−0.33001 − 3.05900I 0
u = −0.457366 − 1.034950I
a = −0.505700 − 0.060882I
b = 0.747461 − 0.669285I
−0.33001 + 3.05900I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.571139 + 0.977969I
a = −0.414828 − 0.730148I
b = 1.62844 + 0.58978I
−3.06278 + 10.75520I 0
u = 0.571139 − 0.977969I
a = −0.414828 + 0.730148I
b = 1.62844 − 0.58978I
−3.06278 − 10.75520I 0
u = −0.637047 + 0.936500I
a = 0.173925 + 0.578410I
b = 0.317828 − 0.930103I
−2.16059 − 1.39700I 0
u = −0.637047 − 0.936500I
a = 0.173925 − 0.578410I
b = 0.317828 + 0.930103I
−2.16059 + 1.39700I 0
u = 0.681051 + 0.492285I
a = 0.499375 + 1.028690I
b = −0.444176 + 0.382574I
−1.66713 − 5.95884I −1.87973 + 5.22029I
u = 0.681051 − 0.492285I
a = 0.499375 − 1.028690I
b = −0.444176 − 0.382574I
−1.66713 + 5.95884I −1.87973 − 5.22029I
u = 0.026760 + 1.174520I
a = 0.625886 + 0.349711I
b = −1.65520 − 0.65340I
−7.09632 − 4.52850I 0
u = 0.026760 − 1.174520I
a = 0.625886 − 0.349711I
b = −1.65520 + 0.65340I
−7.09632 + 4.52850I 0
u = −0.824553 + 0.021951I
a = −0.07187 + 1.73665I
b = 0.732613 − 0.631471I
−7.00163 + 2.10905I −8.59887 − 3.22074I
u = −0.824553 − 0.021951I
a = −0.07187 − 1.73665I
b = 0.732613 + 0.631471I
−7.00163 − 2.10905I −8.59887 + 3.22074I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.816612 + 0.075250I
a = 0.48242 + 2.15457I
b = −0.036633 − 0.982310I
−2.82170 + 5.12577I −2.55858 − 6.00397I
u = −0.816612 − 0.075250I
a = 0.48242 − 2.15457I
b = −0.036633 + 0.982310I
−2.82170 − 5.12577I −2.55858 + 6.00397I
u = 0.792642
a = 4.90851
b = −0.401921
−4.52444 15.6460
u = −0.268889 + 0.735800I
a = −1.80208 + 0.80816I
b = 2.05899 + 1.16628I
−1.59108 − 1.22204I −11.25340 + 3.73985I
u = −0.268889 − 0.735800I
a = −1.80208 − 0.80816I
b = 2.05899 − 1.16628I
−1.59108 + 1.22204I −11.25340 − 3.73985I
u = 0.775998 + 0.055269I
a = −1.05405 − 1.76675I
b = 0.272202 + 0.513943I
−2.68758 − 0.98018I −2.13142 − 1.09675I
u = 0.775998 − 0.055269I
a = −1.05405 + 1.76675I
b = 0.272202 − 0.513943I
−2.68758 + 0.98018I −2.13142 + 1.09675I
u = 0.487308 + 0.547787I
a = −0.01925 − 1.62217I
b = 0.231211 + 0.350100I
1.87042 − 1.68269I 3.98101 + 2.38110I
u = 0.487308 − 0.547787I
a = −0.01925 + 1.62217I
b = 0.231211 − 0.350100I
1.87042 + 1.68269I 3.98101 − 2.38110I
u = 0.432502 + 1.204000I
a = −1.75345 + 0.89087I
b = 2.78335 − 1.12697I
−6.34559 + 3.27358I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.432502 − 1.204000I
a = −1.75345 − 0.89087I
b = 2.78335 + 1.12697I
−6.34559 − 3.27358I 0
u = 0.477979 + 1.199780I
a = 1.55306 + 0.77188I
b = −2.26994 − 1.41320I
−6.01852 + 5.55484I 0
u = 0.477979 − 1.199780I
a = 1.55306 − 0.77188I
b = −2.26994 + 1.41320I
−6.01852 − 5.55484I 0
u = −0.420103 + 1.222350I
a = −2.02050 + 0.09514I
b = 2.61282 − 0.57494I
−6.68706 + 0.82473I 0
u = −0.420103 − 1.222350I
a = −2.02050 − 0.09514I
b = 2.61282 + 0.57494I
−6.68706 − 0.82473I 0
u = 0.457248 + 1.211200I
a = 0.96035 − 3.09348I
b = −1.90067 + 5.72471I
−8.07040 + 4.48064I 0
u = 0.457248 − 1.211200I
a = 0.96035 + 3.09348I
b = −1.90067 − 5.72471I
−8.07040 − 4.48064I 0
u = −0.448174 + 1.226550I
a = −1.149020 − 0.597546I
b = 1.70773 − 0.09090I
−10.71550 − 2.40472I 0
u = −0.448174 − 1.226550I
a = −1.149020 + 0.597546I
b = 1.70773 + 0.09090I
−10.71550 + 2.40472I 0
u = −0.490148 + 1.212660I
a = 2.22210 + 0.44255I
b = −3.07486 − 0.48626I
−6.18604 − 9.87507I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.490148 − 1.212660I
a = 2.22210 − 0.44255I
b = −3.07486 + 0.48626I
−6.18604 + 9.87507I 0
u = −0.468861 + 1.223140I
a = 1.95666 − 0.56765I
b = −2.74601 + 0.33365I
−10.56670 − 6.75210I 0
u = −0.468861 − 1.223140I
a = 1.95666 + 0.56765I
b = −2.74601 − 0.33365I
−10.56670 + 6.75210I 0
u = −0.393745 + 1.260010I
a = 1.72213 − 0.24493I
b = −2.67784 + 1.24472I
−12.22780 + 6.64210I 0
u = −0.393745 − 1.260010I
a = 1.72213 + 0.24493I
b = −2.67784 − 1.24472I
−12.22780 − 6.64210I 0
u = 0.384245 + 1.272530I
a = 0.918549 − 0.118993I
b = −1.61318 − 0.48242I
−11.61320 + 1.86120I 0
u = 0.384245 − 1.272530I
a = 0.918549 + 0.118993I
b = −1.61318 + 0.48242I
−11.61320 − 1.86120I 0
u = −0.517285 + 1.227500I
a = −2.38902 − 0.02987I
b = 3.77402 + 0.28861I
−11.3347 − 16.0510I 0
u = −0.517285 − 1.227500I
a = −2.38902 + 0.02987I
b = 3.77402 − 0.28861I
−11.3347 + 16.0510I 0
u = 0.526288 + 1.234520I
a = −1.41665 − 0.19459I
b = 2.29059 + 0.00902I
−10.58890 + 7.68258I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.526288 − 1.234520I
a = −1.41665 + 0.19459I
b = 2.29059 − 0.00902I
−10.58890 − 7.68258I 0
u = −0.488804 + 0.385911I
a = −0.885850 − 0.643188I
b = −0.403529 + 0.183900I
1.49244 − 0.86359I 5.03880 + 1.53624I
u = −0.488804 − 0.385911I
a = −0.885850 + 0.643188I
b = −0.403529 − 0.183900I
1.49244 + 0.86359I 5.03880 − 1.53624I
u = 0.287539 + 0.230477I
a = −3.01358 − 1.00850I
b = 0.980634 + 0.158120I
−1.91160 − 0.92204I −3.30845 + 0.88312I
u = 0.287539 − 0.230477I
a = −3.01358 + 1.00850I
b = 0.980634 − 0.158120I
−1.91160 + 0.92204I −3.30845 − 0.88312I
11
II. I
u
2
= hb + u, a − u − 1, u
2
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
1
=
1
−u − 1
a
3
=
−u
u
a
7
=
−1
u + 1
a
9
=
u + 1
−u
a
10
=
u + 1
−u
a
5
=
−u
u
a
4
=
−u + 1
−1
a
11
=
0
−u
a
8
=
u + 1
0
a
8
=
u + 1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u − 1
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
u
2
+ u + 1
c
3
, c
4
, c
5
c
11
u
2
− u + 1
c
8
(u − 1)
2
c
9
u
2
c
10
(u + 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
11
y
2
+ y + 1
c
8
, c
10
(y −1)
2
c
9
y
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.500000 + 0.866025I
b = 0.500000 − 0.866025I
−1.64493 − 2.02988I −3.00000 + 3.46410I
u = −0.500000 − 0.866025I
a = 0.500000 − 0.866025I
b = 0.500000 + 0.866025I
−1.64493 + 2.02988I −3.00000 − 3.46410I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)(u
65
− 2u
64
+ ··· + u + 1)
c
2
(u
2
+ u + 1)(u
65
+ 36u
64
+ ··· − 5u − 1)
c
3
(u
2
− u + 1)(u
65
+ 2u
64
+ ··· − 77u − 209)
c
4
(u
2
− u + 1)(u
65
− 14u
63
+ ··· − 51079u − 9713)
c
5
(u
2
− u + 1)(u
65
− 2u
64
+ ··· + u + 1)
c
6
(u
2
+ u + 1)(u
65
+ 2u
64
+ ··· − 27u + 17)
c
7
(u
2
+ u + 1)(u
65
− 2u
64
+ ··· + u − 1)
c
8
((u − 1)
2
)(u
65
− 3u
64
+ ··· − 6u + 1)
c
9
u
2
(u
65
+ 11u
64
+ ··· − 12u − 4)
c
10
((u + 1)
2
)(u
65
− 3u
64
+ ··· − 6u + 1)
c
11
(u
2
− u + 1)(u
65
+ 2u
64
+ ··· − 27u + 17)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
2
+ y + 1)(y
65
+ 36y
64
+ ··· − 5y −1)
c
2
(y
2
+ y + 1)(y
65
− 12y
64
+ ··· − 97y −1)
c
3
(y
2
+ y + 1)(y
65
− 80y
64
+ ··· + 680999y −43681)
c
4
(y
2
+ y + 1)(y
65
− 28y
64
+ ··· − 2.28328 × 10
9
y −9.43424 × 10
7
)
c
6
, c
11
(y
2
+ y + 1)(y
65
− 60y
64
+ ··· − 15013y −289)
c
7
(y
2
+ y + 1)(y
65
+ 12y
64
+ ··· − 5y −1)
c
8
, c
10
((y −1)
2
)(y
65
− 51y
64
+ ··· − 94y −1)
c
9
y
2
(y
65
+ 15y
64
+ ··· − 152y −16)
17
