10
109
(K10a
93
)
A knot diagram
1
Linearized knot diagam
5 7 1 9 2 10 3 4 6 8
Solving Sequence
6,9
10
2,7
3 5 1 4 8
c
9
c
6
c
2
c
5
c
1
c
4
c
8
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.20732 × 10
64
u
47
− 6.80471 × 10
63
u
46
+ ··· + 4.78500 × 10
62
b + 3.10961 × 10
64
,
2.36806 × 10
62
u
47
− 2.05373 × 10
62
u
46
+ ··· + 1.01808 × 10
61
a + 8.42639 × 10
62
, u
48
− u
47
+ ··· + 3u − 1i
I
u
2
= hu
3
+ 2u
2
+ b − u − 1, −2u
5
− 3u
4
+ 4u
3
+ 5u
2
+ a − u − 5, u
6
+ 2u
5
− u
4
− 3u
3
− u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 54 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
= h1.21 × 10
64
u
47
− 6.80 × 10
63
u
46
+ · · · + 4.78 × 10
62
b + 3.11 × 10
64
, 2.37 ×
10
62
u
47
−2.05×10
62
u
46
+· · ·+1.02×10
61
a+8.43×10
62
, u
48
−u
47
+· · ·+3u−1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
2
=
−23.2599u
47
+ 20.1725u
46
+ ··· − 31.6691u − 82.7671
−25.2314u
47
+ 14.2209u
46
+ ··· + 3.95288u − 64.9867
a
7
=
u
−u
3
+ u
a
3
=
−18.5062u
47
+ 19.5774u
46
+ ··· − 44.8752u − 78.5037
−23.7412u
47
+ 14.4735u
46
+ ··· − 1.53060u − 64.8820
a
5
=
−26.4129u
47
+ 22.6599u
46
+ ··· − 30.3151u − 107.768
−4.62565u
47
+ 3.74801u
46
+ ··· − 4.77317u − 19.1854
a
1
=
−34.0857u
47
+ 12.4951u
46
+ ··· + 61.2163u − 60.5527
−23.2847u
47
+ 16.5991u
46
+ ··· − 10.3541u − 74.7687
a
4
=
−21.7873u
47
+ 18.9119u
46
+ ··· − 25.5420u − 88.5823
−4.62565u
47
+ 3.74801u
46
+ ··· − 4.77317u − 19.1854
a
8
=
22.7255u
47
− 19.1834u
46
+ ··· + 16.4869u + 86.5333
14.0451u
47
− 8.17543u
46
+ ··· + 3.87591u + 42.3364
(ii) Obstruction class = −1
(iii) Cusp Shapes = −57.1122u
47
+ 43.2739u
46
+ ··· + 12.3659u − 184.174
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
48
+ u
47
+ ··· − 3u − 1
c
2
, c
7
u
48
− u
47
+ ··· − 27u + 9
c
3
u
48
− 2u
47
+ ··· − 11u + 1
c
4
, c
8
u
48
+ u
47
+ ··· + 27u + 9
c
6
, c
9
u
48
− u
47
+ ··· + 3u − 1
c
10
u
48
+ 2u
47
+ ··· + 11u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
y
48
− 29y
47
+ ··· − 45y + 1
c
2
, c
4
, c
7
c
8
y
48
− 29y
47
+ ··· − 1053y + 81
c
3
, c
10
y
48
− 6y
47
+ ··· − 23y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.632234 + 0.751660I
a = 0.218508 + 0.245850I
b = 0.32704 + 1.62505I
−0.39243 − 4.63681I −1.88077 + 4.18341I
u = −0.632234 − 0.751660I
a = 0.218508 − 0.245850I
b = 0.32704 − 1.62505I
−0.39243 + 4.63681I −1.88077 − 4.18341I
u = −0.240182 + 0.992004I
a = −0.427547 − 1.235530I
b = 0.343258 − 1.370130I
−7.33272 + 2.80822I −7.40390 − 2.13041I
u = −0.240182 − 0.992004I
a = −0.427547 + 1.235530I
b = 0.343258 + 1.370130I
−7.33272 − 2.80822I −7.40390 + 2.13041I
u = −0.894686 + 0.569518I
a = −0.127345 + 0.599296I
b = −0.028616 + 1.106620I
−0.55675 − 4.59934I 0. + 5.05608I
u = −0.894686 − 0.569518I
a = −0.127345 − 0.599296I
b = −0.028616 − 1.106620I
−0.55675 + 4.59934I 0. − 5.05608I
u = 1.051710 + 0.225311I
a = −0.738220 + 0.292695I
b = −0.53476 + 1.78675I
0.417476 + 0.732604I 0. + 18.1961I
u = 1.051710 − 0.225311I
a = −0.738220 − 0.292695I
b = −0.53476 − 1.78675I
0.417476 − 0.732604I 0. − 18.1961I
u = 0.812872 + 0.282184I
a = 0.357660 − 0.200732I
b = −0.596385 − 0.659961I
1.40575 + 0.47751I 6.55789 + 0.10542I
u = 0.812872 − 0.282184I
a = 0.357660 + 0.200732I
b = −0.596385 + 0.659961I
1.40575 − 0.47751I 6.55789 − 0.10542I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.842342 + 0.141502I
a = −1.170590 + 0.464125I
b = 1.45254 + 1.74578I
−0.417476 + 0.732604I −0.8254 + 18.1961I
u = 0.842342 − 0.141502I
a = −1.170590 − 0.464125I
b = 1.45254 − 1.74578I
−0.417476 − 0.732604I −0.8254 − 18.1961I
u = 0.605329 + 0.579618I
a = 0.772614 − 0.128076I
b = −0.077175 − 0.876614I
1.51083 + 0.54816I 4.17228 + 0.02806I
u = 0.605329 − 0.579618I
a = 0.772614 + 0.128076I
b = −0.077175 + 0.876614I
1.51083 − 0.54816I 4.17228 − 0.02806I
u = −1.067460 + 0.548582I
a = 0.489520 + 1.166660I
b = −0.53932 + 1.32606I
−1.80411 − 5.64123I 0
u = −1.067460 − 0.548582I
a = 0.489520 − 1.166660I
b = −0.53932 − 1.32606I
−1.80411 + 5.64123I 0
u = −0.437566 + 0.658376I
a = 1.41174 + 1.11025I
b = 0.192260 + 0.774854I
−3.64950 + 0.92732I −3.47502 − 0.40612I
u = −0.437566 − 0.658376I
a = 1.41174 − 1.11025I
b = 0.192260 − 0.774854I
−3.64950 − 0.92732I −3.47502 + 0.40612I
u = 1.161770 + 0.407343I
a = −0.604688 − 1.001630I
b = 0.0379439 + 0.0548756I
3.40248 + 7.65130I 0
u = 1.161770 − 0.407343I
a = −0.604688 + 1.001630I
b = 0.0379439 − 0.0548756I
3.40248 − 7.65130I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.766769
a = 2.73239
b = −0.792296
−5.07611 4.92140
u = 1.225450 + 0.357549I
a = 0.869607 − 0.646447I
b = −0.146351 − 0.816816I
−2.38978 + 1.27522I 0
u = 1.225450 − 0.357549I
a = 0.869607 + 0.646447I
b = −0.146351 + 0.816816I
−2.38978 − 1.27522I 0
u = −1.200530 + 0.437380I
a = −0.758374 − 0.772570I
b = 1.35305 − 1.50450I
4.19769 − 8.53710I 0
u = −1.200530 − 0.437380I
a = −0.758374 + 0.772570I
b = 1.35305 + 1.50450I
4.19769 + 8.53710I 0
u = −1.328340 + 0.127377I
a = −0.250127 + 0.722817I
b = −0.150574 + 0.021826I
7.33272 − 2.80822I 0
u = −1.328340 − 0.127377I
a = −0.250127 − 0.722817I
b = −0.150574 − 0.021826I
7.33272 + 2.80822I 0
u = −0.541920 + 0.370293I
a = 1.259690 − 0.208818I
b = −0.036236 − 0.338358I
−1.51083 + 0.54816I −4.17228 + 0.02806I
u = −0.541920 − 0.370293I
a = 1.259690 + 0.208818I
b = −0.036236 + 0.338358I
−1.51083 − 0.54816I −4.17228 − 0.02806I
u = 0.227376 + 0.608707I
a = −0.33925 − 1.59654I
b = −0.52148 − 1.52173I
0.55675 + 4.59934I 0.60868 − 5.05608I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.227376 − 0.608707I
a = −0.33925 + 1.59654I
b = −0.52148 + 1.52173I
0.55675 − 4.59934I 0.60868 + 5.05608I
u = −1.296800 + 0.481262I
a = 0.740652 + 0.550584I
b = −1.61489 + 0.94291I
2.38978 − 1.27522I 0
u = −1.296800 − 0.481262I
a = 0.740652 − 0.550584I
b = −1.61489 − 0.94291I
2.38978 + 1.27522I 0
u = −1.248360 + 0.595799I
a = −0.647079 − 0.659192I
b = 0.40624 − 1.67377I
−4.19769 − 8.53710I 0
u = −1.248360 − 0.595799I
a = −0.647079 + 0.659192I
b = 0.40624 + 1.67377I
−4.19769 + 8.53710I 0
u = 1.34869 + 0.44365I
a = 0.437659 + 0.344193I
b = −0.490315 − 0.307215I
3.64950 + 0.92732I 0
u = 1.34869 − 0.44365I
a = 0.437659 − 0.344193I
b = −0.490315 + 0.307215I
3.64950 − 0.92732I 0
u = 0.29450 + 1.40998I
a = −0.441729 + 0.731698I
b = −0.27015 + 1.70315I
−3.40248 − 7.65130I 0
u = 0.29450 − 1.40998I
a = −0.441729 − 0.731698I
b = −0.27015 − 1.70315I
−3.40248 + 7.65130I 0
u = 1.16255 + 0.97682I
a = 0.305811 − 0.728832I
b = −1.23753 − 1.73103I
1.80411 + 5.64123I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.16255 − 0.97682I
a = 0.305811 + 0.728832I
b = −1.23753 + 1.73103I
1.80411 − 5.64123I 0
u = 1.34409 + 0.72046I
a = −0.553617 + 0.832772I
b = 1.16282 + 1.60497I
14.9002I 0
u = 1.34409 − 0.72046I
a = −0.553617 − 0.832772I
b = 1.16282 − 1.60497I
− 14.9002I 0
u = −0.347375 + 0.062244I
a = 2.12622 + 1.19331I
b = 0.296449 + 0.612534I
−1.40575 − 0.47751I −6.55789 − 0.10542I
u = −0.347375 − 0.062244I
a = 2.12622 − 1.19331I
b = 0.296449 − 0.612534I
−1.40575 + 0.47751I −6.55789 + 0.10542I
u = 0.322944 + 0.008808I
a = 2.01970 + 2.27244I
b = −0.52460 + 1.37673I
0.39243 − 4.63681I 1.88077 + 4.18341I
u = 0.322944 − 0.008808I
a = 2.01970 − 2.27244I
b = −0.52460 − 1.37673I
0.39243 + 4.63681I 1.88077 − 4.18341I
u = −2.09511
a = 0.365981
b = −0.814169
5.07611 0
9
II. I
u
2
= hu
3
+ 2u
2
+ b − u − 1, −2u
5
− 3u
4
+ 4u
3
+ 5u
2
+ a − u − 5, u
6
+
2u
5
− u
4
− 3u
3
− u
2
+ 2u + 1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
2
=
2u
5
+ 3u
4
− 4u
3
− 5u
2
+ u + 5
−u
3
− 2u
2
+ u + 1
a
7
=
u
−u
3
+ u
a
3
=
3u
5
+ 5u
4
− 5u
3
− 7u
2
+ u + 6
u
5
+ u
4
− 3u
3
− 3u
2
+ 2u + 2
a
5
=
−5u
5
− 8u
4
+ 8u
3
+ 11u
2
− 9
−u
5
− 2u
4
+ u
3
+ 2u
2
− 1
a
1
=
−7u
5
− 10u
4
+ 13u
3
+ 14u
2
− u − 13
−u
5
− u
4
+ 2u
3
− 1
a
4
=
−4u
5
− 6u
4
+ 7u
3
+ 9u
2
− 8
−u
5
− 2u
4
+ u
3
+ 2u
2
− 1
a
8
=
3u
5
+ 4u
4
− 6u
3
− 6u
2
+ u + 7
−u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8u
5
− 8u
4
+ 16u
3
+ 8u
2
− 12
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
9
u
6
+ 2u
5
− u
4
− 3u
3
− u
2
+ 2u + 1
c
2
, c
8
u
6
− u
4
+ u
3
− u
2
+ 1
c
3
u
6
+ 3u
5
+ 3u
4
+ u
3
− 4u
2
− 4u − 1
c
4
, c
7
u
6
− u
4
− u
3
− u
2
+ 1
c
5
, c
6
u
6
− 2u
5
− u
4
+ 3u
3
− u
2
− 2u + 1
c
10
u
6
− 3u
5
+ 3u
4
− u
3
− 4u
2
+ 4u − 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
y
6
− 6y
5
+ 11y
4
− 13y
3
+ 11y
2
− 6y + 1
c
2
, c
4
, c
7
c
8
y
6
− 2y
5
− y
4
+ 3y
3
− y
2
− 2y + 1
c
3
, c
10
y
6
− 3y
5
− 5y
4
− 3y
3
+ 18y
2
− 8y + 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.967716 + 0.252043I
a = 0.872949 − 0.487811I
b = −0.50000 − 1.41566I
1.00626I − 60.10 + 0.512355I
u = 0.967716 − 0.252043I
a = 0.872949 + 0.487811I
b = −0.50000 + 1.41566I
− 1.00626I − 60.10 − 0.512355I
u = −0.731299 + 0.682057I
a = 0.069597 + 0.997575I
b = −0.50000 + 1.90021I
− 5.76499I 0. + 10.15340I
u = −0.731299 − 0.682057I
a = 0.069597 − 0.997575I
b = −0.50000 − 1.90021I
5.76499I 0. − 10.15340I
u = −0.509281
a = 3.85554
b = 0.104076
−5.56615 −12.3030
u = −1.96355
a = 0.259367
b = −1.10408
5.56615 12.3030
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 2u
5
− u
4
− 3u
3
− u
2
+ 2u + 1)(u
48
+ u
47
+ ··· − 3u − 1)
c
2
(u
6
− u
4
+ u
3
− u
2
+ 1)(u
48
− u
47
+ ··· − 27u + 9)
c
3
(u
6
+ 3u
5
+ 3u
4
+ u
3
− 4u
2
− 4u − 1)(u
48
− 2u
47
+ ··· − 11u + 1)
c
4
(u
6
− u
4
− u
3
− u
2
+ 1)(u
48
+ u
47
+ ··· + 27u + 9)
c
5
(u
6
− 2u
5
− u
4
+ 3u
3
− u
2
− 2u + 1)(u
48
+ u
47
+ ··· − 3u − 1)
c
6
(u
6
− 2u
5
− u
4
+ 3u
3
− u
2
− 2u + 1)(u
48
− u
47
+ ··· + 3u − 1)
c
7
(u
6
− u
4
− u
3
− u
2
+ 1)(u
48
− u
47
+ ··· − 27u + 9)
c
8
(u
6
− u
4
+ u
3
− u
2
+ 1)(u
48
+ u
47
+ ··· + 27u + 9)
c
9
(u
6
+ 2u
5
− u
4
− 3u
3
− u
2
+ 2u + 1)(u
48
− u
47
+ ··· + 3u − 1)
c
10
(u
6
− 3u
5
+ 3u
4
− u
3
− 4u
2
+ 4u − 1)(u
48
+ 2u
47
+ ··· + 11u + 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
(y
6
− 6y
5
+ ··· − 6y + 1)(y
48
− 29y
47
+ ··· − 45y + 1)
c
2
, c
4
, c
7
c
8
(y
6
− 2y
5
− y
4
+ 3y
3
− y
2
− 2y + 1)(y
48
− 29y
47
+ ··· − 1053y + 81)
c
3
, c
10
(y
6
− 3y
5
+ ··· − 8y + 1)(y
48
− 6y
47
+ ··· − 23y + 1)
15
