11n
113
(K11n
113
)
A knot diagram
1
Linearized knot diagam
6 1 7 9 2 10 1 5 4 7 4
Solving Sequence
4,7 1,3
2 11 10 6 9 5 8
c
3
c
2
c
11
c
10
c
6
c
9
c
4
c
8
c
1
, c
5
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h6u
12
− 31u
11
+ ··· + 77b + 51, −16u
12
− 20u
11
+ ··· + 77a + 18,
u
13
+ 9u
11
+ u
10
+ 29u
9
+ 6u
8
+ 37u
7
+ 10u
6
+ 14u
5
+ 3u
4
+ 5u
3
− 2u
2
+ u − 1i
I
u
2
= h27350u
11
− 10434u
10
+ ··· + 116501b + 508418,
− 702574u
11
+ 701168u
10
+ ··· + 2213519a − 5780311,
u
12
− u
11
+ 8u
10
− 7u
9
+ 26u
8
− 13u
7
+ 53u
6
+ 7u
5
+ 80u
4
+ 38u
3
+ 72u
2
+ 24u + 19i
I
u
3
= hu
7
+ 4u
5
− u
4
+ 6u
3
− 2u
2
+ b + 3u, u
7
+ 5u
5
− u
4
+ 10u
3
− 3u
2
+ a + 7u − 2,
u
8
+ 5u
6
− u
5
+ 10u
4
− 3u
3
+ 8u
2
− 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 33 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
= h6u
12
− 31u
11
+ · · · + 77b + 51, −16u
12
− 20u
11
+ · · · + 77a +
18, u
13
+ 9u
11
+ · · · + u − 1i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
1
=
0.207792u
12
+ 0.259740u
11
+ ··· + 0.246753u − 0.233766
−0.0779221u
12
+ 0.402597u
11
+ ··· + 1.53247u − 0.662338
a
3
=
1
u
2
a
2
=
0.259740u
12
+ 0.324675u
11
+ ··· − 0.441558u + 1.20779
−0.376623u
12
− 0.220779u
11
+ ··· + 0.740260u + 0.298701
a
11
=
0.129870u
12
+ 0.662338u
11
+ ··· + 1.77922u − 0.896104
−0.0779221u
12
+ 0.402597u
11
+ ··· + 1.53247u − 0.662338
a
10
=
0.129870u
12
+ 0.662338u
11
+ ··· + 1.77922u − 0.896104
u
a
6
=
−
3
7
u
12
−
2
7
u
11
+ ··· +
10
7
u −
1
7
−0.0779221u
12
+ 0.402597u
11
+ ··· + 1.53247u − 0.662338
a
9
=
0.129870u
12
+ 0.662338u
11
+ ··· + 0.779221u − 0.896104
u
a
5
=
−0.662338u
12
− 0.0779221u
11
+ ··· + 1.02597u + 0.870130
−u
2
a
8
=
0.207792u
12
+ 0.259740u
11
+ ··· − 0.753247u − 0.233766
u
3
+ u
a
8
=
0.207792u
12
+ 0.259740u
11
+ ··· − 0.753247u − 0.233766
u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
222
77
u
12
+
8
77
u
11
+
2008
77
u
10
+
345
77
u
9
+
6465
77
u
8
+ 26u
7
+
8137
77
u
6
+
3748
77
u
5
+
2942
77
u
4
+
285
11
u
3
+
1313
77
u
2
−
54
77
u +
501
77
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
13
− 6u
12
+ ··· + 26u − 4
c
2
u
13
+ 8u
12
+ ··· + 124u − 16
c
3
, c
4
, c
8
c
9
u
13
+ 9u
11
+ ··· + u − 1
c
6
, c
10
u
13
− 9u
12
+ ··· + 40u − 8
c
7
u
13
− 2u
12
+ ··· − 7u − 1
c
11
u
13
− 2u
12
+ ··· − 6u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
13
+ 8y
12
+ ··· + 124y −16
c
2
y
13
− 4y
12
+ ··· + 31600y −256
c
3
, c
4
, c
8
c
9
y
13
+ 18y
12
+ ··· − 3y −1
c
6
, c
10
y
13
− 3y
12
+ ··· + 352y −64
c
7
y
13
+ 26y
12
+ ··· + 53y −1
c
11
y
13
− 24y
12
+ ··· + 50y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.589003 + 0.398981I
a = −0.155544 + 0.694999I
b = −0.701578 − 0.113111I
−1.89853 − 1.81856I 3.56685 + 4.77795I
u = −0.589003 − 0.398981I
a = −0.155544 − 0.694999I
b = −0.701578 + 0.113111I
−1.89853 + 1.81856I 3.56685 − 4.77795I
u = 0.313260 + 0.606523I
a = 0.71205 − 1.73803I
b = −0.241660 − 0.056194I
1.23789 − 1.81241I 3.13803 − 1.59537I
u = 0.313260 − 0.606523I
a = 0.71205 + 1.73803I
b = −0.241660 + 0.056194I
1.23789 + 1.81241I 3.13803 + 1.59537I
u = −0.067844 + 0.603023I
a = 0.009402 + 0.327160I
b = −0.281404 + 1.089340I
1.10712 + 2.64289I 2.15723 − 4.40909I
u = −0.067844 − 0.603023I
a = 0.009402 − 0.327160I
b = −0.281404 − 1.089340I
1.10712 − 2.64289I 2.15723 + 4.40909I
u = 0.435514
a = 0.789752
b = 0.240167
0.684474 14.6290
u = −0.15240 + 1.67572I
a = 1.291360 − 0.096165I
b = −2.11530 − 0.55305I
−12.27390 − 4.64857I 3.70723 + 2.31166I
u = −0.15240 − 1.67572I
a = 1.291360 + 0.096165I
b = −2.11530 + 0.55305I
−12.27390 + 4.64857I 3.70723 − 2.31166I
u = −0.07312 + 1.68645I
a = −1.339690 − 0.391716I
b = 2.00168 − 0.40120I
−16.5929 − 2.0437I 1.74217 + 0.86236I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.07312 − 1.68645I
a = −1.339690 + 0.391716I
b = 2.00168 + 0.40120I
−16.5929 + 2.0437I 1.74217 − 0.86236I
u = 0.35135 + 1.77586I
a = −1.41246 + 0.16455I
b = 2.21818 − 0.62507I
−17.1576 + 11.0164I 1.87407 − 4.91060I
u = 0.35135 − 1.77586I
a = −1.41246 − 0.16455I
b = 2.21818 + 0.62507I
−17.1576 − 11.0164I 1.87407 + 4.91060I
6
II. I
u
2
= h27350u
11
− 10434u
10
+ · · · + 116501b + 508418, −7.03 × 10
5
u
11
+
7.01 × 10
5
u
10
+ · · · + 2.21 × 10
6
a − 5.78 × 10
6
, u
12
− u
11
+ · · · + 24u + 19i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
1
=
0.317401u
11
− 0.316766u
10
+ ··· + 11.2217u + 2.61137
−0.234762u
11
+ 0.0895615u
10
+ ··· − 7.84627u − 4.36407
a
3
=
1
u
2
a
2
=
0.537344u
11
− 0.633335u
10
+ ··· + 18.5569u + 3.49184
−0.413104u
11
+ 0.358821u
10
+ ··· − 14.9788u − 5.59521
a
11
=
0.0826395u
11
− 0.227205u
10
+ ··· + 3.37538u − 1.75270
−0.234762u
11
+ 0.0895615u
10
+ ··· − 7.84627u − 4.36407
a
10
=
0.0826395u
11
− 0.227205u
10
+ ··· + 3.37538u − 1.75270
−0.131415u
11
+ 0.0852353u
10
+ ··· − 5.94685u − 1.61733
a
6
=
0.0300079u
11
− 0.174573u
10
+ ··· − 0.414089u − 3.01586
−0.0241200u
11
+ 0.170445u
10
+ ··· − 0.572871u + 4.03170
a
9
=
0.214055u
11
− 0.312440u
10
+ ··· + 9.32223u − 0.135373
−0.131415u
11
+ 0.0852353u
10
+ ··· − 5.94685u − 1.61733
a
5
=
−0.118075u
11
− 0.244437u
10
+ ··· − 10.4369u − 12.7712
−0.0941194u
11
+ 0.432511u
10
+ ··· + 2.19875u + 7.10565
a
8
=
−0.674354u
11
+ 0.991579u
10
+ ··· − 19.6620u + 0.118551
0.516880u
11
− 0.642235u
10
+ ··· + 16.6038u + 4.18226
a
8
=
−0.674354u
11
+ 0.991579u
10
+ ··· − 19.6620u + 0.118551
0.516880u
11
− 0.642235u
10
+ ··· + 16.6038u + 4.18226
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
7968
116501
u
11
+
34084
116501
u
10
+ ··· −
122912
116501
u −
631486
116501
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
3
+ u
2
+ 2u + 1)
4
c
2
(u
3
+ 3u
2
+ 2u − 1)
4
c
3
, c
4
, c
8
c
9
u
12
− u
11
+ ··· + 24u + 19
c
6
, c
10
(u
2
+ u + 1)
6
c
7
u
12
+ 5u
11
+ ··· + 96u + 37
c
11
u
12
− 3u
11
+ ··· + 18u + 19
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
3
+ 3y
2
+ 2y −1)
4
c
2
(y
3
− 5y
2
+ 10y −1)
4
c
3
, c
4
, c
8
c
9
y
12
+ 15y
11
+ ··· + 2160y + 361
c
6
, c
10
(y
2
+ y + 1)
6
c
7
y
12
+ 19y
11
+ ··· − 1224y + 1369
c
11
y
12
− 17y
11
+ ··· − 2224y + 361
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.538956 + 0.733343I
a = 0.564995 + 0.432837I
b = 0.527133 − 0.553665I
−3.82135 − 2.02988I 7.01951 + 3.46410I
u = −0.538956 − 0.733343I
a = 0.564995 − 0.432837I
b = 0.527133 + 0.553665I
−3.82135 + 2.02988I 7.01951 − 3.46410I
u = −0.230918 + 0.703145I
a = −0.20112 + 2.69084I
b = −0.69983 − 1.68387I
−7.95893 − 0.79824I 0.490245 − 0.484655I
u = −0.230918 − 0.703145I
a = −0.20112 − 2.69084I
b = −0.69983 + 1.68387I
−7.95893 + 0.79824I 0.490245 + 0.484655I
u = 0.161517 + 1.387090I
a = 1.002040 + 0.183839I
b = −1.65945 + 0.10008I
−3.82135 + 2.02988I 7.01951 − 3.46410I
u = 0.161517 − 1.387090I
a = 1.002040 − 0.183839I
b = −1.65945 − 0.10008I
−3.82135 − 2.02988I 7.01951 + 3.46410I
u = −0.22870 + 1.46755I
a = −1.84111 + 0.39110I
b = 2.46907 − 0.14826I
−7.95893 − 4.85801I 0.49024 + 6.44355I
u = −0.22870 − 1.46755I
a = −1.84111 − 0.39110I
b = 2.46907 + 0.14826I
−7.95893 + 4.85801I 0.49024 − 6.44355I
u = 1.31249 + 1.08009I
a = −0.043037 − 0.415642I
b = −0.507847 + 0.209151I
−7.95893 + 4.85801I 0.49024 − 6.44355I
u = 1.31249 − 1.08009I
a = −0.043037 + 0.415642I
b = −0.507847 − 0.209151I
−7.95893 − 4.85801I 0.49024 + 6.44355I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.02457 + 1.83546I
a = −0.902821 + 0.085368I
b = 1.370920 + 0.193309I
−7.95893 + 0.79824I 0.490245 + 0.484655I
u = 0.02457 − 1.83546I
a = −0.902821 − 0.085368I
b = 1.370920 − 0.193309I
−7.95893 − 0.79824I 0.490245 − 0.484655I
11
III. I
u
3
= hu
7
+ 4u
5
− u
4
+ 6u
3
− 2u
2
+ b + 3u, u
7
+ 5u
5
− u
4
+ 10u
3
− 3u
2
+
a + 7u − 2, u
8
+ 5u
6
− u
5
+ 10u
4
− 3u
3
+ 8u
2
− 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
1
=
−u
7
− 5u
5
+ u
4
− 10u
3
+ 3u
2
− 7u + 2
−u
7
− 4u
5
+ u
4
− 6u
3
+ 2u
2
− 3u
a
3
=
1
u
2
a
2
=
u
4
+ 3u
2
+ 4
−u
7
− 4u
5
+ u
4
− 6u
3
+ 3u
2
− 3u + 1
a
11
=
−2u
7
− 9u
5
+ 2u
4
− 16u
3
+ 5u
2
− 10u + 2
−u
7
− 4u
5
+ u
4
− 6u
3
+ 2u
2
− 3u
a
10
=
−2u
7
− 9u
5
+ 2u
4
− 16u
3
+ 5u
2
− 10u + 2
−u
a
6
=
u
7
+ u
6
+ 6u
5
+ 3u
4
+ 12u
3
+ 2u
2
+ 9u − 1
u
7
+ 4u
5
− u
4
+ 6u
3
− 2u
2
+ 3u
a
9
=
−2u
7
− 9u
5
+ 2u
4
− 16u
3
+ 5u
2
− 9u + 2
−u
a
5
=
u
6
+ 4u
4
− u
3
+ 7u
2
− 2u + 3
−u
2
a
8
=
−u
7
− 5u
5
+ u
4
− 9u
3
+ 3u
2
− 6u + 2
−u
3
− u
a
8
=
−u
7
− 5u
5
+ u
4
− 9u
3
+ 3u
2
− 6u + 2
−u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
7
+ u
6
+ 5u
5
+ 7u
4
+ 10u
3
+ 15u
2
+ 5u + 14
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
− u
7
+ 3u
6
− 2u
5
+ 4u
4
− 2u
3
+ 4u
2
− u + 1
c
2
u
8
+ 5u
7
+ 13u
6
+ 24u
5
+ 32u
4
+ 30u
3
+ 20u
2
+ 7u + 1
c
3
, c
8
, c
9
u
8
+ 5u
6
− u
5
+ 10u
4
− 3u
3
+ 8u
2
− 2u + 1
c
4
u
8
+ 5u
6
+ u
5
+ 10u
4
+ 3u
3
+ 8u
2
+ 2u + 1
c
5
u
8
+ u
7
+ 3u
6
+ 2u
5
+ 4u
4
+ 2u
3
+ 4u
2
+ u + 1
c
6
u
8
− 2u
7
+ 3u
5
− 4u
4
+ u
3
+ 3u
2
− 2u + 1
c
7
u
8
− 2u
7
+ 3u
6
+ u
5
− 4u
4
+ 3u
3
− 2u + 1
c
10
u
8
+ 2u
7
− 3u
5
− 4u
4
− u
3
+ 3u
2
+ 2u + 1
c
11
u
8
− 2u
7
+ u
5
+ 2u
4
− 5u
3
+ 6u
2
− 3u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
8
+ 5y
7
+ 13y
6
+ 24y
5
+ 32y
4
+ 30y
3
+ 20y
2
+ 7y + 1
c
2
y
8
+ y
7
− 7y
6
− 4y
5
+ 36y
4
+ 70y
3
+ 44y
2
− 9y + 1
c
3
, c
4
, c
8
c
9
y
8
+ 10y
7
+ 45y
6
+ 115y
5
+ 176y
4
+ 157y
3
+ 72y
2
+ 12y + 1
c
6
, c
10
y
8
− 4y
7
+ 4y
6
+ y
5
+ 4y
4
− 13y
3
+ 5y
2
+ 2y + 1
c
7
y
8
+ 2y
7
+ 5y
6
− 13y
5
+ 4y
4
+ y
3
+ 4y
2
− 4y + 1
c
11
y
8
− 4y
7
+ 8y
6
− 9y
5
+ 4y
4
+ 5y
3
+ 10y
2
+ 3y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.333178 + 1.212560I
a = 0.543877 + 0.445748I
b = −1.43305 − 0.31113I
−5.36621 + 1.77463I 0.03179 − 1.94850I
u = 0.333178 − 1.212560I
a = 0.543877 − 0.445748I
b = −1.43305 + 0.31113I
−5.36621 − 1.77463I 0.03179 + 1.94850I
u = 0.050347 + 1.305130I
a = 0.079860 + 0.540066I
b = −0.318291 + 0.506872I
−1.51415 + 3.01964I 3.37685 − 3.22289I
u = 0.050347 − 1.305130I
a = 0.079860 − 0.540066I
b = −0.318291 − 0.506872I
−1.51415 − 3.01964I 3.37685 + 3.22289I
u = −0.53500 + 1.45526I
a = −0.757549 + 0.849919I
b = 1.119420 − 0.799585I
−8.16060 − 3.11503I −0.52239 + 1.94780I
u = −0.53500 − 1.45526I
a = −0.757549 − 0.849919I
b = 1.119420 + 0.799585I
−8.16060 + 3.11503I −0.52239 − 1.94780I
u = 0.151478 + 0.362294I
a = 1.13381 − 1.98717I
b = −0.368086 − 0.741932I
1.88148 − 2.34966I 12.61375 + 3.05058I
u = 0.151478 − 0.362294I
a = 1.13381 + 1.98717I
b = −0.368086 + 0.741932I
1.88148 + 2.34966I 12.61375 − 3.05058I
15
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
+ 2u + 1)
4
(u
8
− u
7
+ 3u
6
− 2u
5
+ 4u
4
− 2u
3
+ 4u
2
− u + 1)
· (u
13
− 6u
12
+ ··· + 26u − 4)
c
2
(u
3
+ 3u
2
+ 2u − 1)
4
· (u
8
+ 5u
7
+ 13u
6
+ 24u
5
+ 32u
4
+ 30u
3
+ 20u
2
+ 7u + 1)
· (u
13
+ 8u
12
+ ··· + 124u − 16)
c
3
, c
8
, c
9
(u
8
+ 5u
6
+ ··· − 2u + 1)(u
12
− u
11
+ ··· + 24u + 19)
· (u
13
+ 9u
11
+ ··· + u − 1)
c
4
(u
8
+ 5u
6
+ ··· + 2u + 1)(u
12
− u
11
+ ··· + 24u + 19)
· (u
13
+ 9u
11
+ ··· + u − 1)
c
5
(u
3
+ u
2
+ 2u + 1)
4
(u
8
+ u
7
+ 3u
6
+ 2u
5
+ 4u
4
+ 2u
3
+ 4u
2
+ u + 1)
· (u
13
− 6u
12
+ ··· + 26u − 4)
c
6
(u
2
+ u + 1)
6
(u
8
− 2u
7
+ 3u
5
− 4u
4
+ u
3
+ 3u
2
− 2u + 1)
· (u
13
− 9u
12
+ ··· + 40u − 8)
c
7
(u
8
− 2u
7
+ ··· − 2u + 1)(u
12
+ 5u
11
+ ··· + 96u + 37)
· (u
13
− 2u
12
+ ··· − 7u − 1)
c
10
(u
2
+ u + 1)
6
(u
8
+ 2u
7
− 3u
5
− 4u
4
− u
3
+ 3u
2
+ 2u + 1)
· (u
13
− 9u
12
+ ··· + 40u − 8)
c
11
(u
8
− 2u
7
+ ··· − 3u + 1)(u
12
− 3u
11
+ ··· + 18u + 19)
· (u
13
− 2u
12
+ ··· − 6u − 1)
16
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
3
+ 3y
2
+ 2y − 1)
4
· (y
8
+ 5y
7
+ 13y
6
+ 24y
5
+ 32y
4
+ 30y
3
+ 20y
2
+ 7y + 1)
· (y
13
+ 8y
12
+ ··· + 124y − 16)
c
2
(y
3
− 5y
2
+ 10y − 1)
4
· (y
8
+ y
7
− 7y
6
− 4y
5
+ 36y
4
+ 70y
3
+ 44y
2
− 9y + 1)
· (y
13
− 4y
12
+ ··· + 31600y − 256)
c
3
, c
4
, c
8
c
9
(y
8
+ 10y
7
+ 45y
6
+ 115y
5
+ 176y
4
+ 157y
3
+ 72y
2
+ 12y + 1)
· (y
12
+ 15y
11
+ ··· + 2160y + 361)(y
13
+ 18y
12
+ ··· − 3y − 1)
c
6
, c
10
(y
2
+ y + 1)
6
(y
8
− 4y
7
+ 4y
6
+ y
5
+ 4y
4
− 13y
3
+ 5y
2
+ 2y + 1)
· (y
13
− 3y
12
+ ··· + 352y − 64)
c
7
(y
8
+ 2y
7
+ 5y
6
− 13y
5
+ 4y
4
+ y
3
+ 4y
2
− 4y + 1)
· (y
12
+ 19y
11
+ ··· − 1224y + 1369)(y
13
+ 26y
12
+ ··· + 53y − 1)
c
11
(y
8
− 4y
7
+ 8y
6
− 9y
5
+ 4y
4
+ 5y
3
+ 10y
2
+ 3y + 1)
· (y
12
− 17y
11
+ ··· − 2224y + 361)(y
13
− 24y
12
+ ··· + 50y − 1)
17
