11a
60
(K11a
60
)
A knot diagram
1
Linearized knot diagam
5 1 8 2 4 10 11 3 6 7 9
Solving Sequence
6,9
10 7 11
1,3
2 8 4 5
c
9
c
6
c
10
c
11
c
2
c
8
c
3
c
5
c
1
, c
4
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
44
− u
43
+ ··· + 3u
2
+ b, −8u
45
− 5u
44
+ ··· + 2a + 11, u
46
+ 3u
45
+ ··· + 3u − 1i
I
u
2
= hb, a
2
− au + a − u + 2, u
2
− u − 1i
* 2 irreducible components of dim
C
= 0, with total 50 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
=
h−u
44
−u
43
+· · ·+3u
2
+b, −8u
45
−5u
44
+· · ·+2a+11 , u
46
+3u
45
+· · ·+3u−1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
7
=
−u
−u
3
+ u
a
11
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
u
4
− 3u
2
+ 1
−u
4
+ 2u
2
a
3
=
4u
45
+
5
2
u
44
+ ··· + 18u −
11
2
u
44
+ u
43
+ ··· − 7u
3
− 3u
2
a
2
=
2u
45
+
1
2
u
44
+ ··· + 12u −
7
2
−
3
2
u
45
−
3
2
u
44
+ ··· −
9
2
u +
3
2
a
8
=
u
3
− 2u
u
5
− 3u
3
+ u
a
4
=
u
45
−
1
2
u
44
+ ··· + 11u −
7
2
−5u
45
− 7u
44
+ ··· − 14u + 4
a
5
=
1
2
u
44
+ u
43
+ ··· − 5u −
1
2
−u
14
+ 8u
12
+ ··· + u
2
+ 2u
a
5
=
1
2
u
44
+ u
43
+ ··· − 5u −
1
2
−u
14
+ 8u
12
+ ··· + u
2
+ 2u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
21
2
u
45
− 16u
44
+ ··· −
31
2
u + 3
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
46
+ 3u
45
+ ··· + 7u + 1
c
2
, c
5
u
46
+ 15u
45
+ ··· − 45u + 1
c
3
, c
8
u
46
+ u
45
+ ··· − 48u − 16
c
6
, c
7
, c
9
c
10
u
46
+ 3u
45
+ ··· + 3u − 1
c
11
u
46
− 11u
45
+ ··· + 5u − 73
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
46
+ 15y
45
+ ··· − 45y + 1
c
2
, c
5
y
46
+ 35y
45
+ ··· − 2249y + 1
c
3
, c
8
y
46
+ 25y
45
+ ··· + 2176y + 256
c
6
, c
7
, c
9
c
10
y
46
− 53y
45
+ ··· − 9y + 1
c
11
y
46
+ 7y
45
+ ··· + 31219y + 5329
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.683033 + 0.585511I
a = −1.17131 + 1.61239I
b = −0.586768 − 1.279220I
4.58631 − 10.20080I −5.76564 + 8.71859I
u = 0.683033 − 0.585511I
a = −1.17131 − 1.61239I
b = −0.586768 + 1.279220I
4.58631 + 10.20080I −5.76564 − 8.71859I
u = −1.107400 + 0.146429I
a = 0.192350 + 0.087991I
b = −0.167779 − 1.185070I
1.38563 − 2.89669I −7.00000 + 0.I
u = −1.107400 − 0.146429I
a = 0.192350 − 0.087991I
b = −0.167779 + 1.185070I
1.38563 + 2.89669I −7.00000 + 0.I
u = 0.644087 + 0.591749I
a = 1.12925 − 1.65187I
b = 0.490901 + 1.297460I
5.48925 − 4.23240I −3.97125 + 3.86585I
u = 0.644087 − 0.591749I
a = 1.12925 + 1.65187I
b = 0.490901 − 1.297460I
5.48925 + 4.23240I −3.97125 − 3.86585I
u = −0.721560 + 0.271962I
a = 0.078758 − 0.314563I
b = −0.586991 − 0.576410I
−2.76000 + 0.49175I −14.4049 − 1.3153I
u = −0.721560 − 0.271962I
a = 0.078758 + 0.314563I
b = −0.586991 + 0.576410I
−2.76000 − 0.49175I −14.4049 + 1.3153I
u = 0.625541 + 0.443656I
a = −1.32103 + 1.86857I
b = −0.437369 − 0.962184I
−1.57427 − 4.58885I −10.12217 + 8.09100I
u = 0.625541 − 0.443656I
a = −1.32103 − 1.86857I
b = −0.437369 + 0.962184I
−1.57427 + 4.58885I −10.12217 − 8.09100I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.307520 + 0.663659I
a = 0.67086 − 1.68681I
b = −0.327075 + 1.311180I
6.48322 + 0.00049I −1.75811 + 1.98241I
u = 0.307520 − 0.663659I
a = 0.67086 + 1.68681I
b = −0.327075 − 1.311180I
6.48322 − 0.00049I −1.75811 − 1.98241I
u = 0.259302 + 0.676556I
a = −0.61524 + 1.65084I
b = 0.443673 − 1.290370I
5.83960 + 5.95442I −2.89350 − 3.47222I
u = 0.259302 − 0.676556I
a = −0.61524 − 1.65084I
b = 0.443673 + 1.290370I
5.83960 − 5.95442I −2.89350 + 3.47222I
u = −1.280730 + 0.112519I
a = −0.245265 − 0.380738I
b = 0.020723 + 1.301980I
1.51797 + 2.92543I 0
u = −1.280730 − 0.112519I
a = −0.245265 + 0.380738I
b = 0.020723 − 1.301980I
1.51797 − 2.92543I 0
u = −0.529027 + 0.472674I
a = 0.104077 − 0.663139I
b = −1.023760 − 0.238308I
1.28884 + 4.36080I −6.58604 − 6.72191I
u = −0.529027 − 0.472674I
a = 0.104077 + 0.663139I
b = −1.023760 + 0.238308I
1.28884 − 4.36080I −6.58604 + 6.72191I
u = 0.480914 + 0.492416I
a = 0.97784 − 1.95842I
b = 0.137372 + 1.054990I
2.15360 − 1.72767I −2.05511 + 4.46443I
u = 0.480914 − 0.492416I
a = 0.97784 + 1.95842I
b = 0.137372 − 1.054990I
2.15360 + 1.72767I −2.05511 − 4.46443I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.438186 + 0.463380I
a = −0.026707 + 0.771502I
b = 0.986397 + 0.062419I
1.56190 − 1.05001I −5.35085 − 0.93346I
u = −0.438186 − 0.463380I
a = −0.026707 − 0.771502I
b = 0.986397 − 0.062419I
1.56190 + 1.05001I −5.35085 + 0.93346I
u = −0.507626
a = 0.299451
b = 0.385891
−0.763627 −13.0210
u = 1.52489 + 0.10717I
a = −0.593194 + 0.302209I
b = −1.107570 + 0.332603I
−5.01225 − 0.84578I 0
u = 1.52489 − 0.10717I
a = −0.593194 − 0.302209I
b = −1.107570 − 0.332603I
−5.01225 + 0.84578I 0
u = −1.52977 + 0.12312I
a = −0.863933 − 0.983761I
b = −0.377563 + 1.143250I
−4.55511 + 3.84471I 0
u = −1.52977 − 0.12312I
a = −0.863933 + 0.983761I
b = −0.377563 − 1.143250I
−4.55511 − 3.84471I 0
u = −1.53985 + 0.07420I
a = 0.78183 + 1.34401I
b = 0.289274 − 0.982056I
−7.15725 − 0.57650I 0
u = −1.53985 − 0.07420I
a = 0.78183 − 1.34401I
b = 0.289274 + 0.982056I
−7.15725 + 0.57650I 0
u = 1.54840 + 0.12785I
a = 0.555669 − 0.368908I
b = 1.123810 − 0.444850I
−5.69586 − 6.48224I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.54840 − 0.12785I
a = 0.555669 + 0.368908I
b = 1.123810 + 0.444850I
−5.69586 + 6.48224I 0
u = 1.56614
a = −0.397337
b = −0.732082
−7.96363 0
u = 0.374900 + 0.216095I
a = −0.66143 + 2.89217I
b = −0.016090 − 0.601274I
−0.45061 + 1.71194I −2.49876 + 0.88608I
u = 0.374900 − 0.216095I
a = −0.66143 − 2.89217I
b = −0.016090 + 0.601274I
−0.45061 − 1.71194I −2.49876 − 0.88608I
u = −1.57913 + 0.12981I
a = 1.16947 + 0.97231I
b = 0.561226 − 1.073100I
−9.03771 + 6.69933I 0
u = −1.57913 − 0.12981I
a = 1.16947 − 0.97231I
b = 0.561226 + 1.073100I
−9.03771 − 6.69933I 0
u = −1.57933 + 0.18068I
a = −1.126920 − 0.715105I
b = −0.63333 + 1.27572I
−1.94737 + 7.08897I 0
u = −1.57933 − 0.18068I
a = −1.126920 + 0.715105I
b = −0.63333 − 1.27572I
−1.94737 − 7.08897I 0
u = −1.59661 + 0.17970I
a = 1.197120 + 0.701362I
b = 0.70332 − 1.25495I
−3.07316 + 13.05900I 0
u = −1.59661 − 0.17970I
a = 1.197120 − 0.701362I
b = 0.70332 + 1.25495I
−3.07316 − 13.05900I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.60828 + 0.06972I
a = 0.335640 − 0.307192I
b = 0.725228 − 0.531744I
−10.75540 − 1.74430I 0
u = 1.60828 − 0.06972I
a = 0.335640 + 0.307192I
b = 0.725228 + 0.531744I
−10.75540 + 1.74430I 0
u = 0.146575 + 0.355630I
a = −0.07132 + 2.11990I
b = 0.324197 − 0.645662I
−0.43858 + 1.61222I −5.01416 − 3.15107I
u = 0.146575 − 0.355630I
a = −0.07132 − 2.11990I
b = 0.324197 + 0.645662I
−0.43858 − 1.61222I −5.01416 + 3.15107I
u = 1.66888 + 0.01472I
a = 0.052432 − 0.383179I
b = 0.131270 − 0.825055I
−8.02868 + 2.53357I 0
u = 1.66888 − 0.01472I
a = 0.052432 + 0.383179I
b = 0.131270 + 0.825055I
−8.02868 − 2.53357I 0
9
II. I
u
2
= hb, a
2
− au + a − u + 2, u
2
− u − 1i
(i) Arc colorings
a
6
=
0
u
a
9
=
1
0
a
10
=
1
u + 1
a
7
=
−u
−u − 1
a
11
=
−u
−u
a
1
=
0
−u
a
3
=
a
0
a
2
=
a
−au − a
a
8
=
1
0
a
4
=
a
0
a
5
=
a − u + 1
u
a
5
=
a − u + 1
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3au − 2a + u − 16
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
(u
2
+ u + 1)
2
c
3
, c
8
u
4
c
4
(u
2
− u + 1)
2
c
6
, c
7
(u
2
+ u − 1)
2
c
9
, c
10
, c
11
(u
2
− u − 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
2
c
3
, c
8
y
4
c
6
, c
7
, c
9
c
10
, c
11
(y
2
− 3y + 1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = −0.80902 + 1.40126I
b = 0
−0.98696 + 2.02988I −13.5000 − 5.4006I
u = −0.618034
a = −0.80902 − 1.40126I
b = 0
−0.98696 − 2.02988I −13.5000 + 5.4006I
u = 1.61803
a = 0.309017 + 0.535233I
b = 0
−8.88264 − 2.02988I −13.50000 + 1.52761I
u = 1.61803
a = 0.309017 − 0.535233I
b = 0
−8.88264 + 2.02988I −13.50000 − 1.52761I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
2
)(u
46
+ 3u
45
+ ··· + 7u + 1)
c
2
, c
5
((u
2
+ u + 1)
2
)(u
46
+ 15u
45
+ ··· − 45u + 1)
c
3
, c
8
u
4
(u
46
+ u
45
+ ··· − 48u − 16)
c
4
((u
2
− u + 1)
2
)(u
46
+ 3u
45
+ ··· + 7u + 1)
c
6
, c
7
((u
2
+ u − 1)
2
)(u
46
+ 3u
45
+ ··· + 3u − 1)
c
9
, c
10
((u
2
− u − 1)
2
)(u
46
+ 3u
45
+ ··· + 3u − 1)
c
11
((u
2
− u − 1)
2
)(u
46
− 11u
45
+ ··· + 5u − 73)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
2
)(y
46
+ 15y
45
+ ··· − 45y + 1)
c
2
, c
5
((y
2
+ y + 1)
2
)(y
46
+ 35y
45
+ ··· − 2249y + 1)
c
3
, c
8
y
4
(y
46
+ 25y
45
+ ··· + 2176y + 256)
c
6
, c
7
, c
9
c
10
((y
2
− 3y + 1)
2
)(y
46
− 53y
45
+ ··· − 9y + 1)
c
11
((y
2
− 3y + 1)
2
)(y
46
+ 7y
45
+ ··· + 31219y + 5329)
15
