11a
64
(K11a
64
)
A knot diagram
1
Linearized knot diagam
5 1 9 2 4 11 10 3 8 6 7
Solving Sequence
6,10
11 7 8
1,4
5 2 9 3
c
10
c
6
c
7
c
11
c
5
c
1
c
9
c
3
c
2
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−5u
49
− 9u
48
+ ··· + b + 4, 3u
49
+ 4u
48
+ ··· + 2a − 1, u
50
+ 3u
49
+ ··· + 9u
2
− 1i
I
u
2
= hb, a
2
− a + 1, u − 1i
* 2 irreducible components of dim
C
= 0, with total 52 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−5u
49
−9u
48
+· · ·+b+4, 3u
49
+4u
48
+· · ·+2a−1, u
50
+3u
49
+· · ·+9u
2
−1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
7
=
u
−u
3
+ u
a
8
=
−u
3
+ 2u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
4
=
−
3
2
u
49
− 2u
48
+ ··· +
1
2
u +
1
2
5u
49
+ 9u
48
+ ··· + 4u − 4
a
5
=
1
2
u
49
+ u
48
+ ··· −
11
2
u +
1
2
−u
16
+ 6u
14
+ ··· − 6u
3
+ 4u
2
a
2
=
5
2
u
49
+ 4u
48
+ ··· +
1
2
u −
1
2
−
1
2
u
49
− u
48
+ ··· −
1
2
u +
1
2
a
9
=
u
6
− 3u
4
+ 2u
2
+ 1
u
6
− 2u
4
+ u
2
a
3
=
−
9
2
u
49
− 8u
48
+ ··· −
5
2
u +
5
2
−2u
49
− 3u
48
+ ··· − 8u
2
+ 1
a
3
=
−
9
2
u
49
− 8u
48
+ ··· −
5
2
u +
5
2
−2u
49
− 3u
48
+ ··· − 8u
2
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18u
49
− 27u
48
+ ··· − 2u + 25
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
50
+ 2u
49
+ ··· − 3u + 1
c
2
, c
5
u
50
+ 18u
49
+ ··· + u + 1
c
3
, c
8
u
50
+ u
49
+ ··· + 4u − 4
c
6
, c
10
, c
11
u
50
+ 3u
49
+ ··· + 9u
2
− 1
c
7
, c
9
u
50
− 15u
49
+ ··· − 104u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
50
+ 18y
49
+ ··· + y + 1
c
2
, c
5
y
50
+ 30y
49
+ ··· − 119y + 1
c
3
, c
8
y
50
− 15y
49
+ ··· − 104y + 16
c
6
, c
10
, c
11
y
50
− 41y
49
+ ··· − 18y + 1
c
7
, c
9
y
50
+ 37y
49
+ ··· − 3360y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.087890 + 0.165328I
a = 0.139852 − 0.213211I
b = 0.645187 − 0.289728I
1.40881 + 0.77400I 6.94609 + 0.I
u = 1.087890 − 0.165328I
a = 0.139852 + 0.213211I
b = 0.645187 + 0.289728I
1.40881 − 0.77400I 6.94609 + 0.I
u = 0.126757 + 0.868356I
a = −1.47159 − 0.94278I
b = −1.22103 − 1.33662I
−2.73323 + 9.52065I 5.03643 − 7.69857I
u = 0.126757 − 0.868356I
a = −1.47159 + 0.94278I
b = −1.22103 + 1.33662I
−2.73323 − 9.52065I 5.03643 + 7.69857I
u = 0.133262 + 0.831170I
a = 1.011800 + 0.474392I
b = 0.865719 + 1.020570I
−1.38173 + 4.04307I 7.01868 − 3.20265I
u = 0.133262 − 0.831170I
a = 1.011800 − 0.474392I
b = 0.865719 − 1.020570I
−1.38173 − 4.04307I 7.01868 + 3.20265I
u = 1.096200 + 0.388771I
a = −0.323801 − 0.626772I
b = 0.168381 + 0.406270I
1.57629 + 0.36486I 0
u = 1.096200 − 0.388771I
a = −0.323801 + 0.626772I
b = 0.168381 − 0.406270I
1.57629 − 0.36486I 0
u = 0.047274 + 0.835322I
a = 0.00341 − 1.47071I
b = −0.19335 − 1.77874I
−7.20082 + 2.98868I 0.09209 − 2.99503I
u = 0.047274 − 0.835322I
a = 0.00341 + 1.47071I
b = −0.19335 + 1.77874I
−7.20082 − 2.98868I 0.09209 + 2.99503I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.136100 + 0.443889I
a = 0.860244 + 0.826310I
b = 0.311641 − 0.759236I
0.35735 − 4.82997I 0
u = 1.136100 − 0.443889I
a = 0.860244 − 0.826310I
b = 0.311641 + 0.759236I
0.35735 + 4.82997I 0
u = −0.039568 + 0.776582I
a = 1.63186 − 0.95120I
b = 0.93537 − 1.48672I
−3.45504 − 3.62076I 3.32917 + 2.61098I
u = −0.039568 − 0.776582I
a = 1.63186 + 0.95120I
b = 0.93537 + 1.48672I
−3.45504 + 3.62076I 3.32917 − 2.61098I
u = 0.566666 + 0.530676I
a = 1.15612 + 0.89658I
b = 0.785797 + 0.191841I
3.39308 − 0.60483I 12.63177 − 0.83622I
u = 0.566666 − 0.530676I
a = 1.15612 − 0.89658I
b = 0.785797 − 0.191841I
3.39308 + 0.60483I 12.63177 + 0.83622I
u = 0.490724 + 0.589200I
a = −0.95926 − 1.35644I
b = −0.676569 − 0.417065I
3.13688 + 4.70114I 11.25136 − 7.35452I
u = 0.490724 − 0.589200I
a = −0.95926 + 1.35644I
b = −0.676569 + 0.417065I
3.13688 − 4.70114I 11.25136 + 7.35452I
u = −1.260390 + 0.078461I
a = −0.689828 − 0.574408I
b = 0.592579 − 0.232734I
2.80671 − 3.20550I 0
u = −1.260390 − 0.078461I
a = −0.689828 + 0.574408I
b = 0.592579 + 0.232734I
2.80671 + 3.20550I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.015463 + 0.734978I
a = −0.963235 + 0.305603I
b = −0.523840 + 1.031980I
−1.96381 + 1.49641I 5.67052 − 2.83851I
u = 0.015463 − 0.734978I
a = −0.963235 − 0.305603I
b = −0.523840 − 1.031980I
−1.96381 − 1.49641I 5.67052 + 2.83851I
u = −1.241070 + 0.324695I
a = −0.822795 + 0.783089I
b = 0.089700 − 0.769159I
0.243412 − 0.350536I 0
u = −1.241070 − 0.324695I
a = −0.822795 − 0.783089I
b = 0.089700 + 0.769159I
0.243412 + 0.350536I 0
u = 1.224770 + 0.385024I
a = 0.859798 − 0.298010I
b = −0.74436 − 1.63598I
−3.57195 + 1.39688I 0
u = 1.224770 − 0.385024I
a = 0.859798 + 0.298010I
b = −0.74436 + 1.63598I
−3.57195 − 1.39688I 0
u = 1.274810 + 0.306801I
a = 0.023714 + 0.698294I
b = 2.16911 + 1.11902I
1.95830 + 2.25536I 0
u = 1.274810 − 0.306801I
a = 0.023714 − 0.698294I
b = 2.16911 − 1.11902I
1.95830 − 2.25536I 0
u = 1.311800 + 0.024858I
a = 0.171282 − 0.913457I
b = 0.44051 − 2.72877I
5.15830 + 2.67468I 0
u = 1.311800 − 0.024858I
a = 0.171282 + 0.913457I
b = 0.44051 + 2.72877I
5.15830 − 2.67468I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.32705
a = 0.308792
b = −1.01507
5.84071 0
u = −1.290930 + 0.313969I
a = 0.384785 − 0.354450I
b = −0.676082 + 0.534271I
2.12444 − 5.28818I 0
u = −1.290930 − 0.313969I
a = 0.384785 + 0.354450I
b = −0.676082 − 0.534271I
2.12444 + 5.28818I 0
u = 1.297340 + 0.337432I
a = 0.180485 − 1.100720I
b = −2.31845 − 1.85146I
0.72091 + 7.64132I 0
u = 1.297340 − 0.337432I
a = 0.180485 + 1.100720I
b = −2.31845 + 1.85146I
0.72091 − 7.64132I 0
u = −1.302710 + 0.373085I
a = −0.869978 − 0.369291I
b = 1.05915 − 1.45675I
−2.98615 − 7.33040I 0
u = −1.302710 − 0.373085I
a = −0.869978 + 0.369291I
b = 1.05915 + 1.45675I
−2.98615 + 7.33040I 0
u = −1.352760 + 0.362996I
a = 0.035493 + 0.735238I
b = −2.06776 + 0.99691I
3.29225 − 8.34439I 0
u = −1.352760 − 0.362996I
a = 0.035493 − 0.735238I
b = −2.06776 − 0.99691I
3.29225 + 8.34439I 0
u = −1.356030 + 0.382707I
a = −0.148346 − 1.113900I
b = 2.30162 − 1.44569I
1.9302 − 14.0131I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.356030 − 0.382707I
a = −0.148346 + 1.113900I
b = 2.30162 + 1.44569I
1.9302 + 14.0131I 0
u = −1.41586 + 0.11171I
a = −0.068754 + 0.864041I
b = −1.19732 + 1.43891I
9.73666 − 1.34570I 0
u = −1.41586 − 0.11171I
a = −0.068754 − 0.864041I
b = −1.19732 − 1.43891I
9.73666 + 1.34570I 0
u = −1.41536 + 0.14641I
a = −0.125925 − 0.999357I
b = 0.70733 − 1.72091I
9.27302 − 7.09927I 0
u = −1.41536 − 0.14641I
a = −0.125925 + 0.999357I
b = 0.70733 + 1.72091I
9.27302 + 7.09927I 0
u = 0.104654 + 0.432324I
a = −0.39489 − 1.38867I
b = −0.504003 − 0.064352I
−1.18724 + 1.58310I 1.45548 − 5.77798I
u = 0.104654 − 0.432324I
a = −0.39489 + 1.38867I
b = −0.504003 + 0.064352I
−1.18724 − 1.58310I 1.45548 + 5.77798I
u = 0.375797
a = −0.231356
b = 0.443920
0.739246 14.0540
u = −0.263398 + 0.099445I
a = −0.15916 − 3.77330I
b = −0.163758 − 0.657660I
0.39231 − 2.25929I 1.99740 + 3.42645I
u = −0.263398 − 0.099445I
a = −0.15916 + 3.77330I
b = −0.163758 + 0.657660I
0.39231 + 2.25929I 1.99740 − 3.42645I
9
II. I
u
2
= hb, a
2
− a + 1, u − 1i
(i) Arc colorings
a
6
=
0
1
a
10
=
1
0
a
11
=
1
−1
a
7
=
1
0
a
8
=
1
0
a
1
=
0
−1
a
4
=
a
0
a
5
=
a − 1
1
a
2
=
a
−a
a
9
=
1
0
a
3
=
a
0
a
3
=
a
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4a + 7
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
u
2
+ u + 1
c
3
, c
7
, c
8
c
9
u
2
c
4
u
2
− u + 1
c
6
(u + 1)
2
c
10
, c
11
(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
c
3
, c
7
, c
8
c
9
y
2
c
6
, c
10
, c
11
(y −1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.500000 + 0.866025I
b = 0
1.64493 − 2.02988I 9.00000 + 3.46410I
u = 1.00000
a = 0.500000 − 0.866025I
b = 0
1.64493 + 2.02988I 9.00000 − 3.46410I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)(u
50
+ 2u
49
+ ··· − 3u + 1)
c
2
, c
5
(u
2
+ u + 1)(u
50
+ 18u
49
+ ··· + u + 1)
c
3
, c
8
u
2
(u
50
+ u
49
+ ··· + 4u − 4)
c
4
(u
2
− u + 1)(u
50
+ 2u
49
+ ··· − 3u + 1)
c
6
((u + 1)
2
)(u
50
+ 3u
49
+ ··· + 9u
2
− 1)
c
7
, c
9
u
2
(u
50
− 15u
49
+ ··· − 104u + 16)
c
10
, c
11
((u − 1)
2
)(u
50
+ 3u
49
+ ··· + 9u
2
− 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
2
+ y + 1)(y
50
+ 18y
49
+ ··· + y + 1)
c
2
, c
5
(y
2
+ y + 1)(y
50
+ 30y
49
+ ··· − 119y + 1)
c
3
, c
8
y
2
(y
50
− 15y
49
+ ··· − 104y + 16)
c
6
, c
10
, c
11
((y −1)
2
)(y
50
− 41y
49
+ ··· − 18y + 1)
c
7
, c
9
y
2
(y
50
+ 37y
49
+ ··· − 3360y + 256)
15
