11a
62
(K11a
62
)
A knot diagram
1
Linearized knot diagam
5 1 9 2 4 10 11 3 6 7 8
Solving Sequence
7,10
11 8 1
4,6
5 9 3 2
c
10
c
7
c
11
c
6
c
5
c
9
c
3
c
2
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h3u
30
− 3u
29
+ ··· + 2b − 3, −5u
30
+ 8u
29
+ ··· + 2a + 5u, u
31
− 3u
30
+ ··· − 12u
2
+ 1i
I
u
2
= h−au + b, a
2
− a + 1, u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 35 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
=
h3u
30
−3u
29
+· · ·+2b−3, −5u
30
+8u
29
+· · ·+2a+5u, u
31
−3u
30
+· · ·−12u
2
+1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
8
=
u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
4
=
5
2
u
30
− 4u
29
+ ··· +
11
2
u
2
−
5
2
u
−
3
2
u
30
+
3
2
u
29
+ ··· − u +
3
2
a
6
=
−u
u
a
5
=
−
1
2
u
30
+ u
29
+ ··· −
11
2
u + 1
1
2
u
30
−
1
2
u
29
+ ··· +
19
2
u
2
−
1
2
a
9
=
−u
2
+ 1
u
2
a
3
=
−
9
2
u
30
+ 5u
29
+ ··· +
1
2
u + 4
17
2
u
30
−
21
2
u
29
+ ··· − 4u −
9
2
a
2
=
−2u
30
+
3
2
u
29
+ ··· −
3
2
u +
7
2
4u
30
− 5u
29
+ ··· − 2u − 2
a
2
=
−2u
30
+
3
2
u
29
+ ··· −
3
2
u +
7
2
4u
30
− 5u
29
+ ··· − 2u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes =
13
2
u
30
− 8u
29
+ ··· +
31
2
u + 9
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
31
+ 3u
30
+ ··· + 4u − 1
c
2
, c
5
u
31
+ 9u
30
+ ··· + 12u − 1
c
3
, c
8
u
31
+ u
30
+ ··· − 20u
2
+ 16
c
6
, c
7
, c
9
c
10
, c
11
u
31
− 3u
30
+ ··· − 12u
2
+ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
31
+ 9y
30
+ ··· + 12y −1
c
2
, c
5
y
31
+ 29y
30
+ ··· + 524y −1
c
3
, c
8
y
31
− 25y
30
+ ··· + 640y −256
c
6
, c
7
, c
9
c
10
, c
11
y
31
− 43y
30
+ ··· + 24y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.979024 + 0.144758I
a = 0.831915 + 0.090072I
b = 0.119170 + 0.711208I
2.01140 − 3.46353I 11.93946 + 5.35734I
u = −0.979024 − 0.144758I
a = 0.831915 − 0.090072I
b = 0.119170 − 0.711208I
2.01140 + 3.46353I 11.93946 − 5.35734I
u = 1.077390 + 0.054634I
a = 0.229000 − 1.283970I
b = −0.36400 + 2.47719I
4.65693 + 2.79600I 13.44598 − 3.14561I
u = 1.077390 − 0.054634I
a = 0.229000 + 1.283970I
b = −0.36400 − 2.47719I
4.65693 − 2.79600I 13.44598 + 3.14561I
u = −1.11047
a = −1.03356
b = 0.559359
5.42058 16.8260
u = −1.127600 + 0.375707I
a = 0.299700 − 0.775841I
b = −0.43314 + 2.13863I
9.18803 − 8.59967I 14.1525 + 6.5112I
u = −1.127600 − 0.375707I
a = 0.299700 + 0.775841I
b = −0.43314 − 2.13863I
9.18803 + 8.59967I 14.1525 − 6.5112I
u = −1.174380 + 0.329803I
a = −0.642970 + 0.790351I
b = 0.82679 − 1.90155I
9.85498 − 2.40122I 15.3857 + 1.4439I
u = −1.174380 − 0.329803I
a = −0.642970 − 0.790351I
b = 0.82679 + 1.90155I
9.85498 + 2.40122I 15.3857 − 1.4439I
u = 0.422649 + 0.629353I
a = −1.064760 − 0.248038I
b = −0.493860 − 0.673775I
4.80361 − 0.89095I 12.16176 − 0.45664I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.422649 − 0.629353I
a = −1.064760 + 0.248038I
b = −0.493860 + 0.673775I
4.80361 + 0.89095I 12.16176 + 0.45664I
u = 0.348369 + 0.655737I
a = 1.28503 + 0.62780I
b = 0.291890 + 0.578542I
4.57379 + 5.07655I 11.28457 − 5.75893I
u = 0.348369 − 0.655737I
a = 1.28503 − 0.62780I
b = 0.291890 − 0.578542I
4.57379 − 5.07655I 11.28457 + 5.75893I
u = 0.698660 + 0.209211I
a = 0.266260 − 0.231304I
b = −0.762190 + 0.457078I
0.456932 + 0.462087I 9.00639 − 0.86680I
u = 0.698660 − 0.209211I
a = 0.266260 + 0.231304I
b = −0.762190 − 0.457078I
0.456932 − 0.462087I 9.00639 + 0.86680I
u = 0.099887 + 0.392148I
a = −0.03361 + 1.67355I
b = 0.443597 + 0.182843I
−1.25989 + 1.71484I 2.62221 − 5.71238I
u = 0.099887 − 0.392148I
a = −0.03361 − 1.67355I
b = 0.443597 − 0.182843I
−1.25989 − 1.71484I 2.62221 + 5.71238I
u = 0.394527
a = 0.563421
b = −0.451465
0.662850 15.1240
u = −1.63009 + 0.03537I
a = −0.815204 − 0.932358I
b = 1.04001 + 1.19147I
8.61876 − 1.24218I 0
u = −1.63009 − 0.03537I
a = −0.815204 + 0.932358I
b = 1.04001 − 1.19147I
8.61876 + 1.24218I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.268160 + 0.102485I
a = −0.10435 + 2.92800I
b = 0.250893 + 0.701619I
0.38814 − 2.23506I 1.04827 + 4.75217I
u = −0.268160 − 0.102485I
a = −0.10435 − 2.92800I
b = 0.250893 − 0.701619I
0.38814 + 2.23506I 1.04827 − 4.75217I
u = 1.72918 + 0.03341I
a = 0.219808 − 1.029000I
b = −0.95945 + 1.46832I
11.77940 + 4.15554I 0
u = 1.72918 − 0.03341I
a = 0.219808 + 1.029000I
b = −0.95945 − 1.46832I
11.77940 − 4.15554I 0
u = −1.75006 + 0.01346I
a = −0.27253 − 3.19299I
b = 0.33934 + 4.04196I
14.9045 − 3.0785I 0
u = −1.75006 − 0.01346I
a = −0.27253 + 3.19299I
b = 0.33934 − 4.04196I
14.9045 + 3.0785I 0
u = 1.75654
a = 0.528132
b = −0.0669841
15.8245 0
u = 1.76039 + 0.10095I
a = −0.77692 − 2.65214I
b = 0.57757 + 3.62883I
19.5055 + 10.6386I 0
u = 1.76039 − 0.10095I
a = −0.77692 + 2.65214I
b = 0.57757 − 3.62883I
19.5055 − 10.6386I 0
u = 1.77250 + 0.08381I
a = 1.04963 + 2.23983I
b = −0.89708 − 3.04423I
−19.0119 + 4.1870I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.77250 − 0.08381I
a = 1.04963 − 2.23983I
b = −0.89708 + 3.04423I
−19.0119 − 4.1870I 0
8
II. I
u
2
= h−au + b, a
2
− a + 1, u
2
+ u − 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
u − 1
a
8
=
u
−u + 1
a
1
=
u
−u
a
4
=
a
au
a
6
=
−u
u
a
5
=
a − u − 1
au
a
9
=
u
−u + 1
a
3
=
a
au
a
2
=
au + a
0
a
2
=
au + a
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2au + 3a + u + 12
9
(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
10
(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
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 0.500000 + 0.866025I
b = 0.309017 + 0.535233I
0.98696 − 2.02988I 13.50000 + 1.52761I
u = 0.618034
a = 0.500000 − 0.866025I
b = 0.309017 − 0.535233I
0.98696 + 2.02988I 13.50000 − 1.52761I
u = −1.61803
a = 0.500000 + 0.866025I
b = −0.80902 − 1.40126I
8.88264 − 2.02988I 13.5000 + 5.4006I
u = −1.61803
a = 0.500000 − 0.866025I
b = −0.80902 + 1.40126I
8.88264 + 2.02988I 13.5000 − 5.4006I
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
2
)(u
31
+ 3u
30
+ ··· + 4u − 1)
c
2
, c
5
((u
2
+ u + 1)
2
)(u
31
+ 9u
30
+ ··· + 12u − 1)
c
3
, c
8
u
4
(u
31
+ u
30
+ ··· − 20u
2
+ 16)
c
4
((u
2
− u + 1)
2
)(u
31
+ 3u
30
+ ··· + 4u − 1)
c
6
, c
7
((u
2
− u − 1)
2
)(u
31
− 3u
30
+ ··· − 12u
2
+ 1)
c
9
, c
10
, c
11
((u
2
+ u − 1)
2
)(u
31
− 3u
30
+ ··· − 12u
2
+ 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
2
)(y
31
+ 9y
30
+ ··· + 12y −1)
c
2
, c
5
((y
2
+ y + 1)
2
)(y
31
+ 29y
30
+ ··· + 524y −1)
c
3
, c
8
y
4
(y
31
− 25y
30
+ ··· + 640y −256)
c
6
, c
7
, c
9
c
10
, c
11
((y
2
− 3y + 1)
2
)(y
31
− 43y
30
+ ··· + 24y −1)
14
