10
46
(K10a
81
)
A knot diagram
1
Linearized knot diagam
8 5 6 9 3 10 1 2 4 7
Solving Sequence
6,10
7 1
4,8
3 5 2 9
c
6
c
10
c
7
c
3
c
5
c
2
c
9
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
16
+ u
15
+ ··· + b + u, −u
16
− u
15
+ ··· + a + 1, u
17
+ 2u
16
+ ··· − u − 1i
I
u
2
= hb + 1, a, u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 19 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
= hu
16
+ u
15
+ · · · + b + u, −u
16
− u
15
+ · · · + a + 1, u
17
+ 2u
16
+ · · · − u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
u
2
a
1
=
−u
−u
3
+ u
a
4
=
u
16
+ u
15
+ ··· − 5u − 1
−u
16
− u
15
+ ··· − 8u
2
− u
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
−u
10
+ 7u
8
− 16u
6
− 2u
5
+ 13u
4
+ 8u
3
− 3u
2
− 6u − 1
−u
16
− u
15
+ ··· − 8u
2
− u
a
5
=
−u
16
− u
15
+ ··· − 8u
2
− 5u
−u
16
− u
15
+ ··· − 8u
2
− 2u
a
2
=
u
3
− 2u
u
5
− 3u
3
+ u
a
9
=
−u
4
+ 3u
2
− 1
−u
6
+ 4u
4
− 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
16
+ 7u
15
− 39u
14
− 68u
13
+ 147u
12
+ 260u
11
− 262u
10
−
506u
9
+ 183u
8
+ 536u
7
+ 82u
6
− 286u
5
− 192u
4
+ 52u
3
+ 74u
2
+ 6u − 9
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
c
8
, c
10
u
17
+ 2u
16
+ ··· − u − 1
c
2
, c
3
, c
5
u
17
− 3u
16
+ ··· − 2u + 1
c
4
, c
9
u
17
+ u
16
+ ··· + 8u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
7
c
8
, c
10
y
17
− 24y
16
+ ··· + 15y − 1
c
2
, c
3
, c
5
y
17
− 19y
16
+ ··· + 26y − 1
c
4
, c
9
y
17
+ 15y
16
+ ··· + 72y − 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.061550 + 0.132627I
a = −0.032032 + 1.057310I
b = −0.560836 − 0.704658I
−4.50346 − 2.40856I −13.38977 + 3.98608I
u = 1.061550 − 0.132627I
a = −0.032032 − 1.057310I
b = −0.560836 + 0.704658I
−4.50346 + 2.40856I −13.38977 − 3.98608I
u = −1.10417
a = −1.02988
b = −1.38948
−6.53818 −13.8720
u = 1.160740 + 0.369892I
a = −0.033674 − 1.270360I
b = 1.55782 + 0.20538I
−11.54310 − 5.69036I −14.9028 + 4.0871I
u = 1.160740 − 0.369892I
a = −0.033674 + 1.270360I
b = 1.55782 − 0.20538I
−11.54310 + 5.69036I −14.9028 − 4.0871I
u = −0.389835 + 0.662254I
a = −1.45018 + 1.06769I
b = 1.50356 − 0.06755I
−6.67400 + 2.15086I −12.06720 − 3.08735I
u = −0.389835 − 0.662254I
a = −1.45018 − 1.06769I
b = 1.50356 + 0.06755I
−6.67400 − 2.15086I −12.06720 + 3.08735I
u = −0.726749
a = 0.648394
b = 0.235031
−1.27609 −7.02090
u = −0.245709 + 0.306515I
a = 1.04586 − 1.37638I
b = −0.353541 + 0.303071I
−0.413031 + 0.944940I −7.13539 − 7.21571I
u = −0.245709 − 0.306515I
a = 1.04586 + 1.37638I
b = −0.353541 − 0.303071I
−0.413031 − 0.944940I −7.13539 + 7.21571I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.64837
a = 0.374676
b = 0.532039
−9.71406 −6.33030
u = 0.288922
a = −1.61818
b = −1.09525
−2.06625 −1.61000
u = −1.74789 + 0.03164I
a = −0.112337 − 0.821992I
b = −0.626661 + 0.929444I
−14.6712 + 3.0771I −13.60428 − 2.54829I
u = −1.74789 − 0.03164I
a = −0.112337 + 0.821992I
b = −0.626661 − 0.929444I
−14.6712 − 3.0771I −13.60428 + 2.54829I
u = 1.75801
a = −0.853301
b = −1.56221
−16.9433 −14.4070
u = −1.77104 + 0.09789I
a = 0.321515 + 0.925880I
b = 1.61959 − 0.31356I
17.4178 + 7.7170I −15.2806 − 3.2820I
u = −1.77104 − 0.09789I
a = 0.321515 − 0.925880I
b = 1.61959 + 0.31356I
17.4178 − 7.7170I −15.2806 + 3.2820I
6
II. I
u
2
= hb + 1, a, u
2
+ u − 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
7
=
1
−u + 1
a
1
=
−u
−u + 1
a
4
=
0
−1
a
8
=
u
u
a
3
=
−1
−1
a
5
=
0
−1
a
2
=
−1
0
a
9
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −17
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
u
2
− u − 1
c
2
, c
3
(u − 1)
2
c
4
, c
9
u
2
c
5
(u + 1)
2
c
6
, c
7
, c
8
u
2
+ u − 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
7
c
8
, c
10
y
2
− 3y + 1
c
2
, c
3
, c
5
(y −1)
2
c
4
, c
9
y
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 0
b = −1.00000
−2.63189 −17.0000
u = −1.61803
a = 0
b = −1.00000
−10.5276 −17.0000
10
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
2
− u − 1)(u
17
+ 2u
16
+ ··· − u − 1)
c
2
, c
3
((u − 1)
2
)(u
17
− 3u
16
+ ··· − 2u + 1)
c
4
, c
9
u
2
(u
17
+ u
16
+ ··· + 8u + 4)
c
5
((u + 1)
2
)(u
17
− 3u
16
+ ··· − 2u + 1)
c
6
, c
7
, c
8
(u
2
+ u − 1)(u
17
+ 2u
16
+ ··· − u − 1)
11
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
7
c
8
, c
10
(y
2
− 3y + 1)(y
17
− 24y
16
+ ··· + 15y − 1)
c
2
, c
3
, c
5
((y −1)
2
)(y
17
− 19y
16
+ ··· + 26y − 1)
c
4
, c
9
y
2
(y
17
+ 15y
16
+ ··· + 72y − 16)
12
