11n
88
(K11n
88
)
A knot diagram
1
Linearized knot diagam
6 1 8 9 2 3 11 4 5 1 8
Solving Sequence
4,8
9 5
1,3
2 11 7 6 10
c
8
c
4
c
3
c
2
c
11
c
7
c
6
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−68u
10
+ 123u
9
+ ··· + 3382b − 1078, 1249u
10
− 46u
9
+ ··· + 6764a − 1934,
u
11
− u
10
− 10u
9
+ 9u
8
+ 37u
7
− 31u
6
− 54u
5
+ 48u
4
+ 8u
3
− 4u − 4i
I
u
2
= hb + 1, 2a
2
− au + 4a − u + 3, u
2
− 2i
I
v
1
= ha, b − 1, v
2
+ v + 1i
* 3 irreducible components of dim
C
= 0, with total 17 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−68u
10
+ 123u
9
+ · · · + 3382b − 1078, 1249u
10
− 46u
9
+ · · · +
6764a − 1934, u
11
− u
10
+ · · · − 4u − 4i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
5
=
−u
−u
3
+ u
a
1
=
−0.184654u
10
+ 0.00680071u
9
+ ··· − 0.694855u + 0.285925
0.0201064u
10
− 0.0363690u
9
+ ··· + 0.324660u + 0.318746
a
3
=
u
u
a
2
=
0.102750u
10
+ 0.0604672u
9
+ ··· + 2.38705u − 0.0990538
−0.191455u
10
− 0.00295683u
9
+ ··· − 0.937020u − 0.689533
a
11
=
−0.164548u
10
− 0.0295683u
9
+ ··· − 0.370195u + 0.604672
0.0201064u
10
− 0.0363690u
9
+ ··· + 0.324660u + 0.318746
a
7
=
−0.178888u
10
+ 0.0368125u
9
+ ··· − 0.609107u + 0.384684
−0.175636u
10
+ 0.00887049u
9
+ ··· − 1.68894u − 0.931402
a
6
=
−0.184654u
10
+ 0.00680071u
9
+ ··· − 0.694855u + 0.285925
−0.181402u
10
− 0.0211413u
9
+ ··· − 1.77469u − 1.03016
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1322
1691
u
10
−
750
1691
u
9
−
13061
1691
u
8
+
6124
1691
u
7
+
523
19
u
6
−
20067
1691
u
5
−
60106
1691
u
4
+
35628
1691
u
3
−
7299
1691
u
2
+
756
1691
u −
12564
1691
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
11
− 2u
10
+ 7u
9
− 10u
8
+ 17u
7
− 19u
6
+ 14u
5
− 18u
4
− 6u
2
− 6u − 1
c
2
u
11
+ 10u
10
+ ··· + 24u − 1
c
3
, c
4
, c
8
c
9
u
11
− u
10
− 10u
9
+ 9u
8
+ 37u
7
− 31u
6
− 54u
5
+ 48u
4
+ 8u
3
− 4u − 4
c
6
u
11
+ 2u
10
+ ··· − 90u − 13
c
7
, c
11
u
11
+ 3u
10
+ ··· − u − 7
c
10
u
11
+ 23u
10
+ ··· + 225u + 49
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
11
+ 10y
10
+ ··· + 24y −1
c
2
y
11
− 14y
10
+ ··· + 432y −1
c
3
, c
4
, c
8
c
9
y
11
− 21y
10
+ ··· + 16y −16
c
6
y
11
− 38y
10
+ ··· + 4460y −169
c
7
, c
11
y
11
− 23y
10
+ ··· + 225y −49
c
10
y
11
− 63y
10
+ ··· − 61879y −2401
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.927671 + 0.197201I
a = −0.182641 + 0.461344I
b = 0.723376 − 0.590700I
−3.55618 + 2.69456I −12.98158 − 3.53797I
u = 0.927671 − 0.197201I
a = −0.182641 − 0.461344I
b = 0.723376 + 0.590700I
−3.55618 − 2.69456I −12.98158 + 3.53797I
u = 1.36751
a = −1.06580
b = −1.10452
−6.50002 −13.6590
u = −0.128515 + 0.466174I
a = 1.31999 + 0.78489I
b = −0.333924 − 0.361452I
−0.58979 + 1.50760I −5.46704 − 3.06669I
u = −0.128515 − 0.466174I
a = 1.31999 − 0.78489I
b = −0.333924 + 0.361452I
−0.58979 − 1.50760I −5.46704 + 3.06669I
u = −0.464364
a = 0.318779
b = 0.568678
−0.828081 −11.8310
u = −1.75254 + 0.61261I
a = −0.637478 − 0.443047I
b = −1.97688 − 0.71300I
−12.58100 + 1.38651I −13.48038 − 0.69811I
u = −1.75254 − 0.61261I
a = −0.637478 + 0.443047I
b = −1.97688 + 0.71300I
−12.58100 − 1.38651I −13.48038 + 0.69811I
u = 2.03058 + 0.31596I
a = 1.212210 − 0.346594I
b = 2.21938 + 0.57715I
13.7044 − 7.4448I −12.73851 + 2.77525I
u = 2.03058 − 0.31596I
a = 1.212210 + 0.346594I
b = 2.21938 − 0.57715I
13.7044 + 7.4448I −12.73851 − 2.77525I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −2.05754
a = 1.32286
b = 2.27195
18.3080 −11.1750
6
II. I
u
2
= hb + 1, 2a
2
− au + 4a − u + 3, u
2
− 2i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
2
a
5
=
−u
−u
a
1
=
a
−1
a
3
=
u
u
a
2
=
−au + a −
1
2
u + 1
−au
a
11
=
a − 1
−1
a
7
=
a
−1
a
6
=
−a − 2
−2a − 3
a
10
=
−1
0
a
10
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4au + 4u − 16
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
2
− u + 1)
2
c
2
, c
5
(u
2
+ u + 1)
2
c
3
, c
4
, c
8
c
9
(u
2
− 2)
2
c
7
(u + 1)
4
c
10
, c
11
(u − 1)
4
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
(y
2
+ y + 1)
2
c
3
, c
4
, c
8
c
9
(y −2)
4
c
7
, c
10
, c
11
(y −1)
4
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = −0.646447 + 0.612372I
b = −1.00000
−6.57974 − 2.02988I −14.0000 + 3.4641I
u = 1.41421
a = −0.646447 − 0.612372I
b = −1.00000
−6.57974 + 2.02988I −14.0000 − 3.4641I
u = −1.41421
a = −1.35355 + 0.61237I
b = −1.00000
−6.57974 + 2.02988I −14.0000 − 3.4641I
u = −1.41421
a = −1.35355 − 0.61237I
b = −1.00000
−6.57974 − 2.02988I −14.0000 + 3.4641I
10
III. I
v
1
= ha, b − 1, v
2
+ v + 1i
(i) Arc colorings
a
4
=
v
0
a
8
=
1
0
a
9
=
1
0
a
5
=
v
0
a
1
=
0
1
a
3
=
v
0
a
2
=
v
−v
a
11
=
1
1
a
7
=
0
−1
a
6
=
v + 1
−1
a
10
=
1
0
a
10
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 14
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
2
+ u + 1
c
3
, c
4
, c
8
c
9
u
2
c
5
u
2
− u + 1
c
7
, c
10
(u − 1)
2
c
11
(u + 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
y
2
+ y + 1
c
3
, c
4
, c
8
c
9
y
2
c
7
, c
10
, c
11
(y − 1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = 1.00000
−1.64493 + 2.02988I −12.00000 − 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = 1.00000
−1.64493 − 2.02988I −12.00000 + 3.46410I
14
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)
2
(u
2
+ u + 1)
· (u
11
− 2u
10
+ 7u
9
− 10u
8
+ 17u
7
− 19u
6
+ 14u
5
− 18u
4
− 6u
2
− 6u − 1)
c
2
((u
2
+ u + 1)
3
)(u
11
+ 10u
10
+ ··· + 24u − 1)
c
3
, c
4
, c
8
c
9
u
2
(u
2
− 2)
2
· (u
11
− u
10
− 10u
9
+ 9u
8
+ 37u
7
− 31u
6
− 54u
5
+ 48u
4
+ 8u
3
− 4u − 4)
c
5
(u
2
− u + 1)(u
2
+ u + 1)
2
· (u
11
− 2u
10
+ 7u
9
− 10u
8
+ 17u
7
− 19u
6
+ 14u
5
− 18u
4
− 6u
2
− 6u − 1)
c
6
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
11
+ 2u
10
+ ··· − 90u − 13)
c
7
((u − 1)
2
)(u + 1)
4
(u
11
+ 3u
10
+ ··· − u − 7)
c
10
((u − 1)
6
)(u
11
+ 23u
10
+ ··· + 225u + 49)
c
11
((u − 1)
4
)(u + 1)
2
(u
11
+ 3u
10
+ ··· − u − 7)
15
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
2
+ y + 1)
3
)(y
11
+ 10y
10
+ ··· + 24y − 1)
c
2
((y
2
+ y + 1)
3
)(y
11
− 14y
10
+ ··· + 432y − 1)
c
3
, c
4
, c
8
c
9
y
2
(y − 2)
4
(y
11
− 21y
10
+ ··· + 16y − 16)
c
6
((y
2
+ y + 1)
3
)(y
11
− 38y
10
+ ··· + 4460y − 169)
c
7
, c
11
((y − 1)
6
)(y
11
− 23y
10
+ ··· + 225y − 49)
c
10
((y − 1)
6
)(y
11
− 63y
10
+ ··· − 61879y − 2401)
16
