11n
181
(K11n
181
)
A knot diagram
1
Linearized knot diagam
6 8 1 10 9 1 4 2 5 4 8
Solving Sequence
5,9
6
2,10
1 4 3 8 7 11
c
5
c
9
c
1
c
4
c
3
c
8
c
7
c
11
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
12
− 5u
11
+ 18u
10
− 47u
9
+ 95u
8
− 157u
7
+ 208u
6
− 225u
5
+ 194u
4
− 129u
3
+ 62u
2
+ 2b − 19u + 2,
u
12
− 3u
11
+ 14u
10
− 31u
9
+ 73u
8
− 119u
7
+ 178u
6
− 209u
5
+ 208u
4
− 165u
3
+ 104u
2
+ 4a − 45u + 12,
u
13
− 5u
12
+ ··· + 30u − 4i
I
u
2
= h−a
3
u
3
− a
3
u
2
− a
3
u + a
2
u
2
+ u
3
a + a
2
u − u
3
+ au − u
2
+ b + a − 2u + 1,
− a
3
u
3
+ u
3
a
2
+ a
4
− 2a
3
u + 6u
3
a + 2a
2
u + 5u
2
a + 4u
3
− a
2
+ 15au + 6u
2
+ 10a + 11u + 12,
u
4
+ u
3
+ 3u
2
+ 2u + 1i
I
u
3
= hu
4
+ u
3
+ 2u
2
+ b + 2u, u
2
+ a + 2, u
7
+ 5u
5
+ 7u
3
+ 2u − 1i
* 3 irreducible components of dim
C
= 0, with total 36 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
12
−5u
11
+· · ·+2b +2, u
12
−3u
11
+· · ·+4a +12, u
13
−5u
12
+· · ·+30u −4i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
u
2
a
2
=
−
1
4
u
12
+
3
4
u
11
+ ··· +
45
4
u − 3
−
1
2
u
12
+
5
2
u
11
+ ··· +
19
2
u − 1
a
10
=
−u
u
a
1
=
1
4
u
12
−
3
4
u
11
+ ··· +
27
4
u − 2
1
2
u
12
−
5
2
u
11
+ ··· −
37
2
u + 3
a
4
=
u
2
+ 1
−u
2
a
3
=
1
2
u
12
− 2u
11
+ ··· −
29
2
u +
7
2
1
2
u
12
−
5
2
u
11
+ ··· −
31
2
u + 2
a
8
=
u
12
−
9
2
u
11
+ ··· − 28u +
9
2
−
1
2
u
12
+
5
2
u
11
+ ··· +
31
2
u − 2
a
7
=
−
1
2
u
12
+ 2u
11
+ ··· +
5
2
u +
1
2
1
2
u
12
−
5
2
u
11
+ ··· −
25
2
u + 2
a
11
=
−u
3
− 2u
u
3
+ u
a
11
=
−u
3
− 2u
u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
−u
12
+5u
11
−20u
10
+54u
9
−121u
8
+212u
7
−314u
6
+374u
5
−372u
4
+295u
3
−186u
2
+88u−34
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
u
13
+ 5u
11
+ ··· + 2u + 1
c
3
u
13
− 12u
12
+ ··· − 16u + 16
c
4
, c
5
, c
9
c
10
u
13
+ 5u
12
+ ··· + 30u + 4
c
7
, c
11
u
13
+ u
12
+ ··· + 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
13
+ 10y
12
+ ··· + 30y
2
− 1
c
3
y
13
− 6y
12
+ ··· + 4480y −256
c
4
, c
5
, c
9
c
10
y
13
+ 15y
12
+ ··· + 124y −16
c
7
, c
11
y
13
− 17y
12
+ ··· + 25y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.144857 + 0.988588I
a = 0.636883 − 0.256528I
b = −0.881451 − 0.164723I
2.39689 − 1.47210I −6.76905 + 4.68228I
u = 0.144857 − 0.988588I
a = 0.636883 + 0.256528I
b = −0.881451 + 0.164723I
2.39689 + 1.47210I −6.76905 − 4.68228I
u = 0.698010 + 0.761843I
a = −1.308540 − 0.343629I
b = 1.138990 − 0.122915I
−1.53379 − 7.84030I −8.79484 + 6.42108I
u = 0.698010 − 0.761843I
a = −1.308540 + 0.343629I
b = 1.138990 + 0.122915I
−1.53379 + 7.84030I −8.79484 − 6.42108I
u = 0.853563 + 0.271566I
a = 0.142752 − 1.224120I
b = 0.206699 + 0.270697I
−3.02361 + 2.70878I −9.87229 − 2.50117I
u = 0.853563 − 0.271566I
a = 0.142752 + 1.224120I
b = 0.206699 − 0.270697I
−3.02361 − 2.70878I −9.87229 + 2.50117I
u = 0.360660 + 1.314350I
a = 0.518668 + 0.256927I
b = −0.921497 − 0.693070I
1.92199 − 1.66881I −4.76442 + 0.86409I
u = 0.360660 − 1.314350I
a = 0.518668 − 0.256927I
b = −0.921497 + 0.693070I
1.92199 + 1.66881I −4.76442 − 0.86409I
u = 0.22163 + 1.63428I
a = 0.950847 − 0.342173I
b = −3.01495 + 0.10778I
6.50636 − 11.34500I −6.41522 + 5.59283I
u = 0.22163 − 1.63428I
a = 0.950847 + 0.342173I
b = −3.01495 − 0.10778I
6.50636 + 11.34500I −6.41522 − 5.59283I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.314498
a = −1.13389
b = 0.244454
−0.542082 −18.2830
u = 0.06403 + 1.71455I
a = −0.623663 + 0.320565I
b = 2.34998 − 0.02921I
12.09750 − 2.52656I −9.24277 + 2.75851I
u = 0.06403 − 1.71455I
a = −0.623663 − 0.320565I
b = 2.34998 + 0.02921I
12.09750 + 2.52656I −9.24277 − 2.75851I
6
II. I
u
2
=
h−a
3
u
3
+u
3
a+· · ·+a+1, −a
3
u
3
+u
3
a
2
+· · ·+10a+12, u
4
+u
3
+3u
2
+2u+1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
u
2
a
2
=
a
a
3
u
3
+ a
3
u
2
+ a
3
u − a
2
u
2
− u
3
a − a
2
u + u
3
− au + u
2
− a + 2u − 1
a
10
=
−u
u
a
1
=
a
3
u
3
+ a
3
u
2
+ a
3
u − a
2
u
2
− u
3
a − a
2
u − u
2
a + u
3
− au + u
2
+ 2u − 1
−a
3
u
3
− a
3
u
2
+ 2a
2
u
2
+ u
3
a + a
2
u + u
2
a + a
2
− 2u
2
− a + u − 1
a
4
=
u
2
+ 1
−u
2
a
3
=
−a
3
u
2
− a
a
3
u
2
+ a
2
u − 2u
3
− 2u
2
+ a − 6u − 2
a
8
=
a
2
u
−a
3
u
2
− a
2
u + 2u
3
− a + 4u
a
7
=
−a
3
u
3
− 2a
3
u
2
− u
3
a
2
− a
3
u + u
3
a + u
2
a + 2u
3
+ 2au + 4u + 2
2a
3
u
3
+ u
3
a
2
+ ··· + a
3
− 2a
a
11
=
−u
3
− 2u
u
3
+ u
a
11
=
−u
3
− 2u
u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 4u
2
− 12u − 14
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
u
16
− u
15
+ ··· − 22u + 31
c
3
(u
2
+ u − 1)
8
c
4
, c
5
, c
9
c
10
(u
4
− u
3
+ 3u
2
− 2u + 1)
4
c
7
, c
11
u
16
+ u
15
+ ··· − 48u + 19
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
16
+ 7y
15
+ ··· + 4104y + 961
c
3
(y
2
− 3y + 1)
8
c
4
, c
5
, c
9
c
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
4
c
7
, c
11
y
16
− 9y
15
+ ··· − 4356y + 361
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = −1.402280 − 0.070449I
b = 1.27211 + 1.05139I
−4.15885 + 1.41510I −9.82674 − 4.90874I
u = −0.395123 + 0.506844I
a = −1.42285 + 0.49823I
b = 0.435184 − 0.843532I
3.73684 + 1.41510I −9.82674 − 4.90874I
u = −0.395123 + 0.506844I
a = 0.51653 + 1.88406I
b = 0.112797 + 0.286161I
−4.15885 + 1.41510I −9.82674 − 4.90874I
u = −0.395123 + 0.506844I
a = 1.76118 − 1.19097I
b = −0.964169 + 0.332631I
3.73684 + 1.41510I −9.82674 − 4.90874I
u = −0.395123 − 0.506844I
a = −1.402280 + 0.070449I
b = 1.27211 − 1.05139I
−4.15885 − 1.41510I −9.82674 + 4.90874I
u = −0.395123 − 0.506844I
a = −1.42285 − 0.49823I
b = 0.435184 + 0.843532I
3.73684 − 1.41510I −9.82674 + 4.90874I
u = −0.395123 − 0.506844I
a = 0.51653 − 1.88406I
b = 0.112797 − 0.286161I
−4.15885 − 1.41510I −9.82674 + 4.90874I
u = −0.395123 − 0.506844I
a = 1.76118 + 1.19097I
b = −0.964169 − 0.332631I
3.73684 − 1.41510I −9.82674 + 4.90874I
u = −0.10488 + 1.55249I
a = 0.206815 − 1.015740I
b = −0.64998 + 1.32275I
2.84290 + 3.16396I −6.17326 − 2.56480I
u = −0.10488 + 1.55249I
a = −1.051500 − 0.096749I
b = 3.27820 − 0.48455I
10.73860 + 3.16396I −6.17326 − 2.56480I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.10488 + 1.55249I
a = 0.713168 + 0.458702I
b = −1.82216 + 0.28952I
10.73860 + 3.16396I −6.17326 − 2.56480I
u = −0.10488 + 1.55249I
a = 0.678935 + 0.068135I
b = −3.16197 − 0.81217I
2.84290 + 3.16396I −6.17326 − 2.56480I
u = −0.10488 − 1.55249I
a = 0.206815 + 1.015740I
b = −0.64998 − 1.32275I
2.84290 − 3.16396I −6.17326 + 2.56480I
u = −0.10488 − 1.55249I
a = −1.051500 + 0.096749I
b = 3.27820 + 0.48455I
10.73860 − 3.16396I −6.17326 + 2.56480I
u = −0.10488 − 1.55249I
a = 0.713168 − 0.458702I
b = −1.82216 − 0.28952I
10.73860 − 3.16396I −6.17326 + 2.56480I
u = −0.10488 − 1.55249I
a = 0.678935 − 0.068135I
b = −3.16197 + 0.81217I
2.84290 − 3.16396I −6.17326 + 2.56480I
11
III. I
u
3
= hu
4
+ u
3
+ 2u
2
+ b + 2u, u
2
+ a + 2, u
7
+ 5u
5
+ 7u
3
+ 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
6
=
1
u
2
a
2
=
−u
2
− 2
−u
4
− u
3
− 2u
2
− 2u
a
10
=
−u
u
a
1
=
−u
3
− u
2
− 2u − 2
−u
5
− u
4
− 3u
3
− 2u
2
− 2u
a
4
=
u
2
+ 1
−u
2
a
3
=
−u
6
− 5u
4
− 7u
2
− u − 2
−u
4
− u
3
− 3u
2
− u − 1
a
8
=
u
5
+ 4u
3
+ 4u
u
6
− u
5
+ 4u
4
− 3u
3
+ 4u
2
− u + 1
a
7
=
u
6
+ u
5
+ 4u
4
+ 4u
3
+ 4u
2
+ 4u + 1
−u
5
+ u
4
− 3u
3
+ 3u
2
− u + 1
a
11
=
−u
3
− 2u
u
3
+ u
a
11
=
−u
3
− 2u
u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
6
− 2u
5
− 16u
4
− 6u
3
− 15u
2
− 5u − 6
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
7
+ 2u
5
+ u
4
+ u
3
+ u
2
− u − 1
c
2
, c
6
u
7
+ 2u
5
− u
4
+ u
3
− u
2
− u + 1
c
3
u
7
+ 3u
6
+ 3u
5
+ 4u
4
+ 6u
3
+ u
2
− u + 2
c
4
, c
5
u
7
+ 5u
5
+ 7u
3
+ 2u − 1
c
7
, c
11
u
7
− u
6
− u
5
+ u
4
− u
3
+ 2u
2
+ 1
c
9
, c
10
u
7
+ 5u
5
+ 7u
3
+ 2u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
y
7
+ 4y
6
+ 6y
5
+ y
4
− 5y
3
− y
2
+ 3y −1
c
3
y
7
− 3y
6
− 3y
5
+ 12y
4
+ 10y
3
− 29y
2
− 3y −4
c
4
, c
5
, c
9
c
10
y
7
+ 10y
6
+ 39y
5
+ 74y
4
+ 69y
3
+ 28y
2
+ 4y −1
c
7
, c
11
y
7
− 3y
6
+ y
5
+ 5y
4
− y
3
− 6y
2
− 4y −1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.271185 + 0.674379I
a = −1.61875 + 0.36576I
b = 0.943244 − 0.738208I
4.79738 + 0.94912I −1.21872 − 0.82233I
u = −0.271185 − 0.674379I
a = −1.61875 − 0.36576I
b = 0.943244 + 0.738208I
4.79738 − 0.94912I −1.21872 + 0.82233I
u = 0.180054 + 1.394520I
a = −0.087725 − 0.502178I
b = 1.104440 + 0.703496I
0.58425 − 1.95701I −10.82069 + 1.34837I
u = 0.180054 − 1.394520I
a = −0.087725 + 0.502178I
b = 1.104440 − 0.703496I
0.58425 + 1.95701I −10.82069 − 1.34837I
u = 0.344493
a = −2.11868
b = −0.981303
−4.19405 −9.98960
u = −0.08112 + 1.66505I
a = 0.765818 + 0.270123I
b = −2.55703 + 0.29924I
13.16470 + 2.34118I −0.965786 − 0.952471I
u = −0.08112 − 1.66505I
a = 0.765818 − 0.270123I
b = −2.55703 − 0.29924I
13.16470 − 2.34118I −0.965786 + 0.952471I
15
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
7
+ 2u
5
+ u
4
+ u
3
+ u
2
− u − 1)(u
13
+ 5u
11
+ ··· + 2u + 1)
· (u
16
− u
15
+ ··· − 22u + 31)
c
2
, c
6
(u
7
+ 2u
5
− u
4
+ u
3
− u
2
− u + 1)(u
13
+ 5u
11
+ ··· + 2u + 1)
· (u
16
− u
15
+ ··· − 22u + 31)
c
3
(u
2
+ u − 1)
8
(u
7
+ 3u
6
+ 3u
5
+ 4u
4
+ 6u
3
+ u
2
− u + 2)
· (u
13
− 12u
12
+ ··· − 16u + 16)
c
4
, c
5
(u
4
− u
3
+ 3u
2
− 2u + 1)
4
(u
7
+ 5u
5
+ 7u
3
+ 2u − 1)
· (u
13
+ 5u
12
+ ··· + 30u + 4)
c
7
, c
11
(u
7
− u
6
− u
5
+ u
4
− u
3
+ 2u
2
+ 1)(u
13
+ u
12
+ ··· + 3u + 1)
· (u
16
+ u
15
+ ··· − 48u + 19)
c
9
, c
10
(u
4
− u
3
+ 3u
2
− 2u + 1)
4
(u
7
+ 5u
5
+ 7u
3
+ 2u + 1)
· (u
13
+ 5u
12
+ ··· + 30u + 4)
16
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
8
(y
7
+ 4y
6
+ ··· + 3y −1)(y
13
+ 10y
12
+ ··· + 30y
2
− 1)
· (y
16
+ 7y
15
+ ··· + 4104y + 961)
c
3
(y
2
− 3y + 1)
8
(y
7
− 3y
6
− 3y
5
+ 12y
4
+ 10y
3
− 29y
2
− 3y −4)
· (y
13
− 6y
12
+ ··· + 4480y −256)
c
4
, c
5
, c
9
c
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
4
· (y
7
+ 10y
6
+ 39y
5
+ 74y
4
+ 69y
3
+ 28y
2
+ 4y −1)
· (y
13
+ 15y
12
+ ··· + 124y −16)
c
7
, c
11
(y
7
− 3y
6
+ ··· − 4y −1)(y
13
− 17y
12
+ ··· + 25y −1)
· (y
16
− 9y
15
+ ··· − 4356y + 361)
17
