11a
119
(K11a
119
)
A knot diagram
1
Linearized knot diagam
6 1 10 7 2 5 3 11 4 9 8
Solving Sequence
4,9
10 11 3 8 1 2 7 5 6
c
9
c
10
c
3
c
8
c
11
c
2
c
7
c
4
c
6
c
1
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
8
+ u
6
+ 3u
4
+ 2u
2
− u + 1i
I
u
2
= hu
30
− u
29
+ ··· + 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 38 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
8
+ u
6
+ 3u
4
+ 2u
2
− u + 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
11
=
u
2
+ 1
−u
2
a
3
=
−u
u
3
+ u
a
8
=
u
4
+ u
2
+ 1
−u
4
a
1
=
u
6
+ u
4
+ 2u
2
+ 1
−u
6
− u
2
a
2
=
−u
4
− u
2
− 1
u
6
+ 2u
4
+ u
3
+ 2u
2
+ 1
a
7
=
u
u
6
+ u
4
− u
3
+ 2u
2
− u + 1
a
5
=
−u
3
u
5
+ u
4
+ u
3
+ u
2
+ 1
a
6
=
u
5
+ u
−u
7
− u
5
− u
3
+ u
2
− u + 1
a
6
=
u
5
+ u
−u
7
− u
5
− u
3
+ u
2
− u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
− 4u
6
− 4u
4
− 12u
3
− 12u
2
− 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
9
u
8
+ u
6
+ 3u
4
+ 2u
2
− u + 1
c
2
, c
4
, c
6
c
8
, c
10
, c
11
u
8
+ 2u
7
+ 7u
6
+ 10u
5
+ 15u
4
+ 14u
3
+ 10u
2
+ 3u + 1
c
7
u
8
− 7u
7
+ 26u
6
− 57u
5
+ 81u
4
− 71u
3
+ 42u
2
− 20u + 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
9
y
8
+ 2y
7
+ 7y
6
+ 10y
5
+ 15y
4
+ 14y
3
+ 10y
2
+ 3y + 1
c
2
, c
4
, c
6
c
8
, c
10
, c
11
y
8
+ 10y
7
+ 39y
6
+ 74y
5
+ 75y
4
+ 58y
3
+ 46y
2
+ 11y + 1
c
7
y
8
+ 3y
7
+ 40y
6
+ 53y
5
+ 387y
4
− 101y
3
+ 220y
2
+ 272y + 64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.338450 + 0.907350I
−2.36499 − 4.78635I −7.25990 + 9.32742I
u = −0.338450 − 0.907350I
−2.36499 + 4.78635I −7.25990 − 9.32742I
u = −0.894334 + 0.857566I
13.66310 − 0.79369I 4.03459 + 2.11393I
u = −0.894334 − 0.857566I
13.66310 + 0.79369I 4.03459 − 2.11393I
u = 0.840313 + 0.975020I
12.9062 + 12.0580I 2.66730 − 7.52058I
u = 0.840313 − 0.975020I
12.9062 − 12.0580I 2.66730 + 7.52058I
u = 0.392471 + 0.514949I
0.469731 + 1.216760I 2.55801 − 5.53294I
u = 0.392471 − 0.514949I
0.469731 − 1.216760I 2.55801 + 5.53294I
5
II. I
u
2
= hu
30
− u
29
+ · · · + 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
11
=
u
2
+ 1
−u
2
a
3
=
−u
u
3
+ u
a
8
=
u
4
+ u
2
+ 1
−u
4
a
1
=
u
6
+ u
4
+ 2u
2
+ 1
−u
6
− u
2
a
2
=
u
15
+ 2u
13
+ 6u
11
+ 8u
9
+ 10u
7
+ 8u
5
+ 4u
3
−u
15
− u
13
− 4u
11
− 3u
9
− 4u
7
− 2u
5
+ u
a
7
=
u
8
+ u
6
+ 3u
4
+ 2u
2
+ 1
−u
10
− 2u
8
− 3u
6
− 4u
4
− u
2
a
5
=
−u
17
− 2u
15
− 7u
13
− 10u
11
− 15u
9
− 14u
7
− 10u
5
− 4u
3
− u
u
19
+ 3u
17
+ 8u
15
+ 15u
13
+ 19u
11
+ 21u
9
+ 14u
7
+ 6u
5
+ u
3
+ u
a
6
=
u
26
+ 3u
24
+ ··· + 3u
2
+ 1
−u
28
− 4u
26
+ ··· − 7u
4
− 2u
2
a
6
=
u
26
+ 3u
24
+ ··· + 3u
2
+ 1
−u
28
− 4u
26
+ ··· − 7u
4
− 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
25
− 12u
23
− 44u
21
− 88u
19
− 4u
18
− 164u
17
− 12u
16
− 224u
15
− 32u
14
− 256u
13
−
56u
12
−228u
11
−72u
10
−160u
9
−72u
8
−88u
7
−48u
6
−40u
5
−20u
4
−28u
3
−4u
2
−12u −6
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
9
u
30
− u
29
+ ··· + 2u + 1
c
2
, c
4
, c
6
c
8
, c
10
, c
11
u
30
+ 7u
29
+ ··· + 4u
2
+ 1
c
7
(u
15
+ 3u
14
+ ··· − 5u − 7)
2
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
9
y
30
+ 7y
29
+ ··· + 4y
2
+ 1
c
2
, c
4
, c
6
c
8
, c
10
, c
11
y
30
+ 31y
29
+ ··· + 8y + 1
c
7
(y
15
+ 9y
14
+ ··· − 171y −49)
2
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.452252 + 0.939744I
5.01187 + 2.09461I −0.30918 − 3.37423I
u = 0.452252 − 0.939744I
5.01187 − 2.09461I −0.30918 + 3.37423I
u = −0.434887 + 0.955633I
4.70557 − 8.28968I −1.16488 + 8.39094I
u = −0.434887 − 0.955633I
4.70557 + 8.28968I −1.16488 − 8.39094I
u = −0.019728 + 0.944684I
2.41074 + 3.00115I −4.85411 − 2.57684I
u = −0.019728 − 0.944684I
2.41074 − 3.00115I −4.85411 + 2.57684I
u = −0.197860 + 0.871029I
−3.14864 −11.00170 + 0.I
u = −0.197860 − 0.871029I
−3.14864 −11.00170 + 0.I
u = 0.343092 + 0.793576I
−0.34244 + 1.73470I −0.36395 − 4.47971I
u = 0.343092 − 0.793576I
−0.34244 − 1.73470I −0.36395 + 4.47971I
u = 0.847869 + 0.850065I
5.01187 − 2.09461I −0.30918 + 3.37423I
u = 0.847869 − 0.850065I
5.01187 + 2.09461I −0.30918 − 3.37423I
u = 0.799403 + 0.896020I
2.41074 + 3.00115I −4.85411 − 2.57684I
u = 0.799403 − 0.896020I
2.41074 − 3.00115I −4.85411 + 2.57684I
u = −0.849380 + 0.882463I
6.81987 − 1.98171I 4.04276 + 2.49548I
u = −0.849380 − 0.882463I
6.81987 + 1.98171I 4.04276 − 2.49548I
u = 0.895044 + 0.849606I
13.3047 − 5.6388I 3.41159 + 2.70946I
u = 0.895044 − 0.849606I
13.3047 + 5.6388I 3.41159 − 2.70946I
u = 0.658622 + 0.369163I
6.81987 + 1.98171I 4.04276 − 2.49548I
u = 0.658622 − 0.369163I
6.81987 − 1.98171I 4.04276 + 2.49548I
u = −0.832514 + 0.928695I
6.67502 − 4.27520I 3.73863 + 2.74888I
u = −0.832514 − 0.928695I
6.67502 + 4.27520I 3.73863 − 2.74888I
u = 0.815148 + 0.948838I
4.70557 + 8.28968I −1.16488 − 8.39094I
u = 0.815148 − 0.948838I
4.70557 − 8.28968I −1.16488 + 8.39094I
u = −0.661870 + 0.335265I
6.67502 + 4.27520I 3.73863 − 2.74888I
u = −0.661870 − 0.335265I
6.67502 − 4.27520I 3.73863 + 2.74888I
u = −0.844833 + 0.970234I
13.3047 − 5.6388I 3.41159 + 2.70946I
u = −0.844833 − 0.970234I
13.3047 + 5.6388I 3.41159 − 2.70946I
u = −0.470358 + 0.199229I
−0.34244 + 1.73470I −0.36395 − 4.47971I
u = −0.470358 − 0.199229I
−0.34244 − 1.73470I −0.36395 + 4.47971I
9
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
9
(u
8
+ u
6
+ 3u
4
+ 2u
2
− u + 1)(u
30
− u
29
+ ··· + 2u + 1)
c
2
, c
4
, c
6
c
8
, c
10
, c
11
(u
8
+ 2u
7
+ 7u
6
+ 10u
5
+ 15u
4
+ 14u
3
+ 10u
2
+ 3u + 1)
· (u
30
+ 7u
29
+ ··· + 4u
2
+ 1)
c
7
(u
8
− 7u
7
+ 26u
6
− 57u
5
+ 81u
4
− 71u
3
+ 42u
2
− 20u + 8)
· (u
15
+ 3u
14
+ ··· − 5u − 7)
2
10
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
9
(y
8
+ 2y
7
+ 7y
6
+ 10y
5
+ 15y
4
+ 14y
3
+ 10y
2
+ 3y + 1)
· (y
30
+ 7y
29
+ ··· + 4y
2
+ 1)
c
2
, c
4
, c
6
c
8
, c
10
, c
11
(y
8
+ 10y
7
+ 39y
6
+ 74y
5
+ 75y
4
+ 58y
3
+ 46y
2
+ 11y + 1)
· (y
30
+ 31y
29
+ ··· + 8y + 1)
c
7
(y
8
+ 3y
7
+ 40y
6
+ 53y
5
+ 387y
4
− 101y
3
+ 220y
2
+ 272y + 64)
· (y
15
+ 9y
14
+ ··· − 171y −49)
2
11
