11a
191
(K11a
191
)
A knot diagram
1
Linearized knot diagam
6 1 9 10 7 2 3 11 4 5 8
Solving Sequence
5,10
11 4 9 3 8 1 2 7 6
c
10
c
4
c
9
c
3
c
8
c
11
c
2
c
7
c
5
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
41
+ u
40
+ ··· − 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 41 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
41
+ u
40
+ · · · − 3u + 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
4
=
u
u
a
9
=
−u
2
+ 1
−u
2
a
3
=
−u
3
+ 2u
−u
3
+ u
a
8
=
u
4
− 3u
2
+ 1
u
6
− 2u
4
− u
2
a
1
=
u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1
u
10
− 4u
8
+ 3u
6
+ 2u
4
+ u
2
a
2
=
u
21
− 12u
19
+ ··· − 8u
3
+ 3u
u
23
− 11u
21
+ ··· − 3u
5
+ u
a
7
=
u
12
− 7u
10
+ 17u
8
− 16u
6
+ 6u
4
− 5u
2
+ 1
u
12
− 6u
10
+ 12u
8
− 8u
6
+ u
4
− 2u
2
a
6
=
−u
25
+ 14u
23
+ ··· + 10u
3
− u
−u
25
+ 13u
23
+ ··· + 2u
3
+ u
a
6
=
−u
25
+ 14u
23
+ ··· + 10u
3
− u
−u
25
+ 13u
23
+ ··· + 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
39
− 88u
37
+ ··· + 20u − 22
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
41
− u
40
+ ··· − u − 1
c
2
, c
5
u
41
+ 13u
40
+ ··· + 9u + 1
c
3
, c
4
, c
9
c
10
u
41
− u
40
+ ··· − 3u − 1
c
7
u
41
+ u
40
+ ··· − 27u − 13
c
8
, c
11
u
41
− 7u
40
+ ··· + 33u − 23
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
41
− 13y
40
+ ··· + 9y −1
c
2
, c
5
y
41
+ 31y
40
+ ··· + 69y −1
c
3
, c
4
, c
9
c
10
y
41
− 45y
40
+ ··· + 9y −1
c
7
y
41
+ 7y
40
+ ··· + 417y −169
c
8
, c
11
y
41
+ 27y
40
+ ··· + 6701y −529
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.578203 + 0.591978I
4.82587 − 9.58597I −9.09685 + 8.79000I
u = 0.578203 − 0.591978I
4.82587 + 9.58597I −9.09685 − 8.79000I
u = −0.560583 + 0.593399I
5.64442 + 3.73832I −7.40652 − 3.76364I
u = −0.560583 − 0.593399I
5.64442 − 3.73832I −7.40652 + 3.76364I
u = 0.566944 + 0.522538I
−0.95032 − 4.40767I −14.5602 + 7.4521I
u = 0.566944 − 0.522538I
−0.95032 + 4.40767I −14.5602 − 7.4521I
u = −0.727131 + 0.205192I
−0.35537 + 4.91287I −14.9536 − 7.2181I
u = −0.727131 − 0.205192I
−0.35537 − 4.91287I −14.9536 + 7.2181I
u = −0.416867 + 0.614275I
6.06764 + 0.37199I −6.12023 − 2.74369I
u = −0.416867 − 0.614275I
6.06764 − 0.37199I −6.12023 + 2.74369I
u = 0.394899 + 0.619383I
5.36506 + 5.46610I −7.42623 − 2.57301I
u = 0.394899 − 0.619383I
5.36506 − 5.46610I −7.42623 + 2.57301I
u = −0.490771 + 0.541723I
2.34343 + 1.87271I −6.33668 − 4.08392I
u = −0.490771 − 0.541723I
2.34343 − 1.87271I −6.33668 + 4.08392I
u = −0.728695
−4.17004 −21.6690
u = 0.639413 + 0.255948I
0.190368 + 0.170845I −13.47533 + 2.06062I
u = 0.639413 − 0.255948I
0.190368 − 0.170845I −13.47533 − 2.06062I
u = 0.373862 + 0.500528I
−0.399312 + 0.816647I −12.47963 − 0.47721I
u = 0.373862 − 0.500528I
−0.399312 − 0.816647I −12.47963 + 0.47721I
u = −1.45206 + 0.14818I
−0.55160 − 2.78997I 0
u = −1.45206 − 0.14818I
−0.55160 + 2.78997I 0
u = 1.46754 + 0.15667I
−0.01677 − 3.06881I 0
u = 1.46754 − 0.15667I
−0.01677 + 3.06881I 0
u = 0.039862 + 0.468366I
2.07509 − 2.62621I −6.57273 + 3.48222I
u = 0.039862 − 0.468366I
2.07509 + 2.62621I −6.57273 − 3.48222I
u = −1.52852 + 0.10506I
−6.77252 + 0.98297I 0
u = −1.52852 − 0.10506I
−6.77252 − 0.98297I 0
u = 1.52598 + 0.14865I
−4.35344 − 4.30283I 0
u = 1.52598 − 0.14865I
−4.35344 + 4.30283I 0
u = −1.55359 + 0.03904I
−7.11441 + 0.76394I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55359 − 0.03904I
−7.11441 − 0.76394I 0
u = 1.54582 + 0.17878I
−1.34838 − 6.54087I 0
u = 1.54582 − 0.17878I
−1.34838 + 6.54087I 0
u = −1.55308 + 0.15321I
−8.04273 + 6.85644I 0
u = −1.55308 − 0.15321I
−8.04273 − 6.85644I 0
u = −1.55361 + 0.17968I
−2.26534 + 12.39950I 0
u = −1.55361 − 0.17968I
−2.26534 − 12.39950I 0
u = 1.58360 + 0.04172I
−8.17072 − 5.73177I 0
u = 1.58360 − 0.04172I
−8.17072 + 5.73177I 0
u = 1.58454
−12.0025 0
u = 0.384337
−0.582535 −17.0140
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
41
− u
40
+ ··· − u − 1
c
2
, c
5
u
41
+ 13u
40
+ ··· + 9u + 1
c
3
, c
4
, c
9
c
10
u
41
− u
40
+ ··· − 3u − 1
c
7
u
41
+ u
40
+ ··· − 27u − 13
c
8
, c
11
u
41
− 7u
40
+ ··· + 33u − 23
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
41
− 13y
40
+ ··· + 9y −1
c
2
, c
5
y
41
+ 31y
40
+ ··· + 69y −1
c
3
, c
4
, c
9
c
10
y
41
− 45y
40
+ ··· + 9y −1
c
7
y
41
+ 7y
40
+ ··· + 417y −169
c
8
, c
11
y
41
+ 27y
40
+ ··· + 6701y −529
8
