11a
337
(K11a
337
)
A knot diagram
1
Linearized knot diagam
8 7 1 11 10 9 2 3 4 5 6
Solving Sequence
3,7
2 8 9 1 4 10 6 5 11
c
2
c
7
c
8
c
1
c
3
c
9
c
6
c
5
c
11
c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
44
+ u
43
+ ··· + 5u
2
− 1i
* 1 irreducible components of dim
C
= 0, with total 44 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
44
+ u
43
+ · · · + 5u
2
− 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
8
=
−u
u
3
+ u
a
9
=
−u
3
− 2u
u
3
+ u
a
1
=
u
2
+ 1
−u
4
− 2u
2
a
4
=
−u
6
− 3u
4
− 2u
2
+ 1
u
8
+ 4u
6
+ 4u
4
a
10
=
u
17
+ 8u
15
+ 25u
13
+ 36u
11
+ 19u
9
− 4u
7
− 2u
5
+ 2u
3
− 3u
−u
19
− 9u
17
− 32u
15
− 55u
13
− 43u
11
− 9u
9
− 4u
5
+ u
3
+ u
a
6
=
u
7
+ 4u
5
+ 4u
3
−u
7
− 3u
5
− 2u
3
+ u
a
5
=
u
43
+ 20u
41
+ ··· − 14u
5
+ 13u
3
−u
43
− u
42
+ ··· − 5u
2
+ 1
a
11
=
−u
18
− 9u
16
− 32u
14
− 55u
12
− 43u
10
− 9u
8
− 4u
4
+ u
2
+ 1
u
18
+ 8u
16
+ 25u
14
+ 36u
12
+ 19u
10
− 4u
8
− 2u
6
+ 2u
4
− 3u
2
a
11
=
−u
18
− 9u
16
− 32u
14
− 55u
12
− 43u
10
− 9u
8
− 4u
4
+ u
2
+ 1
u
18
+ 8u
16
+ 25u
14
+ 36u
12
+ 19u
10
− 4u
8
− 2u
6
+ 2u
4
− 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
42
− 4u
41
+ ··· − 20u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
44
− u
43
+ ··· + 5u
2
− 1
c
3
, c
6
u
44
− 7u
43
+ ··· − 96u + 17
c
4
, c
5
, c
10
u
44
+ u
43
+ ··· − 2u − 1
c
8
u
44
+ u
43
+ ··· + 20u − 53
c
9
, c
11
u
44
− u
43
+ ··· + 5u
2
− 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y
44
+ 41y
43
+ ··· − 10y + 1
c
3
, c
6
y
44
+ 33y
43
+ ··· − 1770y + 289
c
4
, c
5
, c
10
y
44
+ 37y
43
+ ··· − 10y + 1
c
8
y
44
+ 13y
43
+ ··· + 8822y + 2809
c
9
, c
11
y
44
− 23y
43
+ ··· − 10y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.173491 + 1.180500I
2.34143 + 0.79685I −9.60388 + 0.I
u = 0.173491 − 1.180500I
2.34143 − 0.79685I −9.60388 + 0.I
u = −0.684801 + 0.378128I
3.75424 + 9.27677I −8.25553 − 7.97070I
u = −0.684801 − 0.378128I
3.75424 − 9.27677I −8.25553 + 7.97070I
u = 0.621068 + 0.446082I
8.22635 − 2.04073I −3.94848 + 3.44114I
u = 0.621068 − 0.446082I
8.22635 + 2.04073I −3.94848 − 3.44114I
u = −0.201180 + 1.222030I
−1.22666 + 3.11008I −13.45910 − 3.92090I
u = −0.201180 − 1.222030I
−1.22666 − 3.11008I −13.45910 + 3.92090I
u = 0.668653 + 0.360931I
−1.01882 − 5.34555I −13.0771 + 6.6770I
u = 0.668653 − 0.360931I
−1.01882 + 5.34555I −13.0771 − 6.6770I
u = −0.531587 + 0.532708I
4.39098 − 5.19546I −6.57369 + 1.97435I
u = −0.531587 − 0.532708I
4.39098 + 5.19546I −6.57369 − 1.97435I
u = 0.221809 + 1.250810I
2.95833 − 7.06778I 0
u = 0.221809 − 1.250810I
2.95833 + 7.06778I 0
u = −0.628212 + 0.325456I
1.70221 + 1.51503I −10.15673 − 3.08750I
u = −0.628212 − 0.325456I
1.70221 − 1.51503I −10.15673 + 3.08750I
u = 0.051758 + 1.295040I
3.37520 − 1.28237I 0
u = 0.051758 − 1.295040I
3.37520 + 1.28237I 0
u = 0.491173 + 0.503611I
−0.35195 + 1.46105I −11.42087 − 0.49778I
u = 0.491173 − 0.503611I
−0.35195 − 1.46105I −11.42087 + 0.49778I
u = −0.558081 + 0.379170I
1.91831 + 1.74747I −7.74964 − 4.82540I
u = −0.558081 − 0.379170I
1.91831 − 1.74747I −7.74964 + 4.82540I
u = 0.651243 + 0.045491I
−1.01454 − 3.87980I −14.3154 + 4.0831I
u = 0.651243 − 0.045491I
−1.01454 + 3.87980I −14.3154 − 4.0831I
u = −0.645744
−4.92194 −19.0830
u = −0.075458 + 1.385010I
8.25893 + 3.09453I 0
u = −0.075458 − 1.385010I
8.25893 − 3.09453I 0
u = −0.314368 + 0.485643I
2.57671 + 1.81798I −7.01819 − 3.75999I
u = −0.314368 − 0.485643I
2.57671 − 1.81798I −7.01819 + 3.75999I
u = −0.23908 + 1.43322I
7.36078 + 4.69095I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.23908 − 1.43322I
7.36078 − 4.69095I 0
u = −0.21140 + 1.43954I
7.75201 + 4.59084I 0
u = −0.21140 − 1.43954I
7.75201 − 4.59084I 0
u = 0.18092 + 1.45176I
5.84316 − 0.98909I 0
u = 0.18092 − 1.45176I
5.84316 + 0.98909I 0
u = 0.25323 + 1.44536I
4.78546 − 8.71482I 0
u = 0.25323 − 1.44536I
4.78546 + 8.71482I 0
u = −0.25789 + 1.45367I
9.6461 + 12.7191I 0
u = −0.25789 − 1.45367I
9.6461 − 12.7191I 0
u = −0.17884 + 1.46973I
10.80910 − 2.64998I 0
u = −0.17884 − 1.46973I
10.80910 + 2.64998I 0
u = 0.22386 + 1.46753I
14.3940 − 5.1268I 0
u = 0.22386 − 1.46753I
14.3940 + 5.1268I 0
u = 0.333131
−0.518275 −19.1920
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
44
− u
43
+ ··· + 5u
2
− 1
c
3
, c
6
u
44
− 7u
43
+ ··· − 96u + 17
c
4
, c
5
, c
10
u
44
+ u
43
+ ··· − 2u − 1
c
8
u
44
+ u
43
+ ··· + 20u − 53
c
9
, c
11
u
44
− u
43
+ ··· + 5u
2
− 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y
44
+ 41y
43
+ ··· − 10y + 1
c
3
, c
6
y
44
+ 33y
43
+ ··· − 1770y + 289
c
4
, c
5
, c
10
y
44
+ 37y
43
+ ··· − 10y + 1
c
8
y
44
+ 13y
43
+ ··· + 8822y + 2809
c
9
, c
11
y
44
− 23y
43
+ ··· − 10y + 1
8
