11a
246
(K11a
246
)
A knot diagram
1
Linearized knot diagam
7 1 11 10 9 8 2 6 5 3 4
Solving Sequence
3,10
11 4 5 1 2 9 6 8 7
c
10
c
3
c
4
c
11
c
2
c
9
c
5
c
8
c
7
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
20
− u
19
+ ··· − 4u − 1i
* 1 irreducible components of dim
C
= 0, with total 20 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
20
− u
19
+ · · · − 4u − 1i
(i) Arc colorings
a
3
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
4
=
−u
−u
3
+ u
a
5
=
u
3
− 2u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
9
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
6
+ 2u
4
− u
2
a
6
=
u
9
− 4u
7
+ 5u
5
− 3u
−u
9
+ 3u
7
− 3u
5
+ u
a
8
=
u
12
− 5u
10
+ 9u
8
− 4u
6
− 6u
4
+ 5u
2
+ 1
−u
12
+ 4u
10
− 6u
8
+ 2u
6
+ 3u
4
− 2u
2
a
7
=
u
15
− 6u
13
+ 14u
11
− 12u
9
− 6u
7
+ 16u
5
− 4u
3
− 4u
−u
15
+ 5u
13
− 10u
11
+ 7u
9
+ 4u
7
− 8u
5
+ 2u
3
+ u
a
7
=
u
15
− 6u
13
+ 14u
11
− 12u
9
− 6u
7
+ 16u
5
− 4u
3
− 4u
−u
15
+ 5u
13
− 10u
11
+ 7u
9
+ 4u
7
− 8u
5
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
18
+ 28u
16
+ 4u
15
−80u
14
−24u
13
+ 96u
12
+ 56u
11
+ 16u
10
−
44u
9
− 160u
8
− 40u
7
+ 108u
6
+ 84u
5
+ 60u
4
− 12u
3
− 64u
2
− 36u − 22
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
20
+ u
19
+ ··· − 2u − 1
c
2
, c
4
, c
5
c
6
, c
8
, c
9
u
20
+ 3u
19
+ ··· + 6u + 1
c
3
, c
10
, c
11
u
20
− u
19
+ ··· − 4u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
20
− 3y
19
+ ··· − 6y + 1
c
2
, c
4
, c
5
c
6
, c
8
, c
9
y
20
+ 29y
19
+ ··· + 2y + 1
c
3
, c
10
, c
11
y
20
− 15y
19
+ ··· − 6y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.007607 + 0.949634I
18.4290 + 3.4609I −3.93136 − 2.23046I
u = −0.007607 − 0.949634I
18.4290 − 3.4609I −3.93136 + 2.23046I
u = −1.101030 + 0.131890I
−1.54609 + 0.69516I −7.68521 − 0.30999I
u = −1.101030 − 0.131890I
−1.54609 − 0.69516I −7.68521 + 0.30999I
u = −0.038091 + 0.788227I
7.04605 + 2.82035I −3.80057 − 3.20704I
u = −0.038091 − 0.788227I
7.04605 − 2.82035I −3.80057 + 3.20704I
u = 1.24407
−5.00568 −19.1740
u = 1.239950 + 0.176027I
−3.11470 − 3.99252I −13.6755 + 7.5015I
u = 1.239950 − 0.176027I
−3.11470 + 3.99252I −13.6755 − 7.5015I
u = −1.204290 + 0.369958I
3.49001 + 1.34947I −7.27011 − 0.63614I
u = −1.204290 − 0.369958I
3.49001 − 1.34947I −7.27011 + 0.63614I
u = 1.261210 + 0.352418I
3.03541 − 6.91001I −8.48791 + 6.50357I
u = 1.261210 − 0.352418I
3.03541 + 6.91001I −8.48791 − 6.50357I
u = −1.293390 + 0.470696I
14.4385 + 1.5977I −7.05732 − 0.65036I
u = −1.293390 − 0.470696I
14.4385 − 1.5977I −7.05732 + 0.65036I
u = 1.304330 + 0.464606I
14.3498 − 8.5006I −7.22483 + 5.05516I
u = 1.304330 − 0.464606I
14.3498 + 8.5006I −7.22483 − 5.05516I
u = −0.133388 + 0.482581I
0.98038 + 1.64938I −5.14084 − 6.42836I
u = −0.133388 − 0.482581I
0.98038 − 1.64938I −5.14084 + 6.42836I
u = −0.299460
−0.645282 −16.2790
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
20
+ u
19
+ ··· − 2u − 1
c
2
, c
4
, c
5
c
6
, c
8
, c
9
u
20
+ 3u
19
+ ··· + 6u + 1
c
3
, c
10
, c
11
u
20
− u
19
+ ··· − 4u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
20
− 3y
19
+ ··· − 6y + 1
c
2
, c
4
, c
5
c
6
, c
8
, c
9
y
20
+ 29y
19
+ ··· + 2y + 1
c
3
, c
10
, c
11
y
20
− 15y
19
+ ··· − 6y + 1
7
