11a
309
(K11a
309
)
A knot diagram
1
Linearized knot diagam
7 6 1 10 9 2 3 11 4 5 8
Solving Sequence
5,11
10 4 9 6 8 1 3 2 7
c
10
c
4
c
9
c
5
c
8
c
11
c
3
c
2
c
7
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
46
+ u
45
+ ··· + u − 1i
* 1 irreducible components of dim
C
= 0, with total 46 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
46
+ u
45
+ · · · + u − 1i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
10
=
1
−u
2
a
4
=
u
−u
3
+ u
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
6
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
8
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
a
1
=
u
8
− 3u
6
+ u
4
+ 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
3
=
−u
19
+ 8u
17
− 24u
15
+ 30u
13
− 7u
11
− 10u
9
− 4u
7
+ 6u
5
+ 3u
3
+ 2u
u
19
− 9u
17
+ 32u
15
− 55u
13
+ 43u
11
− 9u
9
− 4u
5
− u
3
+ u
a
2
=
−u
31
+ 14u
29
+ ··· + 6u
3
+ 2u
u
33
− 15u
31
+ ··· − 4u
3
+ u
a
7
=
u
34
− 15u
32
+ ··· − u
2
+ 1
−u
34
+ 16u
32
+ ··· − 2u
4
− 3u
2
a
7
=
u
34
− 15u
32
+ ··· − u
2
+ 1
−u
34
+ 16u
32
+ ··· − 2u
4
− 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
44
+ 84u
42
+ ··· − 4u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
46
+ u
45
+ ··· − 3u − 1
c
3
u
46
− 11u
45
+ ··· − 95u + 11
c
4
, c
9
, c
10
u
46
− u
45
+ ··· − u − 1
c
5
u
46
+ 3u
45
+ ··· + 95u + 56
c
7
u
46
− u
45
+ ··· − 3u − 2
c
8
, c
11
u
46
+ 7u
45
+ ··· + 119u + 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
46
+ 41y
45
+ ··· − 5y + 1
c
3
y
46
+ 5y
45
+ ··· + 2679y + 121
c
4
, c
9
, c
10
y
46
− 43y
45
+ ··· − 5y + 1
c
5
y
46
− 15y
45
+ ··· − 63233y + 3136
c
7
y
46
− 3y
45
+ ··· + 15y + 4
c
8
, c
11
y
46
+ 37y
45
+ ··· − 1337y + 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.165530 + 0.155856I
3.73352 − 1.14194I −3.26529 + 0.I
u = −1.165530 − 0.155856I
3.73352 + 1.14194I −3.26529 + 0.I
u = 0.386832 + 0.683926I
1.91287 − 9.38652I −5.20305 + 7.91054I
u = 0.386832 − 0.683926I
1.91287 + 9.38652I −5.20305 − 7.91054I
u = −0.397188 + 0.664692I
−3.31119 + 5.72979I −10.05626 − 7.33064I
u = −0.397188 − 0.664692I
−3.31119 − 5.72979I −10.05626 + 7.33064I
u = 0.528416 + 0.546036I
1.33332 + 5.27035I −6.71990 − 1.90933I
u = 0.528416 − 0.546036I
1.33332 − 5.27035I −6.71990 + 1.90933I
u = 1.240960 + 0.124497I
−1.94572 − 1.01820I 0
u = 1.240960 − 0.124497I
−1.94572 + 1.01820I 0
u = −0.494882 + 0.561225I
−3.73492 − 1.67350I −11.57713 + 0.85623I
u = −0.494882 − 0.561225I
−3.73492 + 1.67350I −11.57713 − 0.85623I
u = 0.441277 + 0.595069I
−1.58749 − 1.92674I −8.17224 + 4.16982I
u = 0.441277 − 0.595069I
−1.58749 + 1.92674I −8.17224 − 4.16982I
u = 0.407690 + 0.618254I
−1.47350 − 1.99549I −7.38990 + 2.72369I
u = 0.407690 − 0.618254I
−1.47350 + 1.99549I −7.38990 − 2.72369I
u = 1.263800 + 0.221984I
2.87934 − 7.34272I 0
u = 1.263800 − 0.221984I
2.87934 + 7.34272I 0
u = −1.276900 + 0.186164I
−2.59332 + 4.30245I 0
u = −1.276900 − 0.186164I
−2.59332 − 4.30245I 0
u = −0.297294 + 0.620737I
4.69829 + 1.24621I −1.93786 − 3.60564I
u = −0.297294 − 0.620737I
4.69829 − 1.24621I −1.93786 + 3.60564I
u = −0.062298 + 0.646826I
6.95779 + 4.17599I 1.17304 − 4.31736I
u = −0.062298 − 0.646826I
6.95779 − 4.17599I 1.17304 + 4.31736I
u = −1.37176
−5.91200 0
u = 1.386810 + 0.059846I
−2.09433 − 3.02163I 0
u = 1.386810 − 0.059846I
−2.09433 + 3.02163I 0
u = 0.057342 + 0.580744I
1.51039 − 1.50155I −2.27260 + 5.37426I
u = 0.057342 − 0.580744I
1.51039 + 1.50155I −2.27260 − 5.37426I
u = −0.506673 + 0.270240I
3.63229 + 1.96690I −5.76565 − 3.43589I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.506673 − 0.270240I
3.63229 − 1.96690I −5.76565 + 3.43589I
u = 1.42136 + 0.23318I
−0.82034 − 4.36000I 0
u = 1.42136 − 0.23318I
−0.82034 + 4.36000I 0
u = −1.45582 + 0.23236I
−7.46462 + 5.12455I 0
u = −1.45582 − 0.23236I
−7.46462 − 5.12455I 0
u = −1.46312 + 0.21522I
−7.72158 + 4.89307I 0
u = −1.46312 − 0.21522I
−7.72158 − 4.89307I 0
u = 1.45856 + 0.24779I
−9.28633 − 9.06645I 0
u = 1.45856 − 0.24779I
−9.28633 + 9.06645I 0
u = −1.45711 + 0.25642I
−4.02180 + 12.82070I 0
u = −1.45711 − 0.25642I
−4.02180 − 12.82070I 0
u = 1.46935 + 0.19673I
−10.04570 − 1.08177I 0
u = 1.46935 − 0.19673I
−10.04570 + 1.08177I 0
u = −1.47298 + 0.18376I
−5.09568 − 2.64921I 0
u = −1.47298 − 0.18376I
−5.09568 + 2.64921I 0
u = 0.346604
−0.677522 −14.9940
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
46
+ u
45
+ ··· − 3u − 1
c
3
u
46
− 11u
45
+ ··· − 95u + 11
c
4
, c
9
, c
10
u
46
− u
45
+ ··· − u − 1
c
5
u
46
+ 3u
45
+ ··· + 95u + 56
c
7
u
46
− u
45
+ ··· − 3u − 2
c
8
, c
11
u
46
+ 7u
45
+ ··· + 119u + 7
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
46
+ 41y
45
+ ··· − 5y + 1
c
3
y
46
+ 5y
45
+ ··· + 2679y + 121
c
4
, c
9
, c
10
y
46
− 43y
45
+ ··· − 5y + 1
c
5
y
46
− 15y
45
+ ··· − 63233y + 3136
c
7
y
46
− 3y
45
+ ··· + 15y + 4
c
8
, c
11
y
46
+ 37y
45
+ ··· − 1337y + 49
8
