11a
180
(K11a
180
)
A knot diagram
1
Linearized knot diagam
7 1 8 11 10 2 3 4 5 6 9
Solving Sequence
6,11
10 5 4 9 1 8 3 2 7
c
10
c
5
c
4
c
9
c
11
c
8
c
3
c
2
c
7
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
44
+ u
43
+ ··· + u
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
+ · · · + u
2
+ 1i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
5
=
−u
−u
3
+ u
a
4
=
u
3
− 2u
−u
3
+ u
a
9
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
u
6
− 3u
4
+ 2u
2
+ 1
u
8
− 4u
6
+ 4u
4
a
8
=
−u
10
+ 5u
8
− 8u
6
+ 3u
4
+ u
2
+ 1
u
10
− 4u
8
+ 5u
6
− 2u
4
+ u
2
a
3
=
−u
17
+ 8u
15
− 25u
13
+ 36u
11
− 19u
9
− 4u
7
+ 2u
5
+ 4u
3
− u
u
17
− 7u
15
+ 19u
13
− 24u
11
+ 13u
9
− 2u
7
+ u
a
2
=
u
31
− 14u
29
+ ··· + 4u
5
+ 8u
3
u
33
− 15u
31
+ ··· + 4u
5
+ u
a
7
=
u
24
− 11u
22
+ ··· + 2u
2
+ 1
−u
24
+ 10u
22
+ ··· + 8u
6
− 4u
4
a
7
=
u
24
− 11u
22
+ ··· + 2u
2
+ 1
−u
24
+ 10u
22
+ ··· + 8u
6
− 4u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
42
+ 76u
40
+ ··· − 8u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
44
+ u
43
+ ··· + u
2
+ 1
c
2
u
44
+ 25u
43
+ ··· + 2u + 1
c
3
, c
7
, c
8
u
44
− u
43
+ ··· + 16u + 5
c
4
u
44
− 3u
43
+ ··· − 8u + 3
c
5
, c
9
, c
10
u
44
+ u
43
+ ··· + u
2
+ 1
c
11
u
44
− 11u
43
+ ··· − 12u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
44
+ 25y
43
+ ··· + 2y + 1
c
2
y
44
− 11y
43
+ ··· + 6y + 1
c
3
, c
7
, c
8
y
44
− 47y
43
+ ··· − 726y + 25
c
4
y
44
+ 5y
43
+ ··· − 70y + 9
c
5
, c
9
, c
10
y
44
− 39y
43
+ ··· + 2y + 1
c
11
y
44
+ y
43
+ ··· + 62y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.907981 + 0.307169I
−7.95121 + 4.48081I −3.24122 − 4.16997I
u = 0.907981 − 0.307169I
−7.95121 − 4.48081I −3.24122 + 4.16997I
u = −0.864630 + 0.288338I
−4.16526 + 0.15305I 0.227540 + 0.929725I
u = −0.864630 − 0.288338I
−4.16526 − 0.15305I 0.227540 − 0.929725I
u = 0.842517 + 0.328770I
−7.81717 − 4.88382I −2.90557 + 2.15624I
u = 0.842517 − 0.328770I
−7.81717 + 4.88382I −2.90557 − 2.15624I
u = −1.170600 + 0.135808I
−0.38378 − 3.13770I −2.56284 + 4.58087I
u = −1.170600 − 0.135808I
−0.38378 + 3.13770I −2.56284 − 4.58087I
u = 0.238444 + 0.753257I
−9.78827 + 8.91254I −5.51225 − 6.86117I
u = 0.238444 − 0.753257I
−9.78827 − 8.91254I −5.51225 + 6.86117I
u = 0.211452 + 0.753740I
−10.14920 − 0.50010I −6.30668 − 0.52370I
u = 0.211452 − 0.753740I
−10.14920 + 0.50010I −6.30668 + 0.52370I
u = −0.226339 + 0.743021I
−6.22083 − 4.06637I −2.60237 + 3.83342I
u = −0.226339 − 0.743021I
−6.22083 + 4.06637I −2.60237 − 3.83342I
u = 1.27909
2.59443 3.57300
u = −0.265421 + 0.637640I
−1.64111 − 5.49885I −2.09355 + 9.09752I
u = −0.265421 − 0.637640I
−1.64111 + 5.49885I −2.09355 − 9.09752I
u = 1.333120 + 0.238788I
1.11897 + 2.94236I 0
u = 1.333120 − 0.238788I
1.11897 − 2.94236I 0
u = −0.111488 + 0.635085I
−3.42148 + 0.21799I −7.97736 + 0.39083I
u = −0.111488 − 0.635085I
−3.42148 − 0.21799I −7.97736 − 0.39083I
u = 1.38005
2.50705 0
u = 0.244204 + 0.558196I
0.06888 + 1.57750I 1.83089 − 4.70926I
u = 0.244204 − 0.558196I
0.06888 − 1.57750I 1.83089 + 4.70926I
u = 1.390480 + 0.143509I
5.13647 − 0.61365I 0
u = 1.390480 − 0.143509I
5.13647 + 0.61365I 0
u = −1.389040 + 0.181909I
5.88050 − 3.43976I 0
u = −1.389040 − 0.181909I
5.88050 + 3.43976I 0
u = −1.388080 + 0.226393I
5.26596 − 4.49438I 0
u = −1.388080 − 0.226393I
5.26596 + 4.49438I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.38262 + 0.30594I
−5.09640 − 3.33447I 0
u = −1.38262 − 0.30594I
−5.09640 + 3.33447I 0
u = −1.41982 + 0.02499I
−0.91602 + 4.40703I 0
u = −1.41982 − 0.02499I
−0.91602 − 4.40703I 0
u = 1.39798 + 0.25008I
3.65546 + 8.74389I 0
u = 1.39798 − 0.25008I
3.65546 − 8.74389I 0
u = 1.39053 + 0.29925I
−1.08580 + 7.84259I 0
u = 1.39053 − 0.29925I
−1.08580 − 7.84259I 0
u = −1.39749 + 0.30388I
−4.58845 − 12.74280I 0
u = −1.39749 − 0.30388I
−4.58845 + 12.74280I 0
u = −0.474413 + 0.286577I
−0.48387 + 2.27983I 1.28247 − 3.09777I
u = −0.474413 − 0.286577I
−0.48387 − 2.27983I 1.28247 + 3.09777I
u = 0.303652 + 0.417609I
0.553397 + 1.129410I 4.11708 − 5.53577I
u = 0.303652 − 0.417609I
0.553397 − 1.129410I 4.11708 + 5.53577I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
44
+ u
43
+ ··· + u
2
+ 1
c
2
u
44
+ 25u
43
+ ··· + 2u + 1
c
3
, c
7
, c
8
u
44
− u
43
+ ··· + 16u + 5
c
4
u
44
− 3u
43
+ ··· − 8u + 3
c
5
, c
9
, c
10
u
44
+ u
43
+ ··· + u
2
+ 1
c
11
u
44
− 11u
43
+ ··· − 12u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
44
+ 25y
43
+ ··· + 2y + 1
c
2
y
44
− 11y
43
+ ··· + 6y + 1
c
3
, c
7
, c
8
y
44
− 47y
43
+ ··· − 726y + 25
c
4
y
44
+ 5y
43
+ ··· − 70y + 9
c
5
, c
9
, c
10
y
44
− 39y
43
+ ··· + 2y + 1
c
11
y
44
+ y
43
+ ··· + 62y + 1
8
