11a
177
(K11a
177
)
A knot diagram
1
Linearized knot diagam
6 1 11 9 10 2 3 4 5 8 7
Solving Sequence
2,6
7 1 3 8 11 4 9 10 5
c
6
c
1
c
2
c
7
c
11
c
3
c
8
c
10
c
5
c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
48
− u
47
+ ··· + 2u
2
− 1i
* 1 irreducible components of dim
C
= 0, with total 48 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
48
− u
47
+ · · · + 2u
2
− 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
8
=
u
8
− u
6
+ u
4
+ 1
u
8
− 2u
6
+ 2u
4
a
11
=
u
3
u
5
− u
3
+ u
a
4
=
u
11
− 2u
9
+ 2u
7
− u
3
u
13
− 3u
11
+ 5u
9
− 4u
7
+ 2u
5
− u
3
+ u
a
9
=
u
32
− 7u
30
+ ··· + 2u
12
+ 1
u
34
− 8u
32
+ ··· + 4u
6
+ u
2
a
10
=
u
21
− 4u
19
+ 9u
17
− 12u
15
+ 12u
13
− 10u
11
+ 9u
9
− 6u
7
+ 3u
5
+ u
u
21
− 5u
19
+ 13u
17
− 20u
15
+ 20u
13
− 13u
11
+ 7u
9
− 4u
7
+ 3u
5
− u
3
+ u
a
5
=
−u
42
+ 9u
40
+ ··· − u
2
+ 1
−u
42
+ 10u
40
+ ··· + 2u
4
− u
2
a
5
=
−u
42
+ 9u
40
+ ··· − u
2
+ 1
−u
42
+ 10u
40
+ ··· + 2u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
46
+ 44u
44
+ ··· + 8u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
48
− u
47
+ ··· + 2u
2
− 1
c
2
u
48
+ 23u
47
+ ··· + 4u + 1
c
3
u
48
+ 5u
47
+ ··· + 440u + 41
c
4
, c
5
, c
8
c
9
u
48
− u
47
+ ··· − 2u − 1
c
7
u
48
+ u
47
+ ··· − 46u − 13
c
10
u
48
− 13u
47
+ ··· + 248u − 23
c
11
u
48
− 3u
47
+ ··· + 92u − 9
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
48
− 23y
47
+ ··· − 4y + 1
c
2
y
48
+ 5y
47
+ ··· − 12y
2
+ 1
c
3
y
48
+ 17y
47
+ ··· − 50264y + 1681
c
4
, c
5
, c
8
c
9
y
48
− 55y
47
+ ··· − 4y + 1
c
7
y
48
− 7y
47
+ ··· − 6692y + 169
c
10
y
48
− 7y
47
+ ··· − 5752y + 529
c
11
y
48
+ 13y
47
+ ··· − 8824y + 81
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.950359
−7.68002 −11.9160
u = 0.906245 + 0.560228I
−6.74396 + 1.23314I −7.83364 + 0.66658I
u = 0.906245 − 0.560228I
−6.74396 − 1.23314I −7.83364 − 0.66658I
u = 0.654967 + 0.639668I
−6.00272 − 5.94733I −6.48259 + 5.46714I
u = 0.654967 − 0.639668I
−6.00272 + 5.94733I −6.48259 − 5.46714I
u = −0.958032 + 0.533471I
0.422311 + 0.763813I −4.66179 + 1.11475I
u = −0.958032 − 0.533471I
0.422311 − 0.763813I −4.66179 − 1.11475I
u = −1.079460 + 0.276851I
−2.59116 + 0.36031I −7.93807 − 0.87976I
u = −1.079460 − 0.276851I
−2.59116 − 0.36031I −7.93807 + 0.87976I
u = −0.612298 + 0.617824I
1.43265 + 3.79656I −3.21409 − 7.28282I
u = −0.612298 − 0.617824I
1.43265 − 3.79656I −3.21409 + 7.28282I
u = 1.009290 + 0.540403I
1.00278 − 4.13351I −2.80982 + 6.67284I
u = 1.009290 − 0.540403I
1.00278 + 4.13351I −2.80982 − 6.67284I
u = 1.118000 + 0.248646I
−4.32121 + 2.98517I −12.02372 − 4.32221I
u = 1.118000 − 0.248646I
−4.32121 − 2.98517I −12.02372 + 4.32221I
u = 1.109880 + 0.332950I
−5.19194 − 3.05995I −13.8975 + 5.0529I
u = 1.109880 − 0.332950I
−5.19194 + 3.05995I −13.8975 − 5.0529I
u = 0.320233 + 0.770338I
−7.65892 + 8.01718I −7.88582 − 4.62371I
u = 0.320233 − 0.770338I
−7.65892 − 8.01718I −7.88582 + 4.62371I
u = −1.144450 + 0.242249I
−12.21720 − 5.14750I −14.0897 + 2.5540I
u = −1.144450 − 0.242249I
−12.21720 + 5.14750I −14.0897 − 2.5540I
u = −0.466321 + 0.682642I
−3.08169 − 1.06539I −4.15324 + 0.48438I
u = −0.466321 − 0.682642I
−3.08169 + 1.06539I −4.15324 − 0.48438I
u = 0.541320 + 0.609466I
2.38297 − 0.42475I 0.428840 − 0.154422I
u = 0.541320 − 0.609466I
2.38297 + 0.42475I 0.428840 + 0.154422I
u = −0.330482 + 0.744977I
0.08939 − 5.70419I −5.22111 + 6.43741I
u = −0.330482 − 0.744977I
0.08939 + 5.70419I −5.22111 − 6.43741I
u = −1.143670 + 0.342258I
−13.35450 + 4.59259I −15.0956 − 3.6225I
u = −1.143670 − 0.342258I
−13.35450 − 4.59259I −15.0956 + 3.6225I
u = −1.050160 + 0.567901I
−4.79213 + 5.90007I −7.32134 − 5.68166I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.050160 − 0.567901I
−4.79213 − 5.90007I −7.32134 + 5.68166I
u = 0.346872 + 0.703599I
1.51359 + 2.15734I −1.22557 − 1.03658I
u = 0.346872 − 0.703599I
1.51359 − 2.15734I −1.22557 + 1.03658I
u = −1.108460 + 0.518737I
−3.93668 + 4.44888I −11.97527 − 2.81455I
u = −1.108460 − 0.518737I
−3.93668 − 4.44888I −11.97527 + 2.81455I
u = 1.107780 + 0.553922I
−0.69945 − 6.98562I −4.89380 + 5.04107I
u = 1.107780 − 0.553922I
−0.69945 + 6.98562I −4.89380 − 5.04107I
u = 1.134660 + 0.506389I
−12.24490 − 3.33222I −13.52387 + 3.39581I
u = 1.134660 − 0.506389I
−12.24490 + 3.33222I −13.52387 − 3.39581I
u = −1.122190 + 0.562178I
−2.22657 + 10.65640I −8.51135 − 10.01533I
u = −1.122190 − 0.562178I
−2.22657 − 10.65640I −8.51135 + 10.01533I
u = 1.132630 + 0.566501I
−10.0472 − 13.0450I −11.01452 + 8.25936I
u = 1.132630 − 0.566501I
−10.0472 + 13.0450I −11.01452 − 8.25936I
u = 0.180677 + 0.698013I
−9.54554 − 1.19929I −10.13609 + 0.35134I
u = 0.180677 − 0.698013I
−9.54554 + 1.19929I −10.13609 − 0.35134I
u = −0.240215 + 0.625865I
−1.54227 + 0.02620I −8.94545 − 1.26503I
u = −0.240215 − 0.625865I
−1.54227 − 0.02620I −8.94545 + 1.26503I
u = −0.563965
−0.872825 −11.2330
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
48
− u
47
+ ··· + 2u
2
− 1
c
2
u
48
+ 23u
47
+ ··· + 4u + 1
c
3
u
48
+ 5u
47
+ ··· + 440u + 41
c
4
, c
5
, c
8
c
9
u
48
− u
47
+ ··· − 2u − 1
c
7
u
48
+ u
47
+ ··· − 46u − 13
c
10
u
48
− 13u
47
+ ··· + 248u − 23
c
11
u
48
− 3u
47
+ ··· + 92u − 9
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
48
− 23y
47
+ ··· − 4y + 1
c
2
y
48
+ 5y
47
+ ··· − 12y
2
+ 1
c
3
y
48
+ 17y
47
+ ··· − 50264y + 1681
c
4
, c
5
, c
8
c
9
y
48
− 55y
47
+ ··· − 4y + 1
c
7
y
48
− 7y
47
+ ··· − 6692y + 169
c
10
y
48
− 7y
47
+ ··· − 5752y + 529
c
11
y
48
+ 13y
47
+ ··· − 8824y + 81
8
