11a
120
(K11a
120
)
A knot diagram
1
Linearized knot diagam
6 1 8 10 2 5 3 11 4 9 7
Solving Sequence
2,5
6 7 1 3 8 11 9 10 4
c
5
c
6
c
1
c
2
c
7
c
11
c
8
c
10
c
4
c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
54
− u
53
+ ··· + 3u − 1i
* 1 irreducible components of dim
C
= 0, with total 54 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
54
− u
53
+ · · · + 3u − 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
7
=
u
2
+ 1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
8
=
u
10
+ u
8
+ 2u
6
+ u
4
+ u
2
+ 1
−u
12
− 2u
10
− 4u
8
− 4u
6
− 3u
4
− 2u
2
a
11
=
−u
7
− 2u
5
− 2u
3
− 2u
u
7
+ u
5
+ 2u
3
+ u
a
9
=
−u
26
− 5u
24
+ ··· + 3u
2
+ 1
u
26
+ 4u
24
+ ··· − 4u
4
− 3u
2
a
10
=
−u
45
− 8u
43
+ ··· − 4u
3
− 3u
u
45
+ 7u
43
+ ··· + 5u
3
+ u
a
4
=
u
17
+ 2u
15
+ 5u
13
+ 6u
11
+ 7u
9
+ 6u
7
+ 4u
5
+ 2u
3
+ u
−u
19
− 3u
17
− 8u
15
− 13u
13
− 17u
11
− 17u
9
− 12u
7
− 6u
5
− u
3
+ u
a
4
=
u
17
+ 2u
15
+ 5u
13
+ 6u
11
+ 7u
9
+ 6u
7
+ 4u
5
+ 2u
3
+ u
−u
19
− 3u
17
− 8u
15
− 13u
13
− 17u
11
− 17u
9
− 12u
7
− 6u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
53
+ 32u
51
+ ··· − 8u + 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
54
− u
53
+ ··· + 3u − 1
c
2
, c
6
u
54
+ 17u
53
+ ··· − 5u + 1
c
3
, c
7
u
54
− u
53
+ ··· + 5u − 25
c
4
, c
9
u
54
+ u
53
+ ··· − u − 1
c
8
, c
10
u
54
− 19u
53
+ ··· − 5u + 1
c
11
u
54
+ 5u
53
+ ··· − 5u − 21
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
54
+ 17y
53
+ ··· − 5y + 1
c
2
, c
6
y
54
+ 41y
53
+ ··· − 93y + 1
c
3
, c
7
y
54
− 39y
53
+ ··· − 9225y + 625
c
4
, c
9
y
54
− 19y
53
+ ··· − 5y + 1
c
8
, c
10
y
54
+ 33y
53
+ ··· − 13y + 1
c
11
y
54
− 11y
53
+ ··· + 7283y + 441
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.225158 + 0.985509I
2.66174 − 2.82423I 9.41850 + 4.26927I
u = −0.225158 − 0.985509I
2.66174 + 2.82423I 9.41850 − 4.26927I
u = 0.013188 + 1.020430I
−6.28584 + 2.76345I −1.40260 − 3.24602I
u = 0.013188 − 1.020430I
−6.28584 − 2.76345I −1.40260 + 3.24602I
u = −0.322299 + 0.910896I
−0.90934 + 3.04310I 5.53731 − 1.39630I
u = −0.322299 − 0.910896I
−0.90934 − 3.04310I 5.53731 + 1.39630I
u = 0.172024 + 1.019410I
−3.04751 + 3.37129I 1.74364 − 3.43225I
u = 0.172024 − 1.019410I
−3.04751 − 3.37129I 1.74364 + 3.43225I
u = −0.188352 + 1.032560I
−1.89570 − 8.85965I 3.95399 + 8.19419I
u = −0.188352 − 1.032560I
−1.89570 + 8.85965I 3.95399 − 8.19419I
u = 0.130465 + 0.911615I
−1.74890 + 1.55584I 1.72859 − 4.90109I
u = 0.130465 − 0.911615I
−1.74890 − 1.55584I 1.72859 + 4.90109I
u = −0.719799 + 0.809822I
3.52747 − 0.23244I 13.19154 − 1.36658I
u = −0.719799 − 0.809822I
3.52747 + 0.23244I 13.19154 + 1.36658I
u = −0.818638 + 0.718254I
3.52513 + 2.90265I 8.89044 − 0.48035I
u = −0.818638 − 0.718254I
3.52513 − 2.90265I 8.89044 + 0.48035I
u = 0.654895 + 0.871773I
0.94675 + 2.54301I 4.57303 − 2.79240I
u = 0.654895 − 0.871773I
0.94675 − 2.54301I 4.57303 + 2.79240I
u = 0.830157 + 0.717041I
4.86571 − 8.43016I 10.90175 + 5.08103I
u = 0.830157 − 0.717041I
4.86571 + 8.43016I 10.90175 − 5.08103I
u = −0.631705 + 0.643354I
−1.36873 + 3.22618I 6.44583 − 3.29326I
u = −0.631705 − 0.643354I
−1.36873 − 3.22618I 6.44583 + 3.29326I
u = −0.799923 + 0.758789I
4.31402 + 0.26912I 9.66102 + 0.I
u = −0.799923 − 0.758789I
4.31402 − 0.26912I 9.66102 + 0.I
u = 0.826542 + 0.743334I
9.45805 − 1.89794I 15.5987 + 0.I
u = 0.826542 − 0.743334I
9.45805 + 1.89794I 15.5987 + 0.I
u = 0.413630 + 0.782655I
−1.72347 + 2.04419I 4.15028 − 4.01557I
u = 0.413630 − 0.782655I
−1.72347 − 2.04419I 4.15028 + 4.01557I
u = 0.816023 + 0.773035I
5.87973 + 4.75272I 12.23699 − 4.92141I
u = 0.816023 − 0.773035I
5.87973 − 4.75272I 12.23699 + 4.92141I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.637029 + 0.965427I
−2.61478 + 2.76089I 3.34853 + 0.I
u = 0.637029 − 0.965427I
−2.61478 − 2.76089I 3.34853 + 0.I
u = −0.713272 + 0.912768I
3.21684 − 5.24753I 12.07775 + 7.28540I
u = −0.713272 − 0.912768I
3.21684 + 5.24753I 12.07775 − 7.28540I
u = −0.652949 + 0.976409I
−2.30035 − 8.30381I 0. + 8.62112I
u = −0.652949 − 0.976409I
−2.30035 + 8.30381I 0. − 8.62112I
u = 0.501769 + 0.617981I
−1.73704 + 2.07051I 5.30183 − 3.63568I
u = 0.501769 − 0.617981I
−1.73704 − 2.07051I 5.30183 + 3.63568I
u = −0.738963 + 0.973368I
3.65451 − 6.06207I 0
u = −0.738963 − 0.973368I
3.65451 + 6.06207I 0
u = 0.755217 + 0.969347I
5.27505 + 1.13830I 0
u = 0.755217 − 0.969347I
5.27505 − 1.13830I 0
u = 0.749443 + 0.991696I
8.69493 + 7.80028I 0
u = 0.749443 − 0.991696I
8.69493 − 7.80028I 0
u = −0.735797 + 1.001920I
2.65813 − 8.73650I 0
u = −0.735797 − 1.001920I
2.65813 + 8.73650I 0
u = 0.740821 + 1.006800I
3.9780 + 14.3126I 0
u = 0.740821 − 1.006800I
3.9780 − 14.3126I 0
u = −0.638480 + 0.083682I
1.68643 − 6.22008I 11.41350 + 5.62288I
u = −0.638480 − 0.083682I
1.68643 + 6.22008I 11.41350 − 5.62288I
u = −0.633762
5.79098 16.1980
u = 0.593562 + 0.088163I
0.459602 + 0.933389I 9.53888 − 0.84977I
u = 0.593562 − 0.088163I
0.459602 − 0.933389I 9.53888 + 0.84977I
u = 0.334907
0.694593 14.5890
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
54
− u
53
+ ··· + 3u − 1
c
2
, c
6
u
54
+ 17u
53
+ ··· − 5u + 1
c
3
, c
7
u
54
− u
53
+ ··· + 5u − 25
c
4
, c
9
u
54
+ u
53
+ ··· − u − 1
c
8
, c
10
u
54
− 19u
53
+ ··· − 5u + 1
c
11
u
54
+ 5u
53
+ ··· − 5u − 21
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
54
+ 17y
53
+ ··· − 5y + 1
c
2
, c
6
y
54
+ 41y
53
+ ··· − 93y + 1
c
3
, c
7
y
54
− 39y
53
+ ··· − 9225y + 625
c
4
, c
9
y
54
− 19y
53
+ ··· − 5y + 1
c
8
, c
10
y
54
+ 33y
53
+ ··· − 13y + 1
c
11
y
54
− 11y
53
+ ··· + 7283y + 441
8
