12a
0545
(K12a
0545
)
A knot diagram
1
Linearized knot diagam
3 7 8 10 1 2 6 12 11 5 9 4
Solving Sequence
5,11
10 4 9 12 1 6 8 3 7 2
c
10
c
4
c
9
c
11
c
12
c
5
c
8
c
3
c
7
c
2
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
71
− u
70
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 71 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
71
− u
70
+ · · · + 2u − 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
2
a
12
=
u
4
− u
2
+ 1
−u
4
a
1
=
u
8
− u
6
+ 3u
4
− 2u
2
+ 1
u
10
− 2u
8
+ 3u
6
− 4u
4
+ u
2
a
6
=
−u
17
+ 2u
15
− 7u
13
+ 10u
11
− 15u
9
+ 14u
7
− 10u
5
+ 4u
3
− u
−u
19
+ 3u
17
− 8u
15
+ 15u
13
− 19u
11
+ 21u
9
− 14u
7
+ 6u
5
− u
3
+ u
a
8
=
−u
6
+ u
4
− 2u
2
+ 1
u
6
+ u
2
a
3
=
−u
15
+ 2u
13
− 6u
11
+ 8u
9
− 10u
7
+ 8u
5
− 4u
3
u
15
− u
13
+ 4u
11
− 3u
9
+ 4u
7
− 2u
5
+ u
a
7
=
u
42
− 5u
40
+ ··· − u
2
+ 1
u
44
− 6u
42
+ ··· − 12u
6
+ 3u
4
a
2
=
−u
40
+ 5u
38
+ ··· − 2u
2
+ 1
u
40
− 4u
38
+ ··· − 6u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
69
− 4u
68
+ ··· − 8u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
71
+ 25u
70
+ ··· + 4u + 1
c
2
, c
6
u
71
− u
70
+ ··· − 2u + 1
c
3
, c
5
u
71
+ u
70
+ ··· − 406u + 97
c
4
, c
10
u
71
+ u
70
+ ··· + 2u + 1
c
8
, c
9
, c
11
u
71
− 17u
70
+ ··· + 4u − 1
c
12
u
71
− 7u
70
+ ··· + 13008u − 6545
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
71
+ 43y
70
+ ··· − 20y −1
c
2
, c
6
y
71
− 25y
70
+ ··· + 4y −1
c
3
, c
5
y
71
− 53y
70
+ ··· + 348748y −9409
c
4
, c
10
y
71
− 17y
70
+ ··· + 4y −1
c
8
, c
9
, c
11
y
71
+ 75y
70
+ ··· − 20y −1
c
12
y
71
− 25y
70
+ ··· + 292384964y −42837025
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.888190 + 0.459117I
−1.18643 + 1.35824I 0
u = −0.888190 − 0.459117I
−1.18643 − 1.35824I 0
u = −0.932507 + 0.429015I
−4.68486 − 4.91394I 0. + 6.57071I
u = −0.932507 − 0.429015I
−4.68486 + 4.91394I 0. − 6.57071I
u = 0.948249 + 0.398634I
1.14717 + 5.67185I 0. − 6.12958I
u = 0.948249 − 0.398634I
1.14717 − 5.67185I 0. + 6.12958I
u = 0.929272 + 0.279545I
5.07424 + 5.34453I 4.69472 − 7.85817I
u = 0.929272 − 0.279545I
5.07424 − 5.34453I 4.69472 + 7.85817I
u = 0.880577 + 0.406341I
0.12671 + 3.47465I −0.94229 − 7.22764I
u = 0.880577 − 0.406341I
0.12671 − 3.47465I −0.94229 + 7.22764I
u = −0.924346 + 0.256884I
5.20330 + 0.14255I 5.40218 + 1.47024I
u = −0.924346 − 0.256884I
5.20330 − 0.14255I 5.40218 − 1.47024I
u = −0.957821 + 0.407226I
−0.08969 − 11.18150I 0. + 10.67896I
u = −0.957821 − 0.407226I
−0.08969 + 11.18150I 0. − 10.67896I
u = 0.930800 + 0.073679I
1.75758 − 5.86547I 1.99827 + 4.58778I
u = 0.930800 − 0.073679I
1.75758 + 5.86547I 1.99827 − 4.58778I
u = −0.909390 + 0.093581I
2.83229 + 0.49914I 4.26447 + 0.53477I
u = −0.909390 − 0.093581I
2.83229 − 0.49914I 4.26447 − 0.53477I
u = 0.904521
−2.42702 −3.10240
u = 0.795537 + 0.390577I
0.09323 + 3.30566I −3.55215 − 8.38260I
u = 0.795537 − 0.390577I
0.09323 − 3.30566I −3.55215 + 8.38260I
u = 0.848471 + 0.801057I
−1.23479 + 2.37348I 0
u = 0.848471 − 0.801057I
−1.23479 − 2.37348I 0
u = −0.838168 + 0.814555I
−1.68823 + 3.12709I 0
u = −0.838168 − 0.814555I
−1.68823 − 3.12709I 0
u = −0.791932 + 0.194909I
1.33858 − 0.61168I 4.64664 + 0.66052I
u = −0.791932 − 0.194909I
1.33858 + 0.61168I 4.64664 − 0.66052I
u = 0.898302 + 0.814123I
−4.44129 + 3.04587I 0
u = 0.898302 − 0.814123I
−4.44129 − 3.04587I 0
u = 0.931885 + 0.786659I
−0.98086 + 3.59426I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.931885 − 0.786659I
−0.98086 − 3.59426I 0
u = −0.842926 + 0.883227I
−7.08254 + 3.13913I 0
u = −0.842926 − 0.883227I
−7.08254 − 3.13913I 0
u = −0.883855 + 0.842412I
−7.07816 − 0.45998I 0
u = −0.883855 − 0.842412I
−7.07816 + 0.45998I 0
u = 0.841752 + 0.887983I
−8.44517 − 8.69967I 0
u = 0.841752 − 0.887983I
−8.44517 + 8.69967I 0
u = −0.859891 + 0.876442I
−7.92925 + 0.36652I 0
u = −0.859891 − 0.876442I
−7.92925 − 0.36652I 0
u = −0.941693 + 0.791316I
−1.37335 − 9.14747I 0
u = −0.941693 − 0.791316I
−1.37335 + 9.14747I 0
u = 0.853282 + 0.887433I
−13.09820 − 2.09748I 0
u = 0.853282 − 0.887433I
−13.09820 + 2.09748I 0
u = 0.866419 + 0.882936I
−9.56950 + 4.65253I 0
u = 0.866419 − 0.882936I
−9.56950 − 4.65253I 0
u = −0.923308 + 0.829910I
−6.95620 − 5.76655I 0
u = −0.923308 − 0.829910I
−6.95620 + 5.76655I 0
u = −0.414794 + 0.619267I
−2.66917 − 5.34133I −7.85683 + 5.45983I
u = −0.414794 − 0.619267I
−2.66917 + 5.34133I −7.85683 − 5.45983I
u = −0.958060 + 0.835699I
−7.61845 − 6.71466I 0
u = −0.958060 − 0.835699I
−7.61845 + 6.71466I 0
u = 0.957851 + 0.843793I
−9.27928 + 1.74172I 0
u = 0.957851 − 0.843793I
−9.27928 − 1.74172I 0
u = −0.971706 + 0.830064I
−6.67568 − 9.48827I 0
u = −0.971706 − 0.830064I
−6.67568 + 9.48827I 0
u = −0.349192 + 0.628699I
−6.51842 + 1.01634I −11.98104 − 0.35855I
u = −0.349192 − 0.628699I
−6.51842 − 1.01634I −11.98104 + 0.35855I
u = 0.968360 + 0.838404I
−12.7333 + 8.4874I 0
u = 0.968360 − 0.838404I
−12.7333 − 8.4874I 0
u = 0.975008 + 0.831934I
−8.0235 + 15.0692I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.975008 − 0.831934I
−8.0235 − 15.0692I 0
u = 0.404670 + 0.575073I
−1.350410 + 0.201542I −5.94284 − 0.35775I
u = 0.404670 − 0.575073I
−1.350410 − 0.201542I −5.94284 + 0.35775I
u = −0.294052 + 0.637960I
−2.17798 + 7.35569I −7.13193 − 5.37841I
u = −0.294052 − 0.637960I
−2.17798 − 7.35569I −7.13193 + 5.37841I
u = 0.291469 + 0.612077I
−0.90037 − 1.95033I −5.15826 + 0.68407I
u = 0.291469 − 0.612077I
−0.90037 + 1.95033I −5.15826 − 0.68407I
u = 0.377205 + 0.366640I
−1.057850 − 0.229849I −9.46177 + 0.74997I
u = 0.377205 − 0.366640I
−1.057850 + 0.229849I −9.46177 − 0.74997I
u = 0.030464 + 0.507917I
2.51540 − 2.64232I −2.22204 + 3.38040I
u = 0.030464 − 0.507917I
2.51540 + 2.64232I −2.22204 − 3.38040I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
71
+ 25u
70
+ ··· + 4u + 1
c
2
, c
6
u
71
− u
70
+ ··· − 2u + 1
c
3
, c
5
u
71
+ u
70
+ ··· − 406u + 97
c
4
, c
10
u
71
+ u
70
+ ··· + 2u + 1
c
8
, c
9
, c
11
u
71
− 17u
70
+ ··· + 4u − 1
c
12
u
71
− 7u
70
+ ··· + 13008u − 6545
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
71
+ 43y
70
+ ··· − 20y −1
c
2
, c
6
y
71
− 25y
70
+ ··· + 4y −1
c
3
, c
5
y
71
− 53y
70
+ ··· + 348748y −9409
c
4
, c
10
y
71
− 17y
70
+ ··· + 4y −1
c
8
, c
9
, c
11
y
71
+ 75y
70
+ ··· − 20y −1
c
12
y
71
− 25y
70
+ ··· + 292384964y −42837025
9
