12a
0437
(K12a
0437
)
A knot diagram
1
Linearized knot diagam
3 6 10 8 2 1 5 12 11 4 9 7
Solving Sequence
3,6
2 1 7 5 8 4 12 9 11 10
c
2
c
1
c
6
c
5
c
7
c
4
c
12
c
8
c
11
c
10
c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
74
− u
73
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 74 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
74
− u
73
+ · · · + u + 1i
(i) Arc colorings
a
3
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
7
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
5
=
u
−u
3
+ u
a
8
=
−u
9
+ 2u
7
− u
5
− 2u
3
+ u
u
11
− 3u
9
+ 4u
7
− u
5
− u
3
+ u
a
4
=
u
17
− 4u
15
+ 7u
13
− 4u
11
− 3u
9
+ 6u
7
− 2u
5
+ u
−u
19
+ 5u
17
− 12u
15
+ 15u
13
− 9u
11
− u
9
+ 4u
7
− 2u
5
− u
3
+ u
a
12
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
9
=
u
27
− 8u
25
+ ··· − 3u
3
+ 2u
u
27
− 7u
25
+ ··· − u
3
+ u
a
11
=
−u
46
+ 13u
44
+ ··· + 2u
2
+ 1
−u
46
+ 12u
44
+ ··· − 4u
4
+ u
2
a
10
=
−u
65
+ 18u
63
+ ··· + 2u
3
− 3u
−u
65
+ 17u
63
+ ··· + 8u
5
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
73
− 80u
71
+ ··· − 12u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
74
+ 39u
73
+ ··· + 3u + 1
c
2
, c
5
u
74
+ u
73
+ ··· − u + 1
c
3
, c
10
u
74
+ u
73
+ ··· + u + 1
c
4
, c
7
u
74
− 7u
73
+ ··· − 39u + 5
c
6
, c
12
u
74
+ 3u
73
+ ··· + 91u + 39
c
8
, c
9
, c
11
u
74
− 19u
73
+ ··· − 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
74
− 7y
73
+ ··· − 3y + 1
c
2
, c
5
y
74
− 39y
73
+ ··· − 3y + 1
c
3
, c
10
y
74
− 19y
73
+ ··· − 3y + 1
c
4
, c
7
y
74
+ 37y
73
+ ··· + 2209y + 25
c
6
, c
12
y
74
+ 53y
73
+ ··· + 25961y + 1521
c
8
, c
9
, c
11
y
74
+ 73y
73
+ ··· + 5y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.835681 + 0.560605I
−2.03574 + 3.50542I 2.00000 − 4.07643I
u = −0.835681 − 0.560605I
−2.03574 − 3.50542I 2.00000 + 4.07643I
u = 0.832665 + 0.571463I
−1.51570 − 9.58110I 2.00000 + 8.95690I
u = 0.832665 − 0.571463I
−1.51570 + 9.58110I 2.00000 − 8.95690I
u = 0.791742 + 0.569661I
5.17088 − 5.15812I 8.32835 + 7.79457I
u = 0.791742 − 0.569661I
5.17088 + 5.15812I 8.32835 − 7.79457I
u = 1.028500 + 0.160985I
−6.85388 + 0.05460I −5.85707 + 0.I
u = 1.028500 − 0.160985I
−6.85388 − 0.05460I −5.85707 + 0.I
u = −1.038800 + 0.183643I
−6.59018 + 6.05194I 0
u = −1.038800 − 0.183643I
−6.59018 − 6.05194I 0
u = −0.771164 + 0.538007I
2.30346 + 2.17439I 2.29501 − 3.84413I
u = −0.771164 − 0.538007I
2.30346 − 2.17439I 2.29501 + 3.84413I
u = 0.745955 + 0.571289I
5.30206 + 0.62127I 9.02433 − 0.60864I
u = 0.745955 − 0.571289I
5.30206 − 0.62127I 9.02433 + 0.60864I
u = −0.878223 + 0.286781I
−0.13660 + 3.04210I 1.28348 − 9.03887I
u = −0.878223 − 0.286781I
−0.13660 − 3.04210I 1.28348 + 9.03887I
u = 0.694463 + 0.581556I
−1.12248 + 5.01071I 3.66328 − 2.35709I
u = 0.694463 − 0.581556I
−1.12248 − 5.01071I 3.66328 + 2.35709I
u = −0.685413 + 0.567131I
−1.61031 + 0.99347I 2.79378 − 2.74942I
u = −0.685413 − 0.567131I
−1.61031 − 0.99347I 2.79378 + 2.74942I
u = 0.847866 + 0.088742I
−1.39303 − 0.27331I −6.60583 + 0.30491I
u = 0.847866 − 0.088742I
−1.39303 + 0.27331I −6.60583 − 0.30491I
u = 0.173274 + 0.798587I
−4.67079 + 10.47000I 0.63032 − 6.91545I
u = 0.173274 − 0.798587I
−4.67079 − 10.47000I 0.63032 + 6.91545I
u = −1.125660 + 0.366050I
−0.67532 + 2.89635I 0
u = −1.125660 − 0.366050I
−0.67532 − 2.89635I 0
u = −0.166312 + 0.795857I
−5.18741 − 4.27377I −0.40124 + 2.07461I
u = −0.166312 − 0.795857I
−5.18741 + 4.27377I −0.40124 − 2.07461I
u = 0.188589 + 0.769066I
2.46946 + 6.12626I 6.02496 − 6.71747I
u = 0.188589 − 0.769066I
2.46946 − 6.12626I 6.02496 + 6.71747I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.110190 + 0.478729I
−5.42714 + 6.46328I 0
u = −1.110190 − 0.478729I
−5.42714 − 6.46328I 0
u = −0.005571 + 0.786467I
−9.15015 − 3.13723I −3.27787 + 2.62981I
u = −0.005571 − 0.786467I
−9.15015 + 3.13723I −3.27787 − 2.62981I
u = −1.174870 + 0.351936I
−1.57203 − 2.51139I 0
u = −1.174870 − 0.351936I
−1.57203 + 2.51139I 0
u = 1.120020 + 0.499746I
−5.15715 − 0.75516I 0
u = 1.120020 − 0.499746I
−5.15715 + 0.75516I 0
u = 1.169010 + 0.376170I
−3.98603 − 0.84644I 0
u = 1.169010 − 0.376170I
−3.98603 + 0.84644I 0
u = −0.166580 + 0.745150I
−0.14116 − 2.82982I −0.06496 + 2.64345I
u = −0.166580 − 0.745150I
−0.14116 + 2.82982I −0.06496 − 2.64345I
u = 1.169510 + 0.425972I
−5.43464 − 2.14338I 0
u = 1.169510 − 0.425972I
−5.43464 + 2.14338I 0
u = 0.210100 + 0.723982I
3.11981 + 0.43939I 8.03831 + 0.99678I
u = 0.210100 − 0.723982I
3.11981 − 0.43939I 8.03831 − 0.99678I
u = −1.201560 + 0.355229I
−8.81870 − 6.66835I 0
u = −1.201560 − 0.355229I
−8.81870 + 6.66835I 0
u = 1.201080 + 0.360636I
−9.29736 + 0.44713I 0
u = 1.201080 − 0.360636I
−9.29736 − 0.44713I 0
u = −1.165630 + 0.467482I
−5.13613 + 6.19077I 0
u = −1.165630 − 0.467482I
−5.13613 − 6.19077I 0
u = 1.153100 + 0.513557I
0.38073 − 5.11443I 0
u = 1.153100 − 0.513557I
0.38073 + 5.11443I 0
u = −1.168850 + 0.508704I
−3.05084 + 7.51931I 0
u = −1.168850 − 0.508704I
−3.05084 − 7.51931I 0
u = 1.170470 + 0.520288I
−0.40431 − 10.92870I 0
u = 1.170470 − 0.520288I
−0.40431 + 10.92870I 0
u = 0.275029 + 0.663064I
−2.70930 − 3.72938I 2.81438 + 3.00373I
u = 0.275029 − 0.663064I
−2.70930 + 3.72938I 2.81438 − 3.00373I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.204050 + 0.448056I
−12.69820 − 1.26903I 0
u = 1.204050 − 0.448056I
−12.69820 + 1.26903I 0
u = −1.203510 + 0.453057I
−12.6628 + 7.5767I 0
u = −1.203510 − 0.453057I
−12.6628 − 7.5767I 0
u = −1.184440 + 0.519711I
−8.18403 + 9.13195I 0
u = −1.184440 − 0.519711I
−8.18403 − 9.13195I 0
u = −0.054792 + 0.704044I
−2.00051 − 1.86805I −1.34178 + 4.37957I
u = −0.054792 − 0.704044I
−2.00051 + 1.86805I −1.34178 − 4.37957I
u = 1.183790 + 0.522761I
−7.6480 − 15.3506I 0
u = 1.183790 − 0.522761I
−7.6480 + 15.3506I 0
u = −0.281349 + 0.627967I
−3.03701 − 2.14947I 2.22194 + 2.48741I
u = −0.281349 − 0.627967I
−3.03701 + 2.14947I 2.22194 − 2.48741I
u = −0.440598 + 0.299753I
1.125240 − 0.112962I 9.20316 + 0.37924I
u = −0.440598 − 0.299753I
1.125240 + 0.112962I 9.20316 − 0.37924I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
74
+ 39u
73
+ ··· + 3u + 1
c
2
, c
5
u
74
+ u
73
+ ··· − u + 1
c
3
, c
10
u
74
+ u
73
+ ··· + u + 1
c
4
, c
7
u
74
− 7u
73
+ ··· − 39u + 5
c
6
, c
12
u
74
+ 3u
73
+ ··· + 91u + 39
c
8
, c
9
, c
11
u
74
− 19u
73
+ ··· − 3u + 1
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
74
− 7y
73
+ ··· − 3y + 1
c
2
, c
5
y
74
− 39y
73
+ ··· − 3y + 1
c
3
, c
10
y
74
− 19y
73
+ ··· − 3y + 1
c
4
, c
7
y
74
+ 37y
73
+ ··· + 2209y + 25
c
6
, c
12
y
74
+ 53y
73
+ ··· + 25961y + 1521
c
8
, c
9
, c
11
y
74
+ 73y
73
+ ··· + 5y + 1
9
