12a
0443
(K12a
0443
)
A knot diagram
1
Linearized knot diagam
3 6 10 9 2 11 12 5 4 1 8 7
Solving Sequence
3,10 4,6
2 1 11 7 9 5 8 12
c
3
c
2
c
1
c
10
c
6
c
9
c
4
c
8
c
12
c
5
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.75431 × 10
51
u
70
− 2.70378 × 10
52
u
69
+ ··· + 3.02784 × 10
53
b + 1.04182 × 10
54
,
4.41577 × 10
53
u
70
+ 4.23284 × 10
53
u
69
+ ··· + 1.21114 × 10
54
a + 4.82635 × 10
52
, u
71
+ u
70
+ ··· + 32u + 8i
I
u
2
= hb + 1, 4a
3
+ 2a
2
u + u, u
2
+ 2i
I
v
1
= ha, b − 1, v
3
− v
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 80 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
= h−1.75×10
51
u
70
−2.70×10
52
u
69
+· · ·+3.03×10
53
b+1.04×10
54
, 4.42×
10
53
u
70
+4.23×10
53
u
69
+· · ·+1.21×10
54
a+4.83×10
52
, u
71
+u
70
+· · ·+32u+8i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
6
=
−0.364597u
70
− 0.349494u
69
+ ··· − 15.4361u − 0.0398498
0.00579394u
70
+ 0.0892975u
69
+ ··· − 10.7596u − 3.44081
a
2
=
−0.414521u
70
− 0.174320u
69
+ ··· − 2.24303u + 3.28013
0.119562u
70
+ 0.236783u
69
+ ··· + 8.82285u + 1.39838
a
1
=
−0.294959u
70
+ 0.0624626u
69
+ ··· + 6.57981u + 4.67851
0.119562u
70
+ 0.236783u
69
+ ··· + 8.82285u + 1.39838
a
11
=
0.372985u
70
− 0.0387084u
69
+ ··· − 4.38781u − 6.83829
0.199475u
70
+ 0.182332u
69
+ ··· + 8.55984u + 1.28776
a
7
=
−0.652363u
70
− 0.632155u
69
+ ··· − 47.5864u − 10.0345
0.0304439u
70
+ 0.101032u
69
+ ··· − 1.25780u − 1.07234
a
9
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
a
8
=
u
3
+ 2u
u
5
+ 3u
3
+ u
a
12
=
0.317318u
70
− 0.117930u
69
+ ··· − 4.58186u − 5.94027
0.203177u
70
+ 0.232983u
69
+ ··· + 10.0627u + 2.01853
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.358486u
70
− 0.330850u
69
+ ··· + 2.39400u − 7.79623
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
71
+ 32u
70
+ ··· + 7410u + 289
c
2
, c
5
u
71
+ 4u
70
+ ··· + 44u + 17
c
3
, c
4
, c
8
c
9
u
71
+ u
70
+ ··· + 32u + 8
c
6
u
71
− 2u
70
+ ··· + 3285u + 1443
c
7
, c
11
, c
12
u
71
+ 2u
70
+ ··· + 9u + 3
c
10
u
71
− 14u
70
+ ··· − 72303u + 12843
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
71
+ 24y
70
+ ··· + 16243946y −83521
c
2
, c
5
y
71
− 32y
70
+ ··· + 7410y −289
c
3
, c
4
, c
8
c
9
y
71
+ 85y
70
+ ··· − 896y −64
c
6
y
71
+ 10y
70
+ ··· − 7912941y −2082249
c
7
, c
11
, c
12
y
71
+ 66y
70
+ ··· + 147y −9
c
10
y
71
+ 34y
70
+ ··· + 381725991y −164942649
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.473168 + 0.878431I
a = −0.53384 + 1.32798I
b = −0.924551 − 0.698241I
8.02517 − 2.03285I 0
u = 0.473168 − 0.878431I
a = −0.53384 − 1.32798I
b = −0.924551 + 0.698241I
8.02517 + 2.03285I 0
u = 0.470953 + 0.857931I
a = 0.504820 − 0.308904I
b = −0.500500 + 0.833022I
7.98279 − 5.90782I 0
u = 0.470953 − 0.857931I
a = 0.504820 + 0.308904I
b = −0.500500 − 0.833022I
7.98279 + 5.90782I 0
u = −0.602928 + 0.764237I
a = −0.84859 − 1.42584I
b = −1.095350 + 0.666686I
6.21274 + 11.51430I 0
u = −0.602928 − 0.764237I
a = −0.84859 + 1.42584I
b = −1.095350 − 0.666686I
6.21274 − 11.51430I 0
u = 0.559666 + 0.742606I
a = −0.80017 + 1.51996I
b = −1.066630 − 0.626889I
0.56353 − 7.97171I −12.0000 + 9.2145I
u = 0.559666 − 0.742606I
a = −0.80017 − 1.51996I
b = −1.066630 + 0.626889I
0.56353 + 7.97171I −12.0000 − 9.2145I
u = 0.213680 + 0.885890I
a = 0.436649 − 0.549995I
b = −0.596695 + 0.621320I
2.72760 + 0.81021I −5.96136 − 3.20416I
u = 0.213680 − 0.885890I
a = 0.436649 + 0.549995I
b = −0.596695 − 0.621320I
2.72760 − 0.81021I −5.96136 + 3.20416I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.388007 + 0.808336I
a = 0.544183 + 0.375008I
b = −0.479851 − 0.734662I
2.25979 + 2.76832I −7.62287 − 5.00106I
u = −0.388007 − 0.808336I
a = 0.544183 − 0.375008I
b = −0.479851 + 0.734662I
2.25979 − 2.76832I −7.62287 + 5.00106I
u = −0.474266 + 0.757591I
a = −0.59765 − 1.57830I
b = −0.986418 + 0.600186I
1.62234 + 4.02239I −8.44116 − 3.82646I
u = −0.474266 − 0.757591I
a = −0.59765 + 1.57830I
b = −0.986418 − 0.600186I
1.62234 − 4.02239I −8.44116 + 3.82646I
u = −0.293784 + 1.069940I
a = 0.297004 + 0.382780I
b = −0.727299 − 0.693450I
8.58855 − 3.32812I 0
u = −0.293784 − 1.069940I
a = 0.297004 − 0.382780I
b = −0.727299 + 0.693450I
8.58855 + 3.32812I 0
u = −0.745802 + 0.196648I
a = 0.811261 + 0.143661I
b = 0.967672 + 0.630863I
4.51022 − 7.00274I −8.77309 + 4.99855I
u = −0.745802 − 0.196648I
a = 0.811261 − 0.143661I
b = 0.967672 − 0.630863I
4.51022 + 7.00274I −8.77309 − 4.99855I
u = 0.711660 + 0.002490I
a = 0.789258 − 0.064470I
b = 0.695782 − 0.660435I
5.33787 − 1.96354I −7.40260 + 0.33467I
u = 0.711660 − 0.002490I
a = 0.789258 + 0.064470I
b = 0.695782 + 0.660435I
5.33787 + 1.96354I −7.40260 − 0.33467I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.077589 + 1.290690I
a = −0.406058 + 0.481952I
b = −0.440227 − 0.434912I
8.17679 − 3.42433I 0
u = 0.077589 − 1.290690I
a = −0.406058 − 0.481952I
b = −0.440227 + 0.434912I
8.17679 + 3.42433I 0
u = 0.678769 + 0.195846I
a = 0.837299 − 0.131686I
b = 0.945231 − 0.548058I
−1.06972 + 3.78958I −13.5795 − 5.3602I
u = 0.678769 − 0.195846I
a = 0.837299 + 0.131686I
b = 0.945231 + 0.548058I
−1.06972 − 3.78958I −13.5795 + 5.3602I
u = −0.394782 + 0.580703I
a = −0.53228 − 2.28894I
b = −0.993588 + 0.420619I
0.69826 + 4.73455I −10.28912 − 8.44837I
u = −0.394782 − 0.580703I
a = −0.53228 + 2.28894I
b = −0.993588 − 0.420619I
0.69826 − 4.73455I −10.28912 + 8.44837I
u = 0.039785 + 1.313640I
a = −0.124408 − 0.209895I
b = −0.740845 + 0.261890I
3.10359 + 1.08344I 0
u = 0.039785 − 1.313640I
a = −0.124408 + 0.209895I
b = −0.740845 − 0.261890I
3.10359 − 1.08344I 0
u = −0.197696 + 0.588434I
a = 1.150670 + 0.132461I
b = 1.222820 + 0.092714I
2.15066 + 3.68909I −6.75951 − 5.76158I
u = −0.197696 − 0.588434I
a = 1.150670 − 0.132461I
b = 1.222820 − 0.092714I
2.15066 − 3.68909I −6.75951 + 5.76158I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.480637 + 0.353712I
a = 0.949355 + 0.154234I
b = 1.087580 + 0.306374I
0.01328 − 1.64181I −13.08359 − 0.70230I
u = −0.480637 − 0.353712I
a = 0.949355 − 0.154234I
b = 1.087580 − 0.306374I
0.01328 + 1.64181I −13.08359 + 0.70230I
u = −0.589934 + 0.073410I
a = 0.848729 + 0.067863I
b = 0.756750 + 0.455862I
−0.371079 − 0.423170I −11.99532 − 1.09413I
u = −0.589934 − 0.073410I
a = 0.848729 − 0.067863I
b = 0.756750 − 0.455862I
−0.371079 + 0.423170I −11.99532 + 1.09413I
u = 0.275608 + 0.524761I
a = 0.20470 + 2.76427I
b = −0.916396 − 0.328077I
−2.51609 − 1.27707I −13.5327 + 5.3550I
u = 0.275608 − 0.524761I
a = 0.20470 − 2.76427I
b = −0.916396 + 0.328077I
−2.51609 + 1.27707I −13.5327 − 5.3550I
u = 0.447268 + 0.362108I
a = 0.816358 − 0.152133I
b = 0.020184 + 0.537693I
3.09578 − 1.52595I −6.90999 + 4.44326I
u = 0.447268 − 0.362108I
a = 0.816358 + 0.152133I
b = 0.020184 − 0.537693I
3.09578 + 1.52595I −6.90999 − 4.44326I
u = −0.12368 + 1.44056I
a = 0.0840639 + 0.1065960I
b = −1.114330 − 0.285742I
5.83734 + 0.43964I 0
u = −0.12368 − 1.44056I
a = 0.0840639 − 0.1065960I
b = −1.114330 + 0.285742I
5.83734 − 0.43964I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.255877 + 0.439131I
a = 1.058100 − 0.114052I
b = 1.143450 − 0.135051I
−2.79040 − 0.81044I −13.3265 + 8.2869I
u = 0.255877 − 0.439131I
a = 1.058100 + 0.114052I
b = 1.143450 + 0.135051I
−2.79040 + 0.81044I −13.3265 − 8.2869I
u = −0.182759 + 0.460133I
a = 1.40097 − 3.17425I
b = −0.866846 + 0.230070I
1.76227 − 2.18935I −6.07240 − 3.75678I
u = −0.182759 − 0.460133I
a = 1.40097 + 3.17425I
b = −0.866846 − 0.230070I
1.76227 + 2.18935I −6.07240 + 3.75678I
u = 0.03672 + 1.55370I
a = 0.1203480 − 0.0192448I
b = −1.325930 + 0.075525I
4.07818 − 1.65568I 0
u = 0.03672 − 1.55370I
a = 0.1203480 + 0.0192448I
b = −1.325930 − 0.075525I
4.07818 + 1.65568I 0
u = −0.02020 + 1.56511I
a = −0.92628 + 1.67895I
b = 0.742888 − 0.585187I
8.77642 − 1.63481I 0
u = −0.02020 − 1.56511I
a = −0.92628 − 1.67895I
b = 0.742888 + 0.585187I
8.77642 + 1.63481I 0
u = 0.05432 + 1.57233I
a = −0.71603 − 1.85678I
b = 0.856026 + 0.592276I
4.70486 − 2.34368I 0
u = 0.05432 − 1.57233I
a = −0.71603 + 1.85678I
b = 0.856026 − 0.592276I
4.70486 + 2.34368I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.08890 + 1.58049I
a = −0.46821 + 1.92084I
b = 0.956953 − 0.607831I
8.07800 + 6.38167I 0
u = −0.08890 − 1.58049I
a = −0.46821 − 1.92084I
b = 0.956953 + 0.607831I
8.07800 − 6.38167I 0
u = −0.04875 + 1.59629I
a = 0.141154 + 0.020655I
b = −1.41234 − 0.09672I
9.75959 + 4.55275I 0
u = −0.04875 − 1.59629I
a = 0.141154 − 0.020655I
b = −1.41234 + 0.09672I
9.75959 − 4.55275I 0
u = −0.13952 + 1.62693I
a = −0.17731 + 1.71608I
b = 1.093090 − 0.710505I
9.76099 + 6.35219I 0
u = −0.13952 − 1.62693I
a = −0.17731 − 1.71608I
b = 1.093090 + 0.710505I
9.76099 − 6.35219I 0
u = 0.16688 + 1.62451I
a = −0.06936 − 1.71160I
b = 1.153480 + 0.697425I
8.59519 − 10.71740I 0
u = 0.16688 − 1.62451I
a = −0.06936 + 1.71160I
b = 1.153480 − 0.697425I
8.59519 + 10.71740I 0
u = −0.10924 + 1.63954I
a = −0.659425 − 1.130220I
b = 0.474065 + 0.961082I
10.67430 + 4.66551I 0
u = −0.10924 − 1.63954I
a = −0.659425 + 1.130220I
b = 0.474065 − 0.961082I
10.67430 − 4.66551I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.18327 + 1.63330I
a = −0.01989 + 1.66522I
b = 1.190990 − 0.711791I
14.3314 + 14.5071I 0
u = −0.18327 − 1.63330I
a = −0.01989 − 1.66522I
b = 1.190990 + 0.711791I
14.3314 − 14.5071I 0
u = 0.07202 + 1.64319I
a = −0.659313 + 1.211360I
b = 0.567494 − 0.917086I
11.37510 − 0.37143I 0
u = 0.07202 − 1.64319I
a = −0.659313 − 1.211360I
b = 0.567494 + 0.917086I
11.37510 + 0.37143I 0
u = −0.341237
a = 0.915714
b = 0.265068
−0.572304 −17.1420
u = 0.13087 + 1.65640I
a = −0.622798 + 1.098490I
b = 0.450328 − 1.030270I
16.6202 − 8.2151I 0
u = 0.13087 − 1.65640I
a = −0.622798 − 1.098490I
b = 0.450328 + 1.030270I
16.6202 + 8.2151I 0
u = 0.12532 + 1.66383I
a = −0.22258 − 1.58081I
b = 1.075030 + 0.800211I
16.7894 − 4.3149I 0
u = 0.12532 − 1.66383I
a = −0.22258 + 1.58081I
b = 1.075030 − 0.800211I
16.7894 + 4.3149I 0
u = −0.05538 + 1.68155I
a = −0.568584 − 1.235360I
b = 0.655457 + 0.988237I
18.0829 − 2.1627I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.05538 − 1.68155I
a = −0.568584 + 1.235360I
b = 0.655457 − 0.988237I
18.0829 + 2.1627I 0
12
II. I
u
2
= hb + 1, 4a
3
+ 2a
2
u + u, u
2
+ 2i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−2
a
6
=
a
−1
a
2
=
a + 1
−1
a
1
=
a
−1
a
11
=
−a
2
u
au + u
a
7
=
−a
2
u + a −
1
2
u
−2a
2
− 2a − 1
a
9
=
u
−u
a
5
=
−1
0
a
8
=
0
−u
a
12
=
−a
2
u
2a
2
u + au + u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4au − 12
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)
6
c
2
(u + 1)
6
c
3
, c
4
, c
8
c
9
(u
2
+ 2)
3
c
6
(u
3
− u
2
+ 1)
2
c
7
(u
3
+ u
2
+ 2u + 1)
2
c
10
(u
3
+ u
2
− 1)
2
c
11
, c
12
(u
3
− u
2
+ 2u − 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
6
c
3
, c
4
, c
8
c
9
(y + 2)
6
c
6
, c
10
(y
3
− y
2
+ 2y −1)
2
c
7
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = 0.526697 − 0.620443I
b = −1.00000
6.31400 − 2.82812I −8.49024 + 2.97945I
u = 1.414210I
a = −0.526697 − 0.620443I
b = −1.00000
6.31400 + 2.82812I −8.49024 − 2.97945I
u = 1.414210I
a = 0.533779I
b = −1.00000
2.17641 −15.0200
u = − 1.414210I
a = 0.526697 + 0.620443I
b = −1.00000
6.31400 + 2.82812I −8.49024 − 2.97945I
u = − 1.414210I
a = −0.526697 + 0.620443I
b = −1.00000
6.31400 − 2.82812I −8.49024 + 2.97945I
u = − 1.414210I
a = − 0.533779I
b = −1.00000
2.17641 −15.0200
16
III. I
v
1
= ha, b − 1, v
3
− v
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
v
0
a
4
=
1
0
a
6
=
0
1
a
2
=
1
−1
a
1
=
0
−1
a
11
=
v
v
a
7
=
−v
2
−v
2
+ 1
a
9
=
v
0
a
5
=
1
0
a
8
=
v
0
a
12
=
−v
2
+ v + 1
v
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2v
2
+ 2v −14
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
4
, c
8
c
9
u
3
c
5
(u + 1)
3
c
6
, c
10
u
3
+ u
2
− 1
c
7
u
3
− u
2
+ 2u − 1
c
11
, c
12
u
3
+ u
2
+ 2u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
3
c
3
, c
4
, c
8
c
9
y
3
c
6
, c
10
y
3
− y
2
+ 2y −1
c
7
, c
11
, c
12
y
3
+ 3y
2
+ 2y −1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.877439 + 0.744862I
a = 0
b = 1.00000
1.37919 − 2.82812I −11.81496 + 4.10401I
v = 0.877439 − 0.744862I
a = 0
b = 1.00000
1.37919 + 2.82812I −11.81496 − 4.10401I
v = −0.754878
a = 0
b = 1.00000
−2.75839 −14.3700
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
71
+ 32u
70
+ ··· + 7410u + 289)
c
2
((u − 1)
3
)(u + 1)
6
(u
71
+ 4u
70
+ ··· + 44u + 17)
c
3
, c
4
, c
8
c
9
u
3
(u
2
+ 2)
3
(u
71
+ u
70
+ ··· + 32u + 8)
c
5
((u − 1)
6
)(u + 1)
3
(u
71
+ 4u
70
+ ··· + 44u + 17)
c
6
((u
3
− u
2
+ 1)
2
)(u
3
+ u
2
− 1)(u
71
− 2u
70
+ ··· + 3285u + 1443)
c
7
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
2
(u
71
+ 2u
70
+ ··· + 9u + 3)
c
10
((u
3
+ u
2
− 1)
3
)(u
71
− 14u
70
+ ··· − 72303u + 12843)
c
11
, c
12
((u
3
− u
2
+ 2u − 1)
2
)(u
3
+ u
2
+ 2u + 1)(u
71
+ 2u
70
+ ··· + 9u + 3)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
71
+ 24y
70
+ ··· + 1.62439 × 10
7
y −83521)
c
2
, c
5
((y −1)
9
)(y
71
− 32y
70
+ ··· + 7410y −289)
c
3
, c
4
, c
8
c
9
y
3
(y + 2)
6
(y
71
+ 85y
70
+ ··· − 896y −64)
c
6
((y
3
− y
2
+ 2y −1)
3
)(y
71
+ 10y
70
+ ··· − 7912941y −2082249)
c
7
, c
11
, c
12
((y
3
+ 3y
2
+ 2y −1)
3
)(y
71
+ 66y
70
+ ··· + 147y −9)
c
10
((y
3
− y
2
+ 2y −1)
3
)(y
71
+ 34y
70
+ ··· + 3.81726 × 10
8
y −1.64943 × 10
8
)
22
