12a
0606
(K12a
0606
)
A knot diagram
1
Linearized knot diagam
3 7 9 12 10 2 6 11 1 8 5 4
Solving Sequence
5,11
12 4
1,9
3 8 10 6 7 2
c
11
c
4
c
12
c
3
c
8
c
10
c
5
c
7
c
2
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.74463 × 10
127
u
83
+ 1.59218 × 10
128
u
82
+ ··· + 3.44840 × 10
128
b − 2.29894 × 10
128
,
− 3.01103 × 10
128
u
83
+ 9.56492 × 10
128
u
82
+ ··· + 3.44840 × 10
128
a + 2.95385 × 10
128
,
u
84
− 3u
83
+ ··· − 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 84 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−6.74 × 10
127
u
83
+ 1.59 × 10
128
u
82
+ · · · + 3.45 × 10
128
b − 2.30 ×
10
128
, −3.01 × 10
128
u
83
+ 9.56 × 10
128
u
82
+ · · · + 3.45 × 10
128
a + 2.95 ×
10
128
, u
84
− 3u
83
+ · · · − 2u + 1i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
4
=
−u
u
3
+ u
a
1
=
u
2
+ 1
−u
4
− 2u
2
a
9
=
0.873168u
83
− 2.77373u
82
+ ··· − 12.8263u − 0.856587
0.195587u
83
− 0.461715u
82
+ ··· + 0.0665166u + 0.666670
a
3
=
−3.59196u
83
+ 30.5345u
82
+ ··· − 21.0237u + 15.6011
1.26933u
83
− 3.73690u
82
+ ··· + 3.06667u − 1.23274
a
8
=
0.677581u
83
− 2.31201u
82
+ ··· − 12.8928u − 1.52326
0.195587u
83
− 0.461715u
82
+ ··· + 0.0665166u + 0.666670
a
10
=
0.681360u
83
− 2.29472u
82
+ ··· − 12.9913u − 0.464526
0.284715u
83
− 0.696196u
82
+ ··· + 0.0869901u + 0.486513
a
6
=
4.98831u
83
− 35.4998u
82
+ ··· + 29.5605u − 5.16163
−0.534425u
83
+ 1.36777u
82
+ ··· + 1.91603u − 0.186017
a
7
=
−20.3353u
83
+ 57.5455u
82
+ ··· − 13.6819u − 4.17574
0.951845u
83
− 1.18145u
82
+ ··· − 1.05176u − 0.348775
a
2
=
−19.4294u
83
+ 55.1803u
82
+ ··· − 13.4541u + 2.38119
0.336489u
83
+ 0.297026u
82
+ ··· − 1.10082u + 0.813010
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3.96005u
83
+ 5.91536u
82
+ ··· + 26.5735u − 14.4137
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
84
+ 23u
83
+ ··· + 6u + 1
c
2
, c
6
u
84
− u
83
+ ··· − 3u
2
+ 1
c
3
u
84
− 65u
83
+ ··· + 2u + 1
c
4
, c
11
, c
12
u
84
+ 3u
83
+ ··· + 2u + 1
c
5
u
84
+ 63u
83
+ ··· + 57180u − 86897
c
8
, c
10
u
84
+ u
83
+ ··· − 34u + 1
c
9
u
84
+ 7u
83
+ ··· + 8u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
84
+ 77y
83
+ ··· − 6y + 1
c
2
, c
6
y
84
− 23y
83
+ ··· − 6y + 1
c
3
y
84
− 1667y
83
+ ··· + 622y + 1
c
4
, c
11
, c
12
y
84
+ 81y
83
+ ··· − 6y + 1
c
5
y
84
− 1711y
83
+ ··· − 279584806794y + 7551088609
c
8
, c
10
y
84
− 55y
83
+ ··· + 754y + 1
c
9
y
84
− 3y
83
+ ··· + 226y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.841085 + 0.491787I
a = 0.458081 + 0.952887I
b = −1.36898 + 0.43042I
8.55629 − 6.70046I 0
u = −0.841085 − 0.491787I
a = 0.458081 − 0.952887I
b = −1.36898 − 0.43042I
8.55629 + 6.70046I 0
u = 0.395039 + 0.889142I
a = 0.299173 − 0.145406I
b = −0.578416 + 0.157326I
−1.33288 − 2.11542I 0
u = 0.395039 − 0.889142I
a = 0.299173 + 0.145406I
b = −0.578416 − 0.157326I
−1.33288 + 2.11542I 0
u = 0.830958 + 0.488150I
a = 0.499768 − 0.996423I
b = −1.36888 − 0.48638I
7.7472 + 13.0248I 0
u = 0.830958 − 0.488150I
a = 0.499768 + 0.996423I
b = −1.36888 + 0.48638I
7.7472 − 13.0248I 0
u = 0.857305 + 0.428649I
a = 0.649452 − 0.755906I
b = −1.126900 − 0.419335I
0.10242 + 7.46364I 0
u = 0.857305 − 0.428649I
a = 0.649452 + 0.755906I
b = −1.126900 + 0.419335I
0.10242 − 7.46364I 0
u = 0.808233 + 0.660887I
a = −0.087128 − 0.445454I
b = −1.260470 + 0.320226I
7.27039 − 7.59198I 0
u = 0.808233 − 0.660887I
a = −0.087128 + 0.445454I
b = −1.260470 − 0.320226I
7.27039 + 7.59198I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.951611 + 0.456794I
a = 0.460493 + 0.572983I
b = −1.131900 + 0.209269I
3.49418 − 3.27329I 0
u = −0.951611 − 0.456794I
a = 0.460493 − 0.572983I
b = −1.131900 − 0.209269I
3.49418 + 3.27329I 0
u = −0.836469 + 0.662101I
a = −0.033924 + 0.476709I
b = −1.262520 − 0.240610I
8.09488 + 1.17071I 0
u = −0.836469 − 0.662101I
a = −0.033924 − 0.476709I
b = −1.262520 + 0.240610I
8.09488 − 1.17071I 0
u = 0.925944
a = 0.813290
b = −0.772047
−1.56515 0
u = 0.007440 + 1.230010I
a = 1.56019 + 0.08942I
b = 1.83888 + 0.03682I
4.48868 + 3.01865I 0
u = 0.007440 − 1.230010I
a = 1.56019 − 0.08942I
b = 1.83888 − 0.03682I
4.48868 − 3.01865I 0
u = 0.511792 + 1.130900I
a = 0.244866 − 0.380174I
b = −0.757105 − 0.005600I
−1.34459 − 2.08242I 0
u = 0.511792 − 1.130900I
a = 0.244866 + 0.380174I
b = −0.757105 + 0.005600I
−1.34459 + 2.08242I 0
u = 0.036951 + 1.305380I
a = 0.565454 + 0.681799I
b = 1.43082 + 0.21052I
−1.38495 + 1.38895I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.036951 − 1.305380I
a = 0.565454 − 0.681799I
b = 1.43082 − 0.21052I
−1.38495 − 1.38895I 0
u = 0.488142 + 0.482785I
a = 0.031188 + 0.410920I
b = −0.148976 + 0.767569I
−2.79385 + 3.17067I −6.19468 − 7.29951I
u = 0.488142 − 0.482785I
a = 0.031188 − 0.410920I
b = −0.148976 − 0.767569I
−2.79385 − 3.17067I −6.19468 + 7.29951I
u = 0.142621 + 1.317630I
a = 1.00564 + 1.87617I
b = 1.38650 + 0.96883I
2.97262 + 1.36691I 0
u = 0.142621 − 1.317630I
a = 1.00564 − 1.87617I
b = 1.38650 − 0.96883I
2.97262 − 1.36691I 0
u = 0.544314 + 0.397133I
a = −0.143255 + 0.627268I
b = 0.132496 + 1.098020I
3.07508 + 7.54785I 1.67086 − 9.24892I
u = 0.544314 − 0.397133I
a = −0.143255 − 0.627268I
b = 0.132496 − 1.098020I
3.07508 − 7.54785I 1.67086 + 9.24892I
u = −0.149362 + 1.325160I
a = 0.94788 − 1.95347I
b = 1.32824 − 1.03783I
2.73190 − 7.38832I 0
u = −0.149362 − 1.325160I
a = 0.94788 + 1.95347I
b = 1.32824 + 1.03783I
2.73190 + 7.38832I 0
u = 0.083022 + 1.342940I
a = 0.56214 + 1.54984I
b = 1.170010 + 0.494704I
−2.00569 + 1.65992I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.083022 − 1.342940I
a = 0.56214 − 1.54984I
b = 1.170010 − 0.494704I
−2.00569 − 1.65992I 0
u = −0.530735 + 0.378249I
a = −0.112600 − 0.681713I
b = 0.237830 − 1.043500I
3.56923 − 1.66317I 2.96826 + 4.34619I
u = −0.530735 − 0.378249I
a = −0.112600 + 0.681713I
b = 0.237830 + 1.043500I
3.56923 + 1.66317I 2.96826 − 4.34619I
u = −0.124292 + 1.367670I
a = 0.62258 − 1.80283I
b = 0.932347 − 0.818895I
−3.57253 − 4.34184I 0
u = −0.124292 − 1.367670I
a = 0.62258 + 1.80283I
b = 0.932347 + 0.818895I
−3.57253 + 4.34184I 0
u = −0.058832 + 1.393540I
a = 0.66333 − 2.39711I
b = 0.870044 − 0.206745I
−4.73549 − 0.52192I 0
u = −0.058832 − 1.393540I
a = 0.66333 + 2.39711I
b = 0.870044 + 0.206745I
−4.73549 + 0.52192I 0
u = −0.007361 + 1.411650I
a = −5.3069 − 21.3383I
b = 0.997042 − 0.002480I
−0.27149 + 2.82297I 0
u = −0.007361 − 1.411650I
a = −5.3069 + 21.3383I
b = 0.997042 + 0.002480I
−0.27149 − 2.82297I 0
u = −0.02514 + 1.42770I
a = 0.943312 − 0.184770I
b = 0.0166012 − 0.0228494I
−1.89129 − 2.85052I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.02514 − 1.42770I
a = 0.943312 + 0.184770I
b = 0.0166012 + 0.0228494I
−1.89129 + 2.85052I 0
u = 0.450025 + 0.338178I
a = 1.89922 + 0.06419I
b = 0.156737 − 0.547212I
3.05606 − 4.29554I 1.23916 + 0.97121I
u = 0.450025 − 0.338178I
a = 1.89922 − 0.06419I
b = 0.156737 + 0.547212I
3.05606 + 4.29554I 1.23916 − 0.97121I
u = −0.532578 + 0.127338I
a = −0.482244 − 0.702775I
b = 1.45794 − 0.58858I
7.22969 − 4.94035I 8.76064 + 6.43722I
u = −0.532578 − 0.127338I
a = −0.482244 + 0.702775I
b = 1.45794 + 0.58858I
7.22969 + 4.94035I 8.76064 − 6.43722I
u = 0.530525 + 0.109986I
a = −0.527197 + 0.634287I
b = 1.50206 + 0.51079I
7.37206 − 1.04586I 9.31067 − 0.66517I
u = 0.530525 − 0.109986I
a = −0.527197 − 0.634287I
b = 1.50206 − 0.51079I
7.37206 + 1.04586I 9.31067 + 0.66517I
u = −0.18758 + 1.44911I
a = −0.32881 − 1.77671I
b = −0.020646 − 1.346400I
−2.33863 − 4.29175I 0
u = −0.18758 − 1.44911I
a = −0.32881 + 1.77671I
b = −0.020646 + 1.346400I
−2.33863 + 4.29175I 0
u = 0.537541
a = 1.24481
b = −0.258009
−1.72341 −5.57880
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.407510 + 0.345674I
a = 1.99195 − 0.30079I
b = 0.300889 + 0.482319I
3.44624 − 1.42162I 2.41052 + 4.86035I
u = −0.407510 − 0.345674I
a = 1.99195 + 0.30079I
b = 0.300889 − 0.482319I
3.44624 + 1.42162I 2.41052 − 4.86035I
u = 0.19354 + 1.45472I
a = −0.43885 + 1.77233I
b = −0.106526 + 1.390560I
−2.91247 + 10.25220I 0
u = 0.19354 − 1.45472I
a = −0.43885 − 1.77233I
b = −0.106526 − 1.390560I
−2.91247 − 10.25220I 0
u = −0.349251 + 0.398009I
a = 0.463559 − 0.576542I
b = 0.121636 − 0.363687I
0.097200 − 1.073830I 1.41884 + 6.13630I
u = −0.349251 − 0.398009I
a = 0.463559 + 0.576542I
b = 0.121636 + 0.363687I
0.097200 + 1.073830I 1.41884 − 6.13630I
u = −0.14497 + 1.47396I
a = −0.115149 − 1.228520I
b = −0.119724 − 0.853117I
−6.10460 − 2.97941I 0
u = −0.14497 − 1.47396I
a = −0.115149 + 1.228520I
b = −0.119724 + 0.853117I
−6.10460 + 2.97941I 0
u = 0.17702 + 1.48022I
a = −0.45899 + 1.37729I
b = −0.290897 + 1.109090I
−9.16614 + 5.65167I 0
u = 0.17702 − 1.48022I
a = −0.45899 − 1.37729I
b = −0.290897 − 1.109090I
−9.16614 − 5.65167I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.33509 + 1.46619I
a = 0.026808 − 1.216630I
b = −1.038500 − 0.483600I
−6.87683 + 4.53261I 0
u = 0.33509 − 1.46619I
a = 0.026808 + 1.216630I
b = −1.038500 + 0.483600I
−6.87683 − 4.53261I 0
u = −0.447686 + 0.188181I
a = −0.464571 − 1.212230I
b = 1.015710 − 0.483092I
1.32341 − 2.30363I 3.96226 + 8.75508I
u = −0.447686 − 0.188181I
a = −0.464571 + 1.212230I
b = 1.015710 + 0.483092I
1.32341 + 2.30363I 3.96226 − 8.75508I
u = 0.14699 + 1.51880I
a = −0.378486 + 0.859627I
b = −0.451586 + 0.719967I
−8.70614 − 0.03593I 0
u = 0.14699 − 1.51880I
a = −0.378486 − 0.859627I
b = −0.451586 − 0.719967I
−8.70614 + 0.03593I 0
u = 0.30952 + 1.50098I
a = −0.21841 − 1.53013I
b = −1.236060 − 0.607000I
−6.13770 + 11.67340I 0
u = 0.30952 − 1.50098I
a = −0.21841 + 1.53013I
b = −1.236060 + 0.607000I
−6.13770 − 11.67340I 0
u = −0.32984 + 1.50339I
a = −0.261761 + 1.310870I
b = −1.214960 + 0.477499I
−2.77472 − 7.81025I 0
u = −0.32984 − 1.50339I
a = −0.261761 − 1.310870I
b = −1.214960 − 0.477499I
−2.77472 + 7.81025I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.30146 + 1.51855I
a = −0.46246 − 1.67394I
b = −1.40190 − 0.63658I
1.2539 + 17.1533I 0
u = 0.30146 − 1.51855I
a = −0.46246 + 1.67394I
b = −1.40190 + 0.63658I
1.2539 − 17.1533I 0
u = −0.30534 + 1.51982I
a = −0.48315 + 1.60769I
b = −1.39950 + 0.59507I
2.05270 − 10.87810I 0
u = −0.30534 − 1.51982I
a = −0.48315 − 1.60769I
b = −1.39950 − 0.59507I
2.05270 + 10.87810I 0
u = −0.021197 + 0.442171I
a = 5.00384 − 0.18590I
b = 1.224420 + 0.035696I
5.40831 + 2.92977I −7.93391 − 1.35741I
u = −0.021197 − 0.442171I
a = 5.00384 + 0.18590I
b = 1.224420 − 0.035696I
5.40831 − 2.92977I −7.93391 + 1.35741I
u = 0.402662 + 0.040328I
a = −1.74577 + 0.54116I
b = 1.210520 + 0.088141I
2.31902 + 0.04888I 6.20623 + 2.48259I
u = 0.402662 − 0.040328I
a = −1.74577 − 0.54116I
b = 1.210520 − 0.088141I
2.31902 − 0.04888I 6.20623 − 2.48259I
u = −0.47819 + 1.52925I
a = −0.173130 + 0.644015I
b = −1.044910 + 0.145798I
0.51053 − 3.91054I 0
u = −0.47819 − 1.52925I
a = −0.173130 − 0.644015I
b = −1.044910 − 0.145798I
0.51053 + 3.91054I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.185686 + 0.290768I
a = 3.73194 − 3.36818I
b = 0.942958 + 0.095108I
0.484592 + 0.422993I 3.2353 + 15.0846I
u = −0.185686 − 0.290768I
a = 3.73194 + 3.36818I
b = 0.942958 − 0.095108I
0.484592 − 0.422993I 3.2353 − 15.0846I
u = 0.13032 + 1.77960I
a = −0.437102 − 0.021346I
b = −0.929304 + 0.091594I
−0.92312 − 3.47741I 0
u = 0.13032 − 1.77960I
a = −0.437102 + 0.021346I
b = −0.929304 − 0.091594I
−0.92312 + 3.47741I 0
13
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
84
+ 23u
83
+ ··· + 6u + 1
c
2
, c
6
u
84
− u
83
+ ··· − 3u
2
+ 1
c
3
u
84
− 65u
83
+ ··· + 2u + 1
c
4
, c
11
, c
12
u
84
+ 3u
83
+ ··· + 2u + 1
c
5
u
84
+ 63u
83
+ ··· + 57180u − 86897
c
8
, c
10
u
84
+ u
83
+ ··· − 34u + 1
c
9
u
84
+ 7u
83
+ ··· + 8u + 1
14
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
84
+ 77y
83
+ ··· − 6y + 1
c
2
, c
6
y
84
− 23y
83
+ ··· − 6y + 1
c
3
y
84
− 1667y
83
+ ··· + 622y + 1
c
4
, c
11
, c
12
y
84
+ 81y
83
+ ··· − 6y + 1
c
5
y
84
− 1711y
83
+ ··· − 279584806794y + 7551088609
c
8
, c
10
y
84
− 55y
83
+ ··· + 754y + 1
c
9
y
84
− 3y
83
+ ··· + 226y + 1
15
