12n
0097
(K12n
0097
)
A knot diagram
1
Linearized knot diagam
3 5 6 2 9 3 11 5 8 12 7 10
Solving Sequence
5,8
9 6
3,10
2 1 4 12 11 7
c
8
c
5
c
9
c
2
c
1
c
4
c
12
c
10
c
7
c
3
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.08330 × 10
15
u
28
+ 2.63231 × 10
15
u
27
+ ··· + 2.88806 × 10
15
b − 3.18100 × 10
15
,
− 1.08330 × 10
15
u
28
+ 2.63231 × 10
15
u
27
+ ··· + 2.88806 × 10
15
a − 3.18100 × 10
15
, u
29
− 2u
28
+ ··· + u − 1i
I
u
2
= h−u
8
− u
7
+ 2u
6
+ 3u
5
− u
4
− 3u
3
− 2u
2
+ b + u + 1, −u
8
− u
7
+ 2u
6
+ 3u
5
− u
4
− 3u
3
− 2u
2
+ a + 1,
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
* 2 irreducible components of dim
C
= 0, with total 38 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−1.08×10
15
u
28
+2.63×10
15
u
27
+· · ·+2.89×10
15
b−3.18×10
15
, −1.08×
10
15
u
28
+2.63×10
15
u
27
+· · ·+2.89×10
15
a−3.18×10
15
, u
29
−2u
28
+· · ·+u−1i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
6
=
u
−u
3
+ u
a
3
=
0.375096u
28
− 0.911447u
27
+ ··· − 0.238354u + 1.10143
0.375096u
28
− 0.911447u
27
+ ··· + 0.761646u + 1.10143
a
10
=
−u
2
+ 1
−u
2
a
2
=
0.375096u
28
− 0.911447u
27
+ ··· − 0.238354u + 1.10143
0.240332u
28
− 0.538132u
27
+ ··· + 0.225295u + 1.26269
a
1
=
0.360721u
28
− 0.778371u
27
+ ··· − 0.736984u + 0.338038
0.0965394u
28
− 0.0157569u
27
+ ··· − 0.674515u + 0.641092
a
4
=
0.259382u
28
− 0.660563u
27
+ ··· + 0.000197369u + 0.997644
0.264728u
28
− 0.644578u
27
+ ··· + 1.13537u + 0.978187
a
12
=
−0.0381007u
28
+ 0.244861u
27
+ ··· − 0.549804u + 0.530085
−0.153814u
28
+ 0.495745u
27
+ ··· − 0.311253u + 0.426298
a
11
=
0.00860430u
28
− 0.157377u
27
+ ··· + 0.318117u − 0.890976
−0.00366395u
28
− 0.0860215u
27
+ ··· + 0.240983u − 1.25230
a
7
=
−0.264182u
28
+ 0.762614u
27
+ ··· + 0.0624682u + 0.303054
−0.148468u
28
+ 0.511730u
27
+ ··· − 0.176083u + 0.406841
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
16119990594582668
2888060083449331
u
28
−
28126461598340071
2888060083449331
u
27
+ ···+
17982394285452960
2888060083449331
u +
11832001216098990
2888060083449331
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
29
+ 48u
28
+ ··· + 79u + 1
c
2
, c
4
u
29
− 10u
28
+ ··· + 19u − 1
c
3
, c
6
u
29
+ 5u
28
+ ··· + 1536u − 512
c
5
, c
8
u
29
− 2u
28
+ ··· + u − 1
c
7
, c
11
u
29
+ 2u
28
+ ··· − u − 1
c
9
u
29
+ 30u
27
+ ··· − u − 1
c
10
, c
12
u
29
+ 12u
28
+ ··· − u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
− 124y
28
+ ··· − 7313y −1
c
2
, c
4
y
29
− 48y
28
+ ··· + 79y −1
c
3
, c
6
y
29
+ 57y
28
+ ··· + 3932160y −262144
c
5
, c
8
y
29
+ 30y
27
+ ··· − y −1
c
7
, c
11
y
29
+ 12y
28
+ ··· − y −1
c
9
y
29
+ 60y
28
+ ··· − 5y −1
c
10
, c
12
y
29
+ 12y
28
+ ··· + 19y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.365827 + 0.867755I
a = −0.58586 − 1.71900I
b = −0.220028 − 0.851246I
−3.76536 + 5.51790I −3.77377 − 7.24287I
u = 0.365827 − 0.867755I
a = −0.58586 + 1.71900I
b = −0.220028 + 0.851246I
−3.76536 − 5.51790I −3.77377 + 7.24287I
u = 1.038780 + 0.399171I
a = −0.532542 − 0.137121I
b = 0.506240 + 0.262051I
3.61222 + 0.74335I 9.35759 + 0.47912I
u = 1.038780 − 0.399171I
a = −0.532542 + 0.137121I
b = 0.506240 − 0.262051I
3.61222 − 0.74335I 9.35759 − 0.47912I
u = 0.149316 + 0.856366I
a = −0.21482 − 2.05855I
b = −0.065503 − 1.202180I
−4.88663 − 0.95031I −6.59475 + 1.19001I
u = 0.149316 − 0.856366I
a = −0.21482 + 2.05855I
b = −0.065503 + 1.202180I
−4.88663 + 0.95031I −6.59475 − 1.19001I
u = −1.024520 + 0.534163I
a = 0.624645 − 0.175606I
b = −0.399874 + 0.358557I
2.77162 − 6.24281I 6.28797 + 4.80418I
u = −1.024520 − 0.534163I
a = 0.624645 + 0.175606I
b = −0.399874 − 0.358557I
2.77162 + 6.24281I 6.28797 − 4.80418I
u = −0.350587 + 0.709669I
a = 0.21366 − 1.51930I
b = −0.136928 − 0.809633I
−1.85641 − 1.40408I −0.21276 + 2.68754I
u = −0.350587 − 0.709669I
a = 0.21366 + 1.51930I
b = −0.136928 + 0.809633I
−1.85641 + 1.40408I −0.21276 − 2.68754I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.563294 + 0.524681I
a = 0.170413 − 0.678152I
b = −0.392881 − 0.153472I
−1.43698 − 1.52178I −1.26786 + 4.70761I
u = −0.563294 − 0.524681I
a = 0.170413 + 0.678152I
b = −0.392881 + 0.153472I
−1.43698 + 1.52178I −1.26786 − 4.70761I
u = 0.702050
a = −0.244600
b = 0.457450
0.941539 11.3890
u = −0.121762 + 0.604163I
a = −0.084430 + 0.174292I
b = −0.206192 + 0.778455I
0.47173 + 2.34023I 2.64159 − 2.77169I
u = −0.121762 − 0.604163I
a = −0.084430 − 0.174292I
b = −0.206192 − 0.778455I
0.47173 − 2.34023I 2.64159 + 2.77169I
u = −0.444471 + 0.402241I
a = −0.957420 − 0.680211I
b = −1.40189 − 0.27797I
−1.17268 − 1.39986I −2.59264 + 6.14012I
u = −0.444471 − 0.402241I
a = −0.957420 + 0.680211I
b = −1.40189 + 0.27797I
−1.17268 + 1.39986I −2.59264 − 6.14012I
u = 0.508912 + 0.193701I
a = 1.88309 − 0.38641I
b = 2.39201 − 0.19271I
−1.87493 − 2.49067I 4.89703 − 8.29090I
u = 0.508912 − 0.193701I
a = 1.88309 + 0.38641I
b = 2.39201 + 0.19271I
−1.87493 + 2.49067I 4.89703 + 8.29090I
u = 1.07631 + 1.11196I
a = −0.679049 + 1.085630I
b = 0.39726 + 2.19758I
−14.1601 + 12.3738I −0.83426 − 6.38685I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.07631 − 1.11196I
a = −0.679049 − 1.085630I
b = 0.39726 − 2.19758I
−14.1601 − 12.3738I −0.83426 + 6.38685I
u = −1.08388 + 1.11855I
a = 0.705879 + 1.020200I
b = −0.37800 + 2.13875I
−12.19450 − 6.48359I 1.17949 + 2.27770I
u = −1.08388 − 1.11855I
a = 0.705879 − 1.020200I
b = −0.37800 − 2.13875I
−12.19450 + 6.48359I 1.17949 − 2.27770I
u = 1.09561 + 1.10785I
a = −0.847927 + 1.022520I
b = 0.24768 + 2.13037I
−18.7416 + 4.0694I −3.78877 − 1.98533I
u = 1.09561 − 1.10785I
a = −0.847927 − 1.022520I
b = 0.24768 − 2.13037I
−18.7416 − 4.0694I −3.78877 + 1.98533I
u = 1.11251 + 1.10380I
a = −0.923170 + 0.842832I
b = 0.18934 + 1.94663I
−14.0670 − 4.2413I −1.00950 + 2.34740I
u = 1.11251 − 1.10380I
a = −0.923170 − 0.842832I
b = 0.18934 − 1.94663I
−14.0670 + 4.2413I −1.00950 − 2.34740I
u = −1.10978 + 1.11274I
a = 0.849824 + 0.873104I
b = −0.25996 + 1.98584I
−12.12700 − 1.69249I 1.01629 + 1.84111I
u = −1.10978 − 1.11274I
a = 0.849824 − 0.873104I
b = −0.25996 − 1.98584I
−12.12700 + 1.69249I 1.01629 − 1.84111I
7
II. I
u
2
= h−u
8
− u
7
+ · · · + b + 1, −u
8
− u
7
+ · · · + a + 1, u
9
+ u
8
− 2u
7
−
3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
6
=
u
−u
3
+ u
a
3
=
u
8
+ u
7
− 2u
6
− 3u
5
+ u
4
+ 3u
3
+ 2u
2
− 1
u
8
+ u
7
− 2u
6
− 3u
5
+ u
4
+ 3u
3
+ 2u
2
− u − 1
a
10
=
−u
2
+ 1
−u
2
a
2
=
u
8
+ u
7
− 2u
6
− 3u
5
+ u
4
+ 3u
3
+ 2u
2
− 1
u
8
+ u
7
− 2u
6
− 3u
5
+ u
4
+ 3u
3
+ 2u
2
− 2u − 1
a
1
=
0
−u
a
4
=
u
8
+ u
7
− 2u
6
− 3u
5
+ u
4
+ 3u
3
+ 2u
2
− 1
u
8
+ u
7
− 2u
6
− 3u
5
+ u
4
+ 3u
3
+ 2u
2
− u − 1
a
12
=
−u
5
+ 2u
3
− u
−u
5
+ u
3
− u
a
11
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
7
=
u
−u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
8
+ 2u
7
+ 2u
6
− 3u
5
− 6u
4
+ 3u
3
+ 3u
2
+ 4u − 2
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
6
u
9
c
4
(u + 1)
9
c
5
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
7
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
8
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
9
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
10
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
11
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
12
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
6
y
9
c
5
, c
8
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
7
, c
11
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
9
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
10
, c
12
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.772920 + 0.510351I
a = −0.900982 − 0.594909I
b = −0.128062 − 1.105260I
−3.42837 − 2.09337I −3.06656 + 3.71284I
u = −0.772920 − 0.510351I
a = −0.900982 + 0.594909I
b = −0.128062 + 1.105260I
−3.42837 + 2.09337I −3.06656 − 3.71284I
u = 0.825933
a = 1.21075
b = 0.384820
−0.446489 2.03810
u = 1.173910 + 0.391555I
a = 0.766570 − 0.255687I
b = −0.407341 − 0.647242I
2.72642 + 1.33617I 2.51011 − 2.54413I
u = 1.173910 − 0.391555I
a = 0.766570 + 0.255687I
b = −0.407341 + 0.647242I
2.72642 − 1.33617I 2.51011 + 2.54413I
u = −0.141484 + 0.739668I
a = −0.249476 − 1.304240I
b = −0.10799 − 2.04391I
−1.02799 + 2.45442I −4.16828 − 1.00072I
u = −0.141484 − 0.739668I
a = −0.249476 + 1.304240I
b = −0.10799 + 2.04391I
−1.02799 − 2.45442I −4.16828 + 1.00072I
u = −1.172470 + 0.500383I
a = −0.721488 − 0.307914I
b = 0.450985 − 0.808297I
1.95319 − 7.08493I 1.70570 + 8.17350I
u = −1.172470 − 0.500383I
a = −0.721488 + 0.307914I
b = 0.450985 + 0.808297I
1.95319 + 7.08493I 1.70570 − 8.17350I
11
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
29
+ 48u
28
+ ··· + 79u + 1)
c
2
((u − 1)
9
)(u
29
− 10u
28
+ ··· + 19u − 1)
c
3
, c
6
u
9
(u
29
+ 5u
28
+ ··· + 1536u − 512)
c
4
((u + 1)
9
)(u
29
− 10u
28
+ ··· + 19u − 1)
c
5
(u
9
− u
8
+ ··· − u + 1)(u
29
− 2u
28
+ ··· + u − 1)
c
7
(u
9
− u
8
+ ··· + u + 1)(u
29
+ 2u
28
+ ··· − u − 1)
c
8
(u
9
+ u
8
+ ··· − u − 1)(u
29
− 2u
28
+ ··· + u − 1)
c
9
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
29
+ 30u
27
+ ··· − u − 1)
c
10
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
29
+ 12u
28
+ ··· − u − 1)
c
11
(u
9
+ u
8
+ ··· + u − 1)(u
29
+ 2u
28
+ ··· − u − 1)
c
12
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
29
+ 12u
28
+ ··· − u − 1)
12
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
29
− 124y
28
+ ··· − 7313y −1)
c
2
, c
4
((y −1)
9
)(y
29
− 48y
28
+ ··· + 79y −1)
c
3
, c
6
y
9
(y
29
+ 57y
28
+ ··· + 3932160y −262144)
c
5
, c
8
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
29
+ 30y
27
+ ··· − y −1)
c
7
, c
11
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
29
+ 12y
28
+ ··· − y −1)
c
9
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
29
+ 60y
28
+ ··· − 5y −1)
c
10
, c
12
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
29
+ 12y
28
+ ··· + 19y −1)
13
