12a
0251
(K12a
0251
)
A knot diagram
1
Linearized knot diagam
3 6 7 10 9 2 1 12 11 5 4 8
Solving Sequence
2,6
3 7 4 1 8 12 9 5 11 10
c
2
c
6
c
3
c
1
c
7
c
12
c
8
c
5
c
11
c
10
c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
79
− u
78
+ ··· + 4u
3
+ 1i
* 1 irreducible components of dim
C
= 0, with total 79 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
79
− u
78
+ · · · + 4u
3
+ 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
1
=
u
2
+ 1
−u
4
a
8
=
−u
7
− 2u
5
− 2u
3
u
9
+ u
7
+ u
5
+ u
a
12
=
u
12
+ 3u
10
+ 5u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
−u
14
− 2u
12
− 3u
10
− 2u
8
− 2u
6
− 2u
4
− u
2
a
9
=
−u
17
− 4u
15
− 9u
13
− 12u
11
− 11u
9
− 8u
7
− 6u
5
− 4u
3
− u
u
19
+ 3u
17
+ 6u
15
+ 7u
13
+ 7u
11
+ 7u
9
+ 6u
7
+ 4u
5
+ u
3
+ u
a
5
=
−u
35
− 8u
33
+ ··· − 8u
5
− u
3
u
37
+ 7u
35
+ ··· + u
3
+ u
a
11
=
u
22
+ 5u
20
+ ··· + 2u
2
+ 1
u
22
+ 4u
20
+ 9u
18
+ 12u
16
+ 10u
14
+ 6u
12
+ 3u
10
+ 2u
8
− u
6
− 2u
4
− u
2
a
10
=
−u
63
− 14u
61
+ ··· − 8u
3
− 2u
−u
63
− 13u
61
+ ··· + 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
78
+ 4u
77
+ ··· − 8u
2
− 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
79
+ 35u
78
+ ··· + 8u
2
− 1
c
2
, c
6
u
79
− u
78
+ ··· + 4u
3
+ 1
c
3
u
79
+ u
78
+ ··· + 9u + 2
c
4
, c
10
u
79
− u
78
+ ··· − 2u
4
+ 1
c
5
, c
11
u
79
− 3u
78
+ ··· − 445u + 88
c
7
, c
8
, c
12
u
79
− 5u
78
+ ··· − 24u + 1
c
9
u
79
+ 41u
78
+ ··· − 4u
2
+ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
79
+ 19y
78
+ ··· + 16y −1
c
2
, c
6
y
79
+ 35y
78
+ ··· + 8y
2
− 1
c
3
y
79
+ 3y
78
+ ··· − 139y −4
c
4
, c
10
y
79
− 41y
78
+ ··· + 4y
2
− 1
c
5
, c
11
y
79
+ 51y
78
+ ··· + 140825y −7744
c
7
, c
8
, c
12
y
79
+ 79y
78
+ ··· + 72y −1
c
9
y
79
− 5y
78
+ ··· + 8y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.518439 + 0.839977I
−2.47695 + 1.61220I 0
u = −0.518439 − 0.839977I
−2.47695 − 1.61220I 0
u = −0.250874 + 0.935800I
−2.18929 + 0.78848I −9.38930 − 3.30417I
u = −0.250874 − 0.935800I
−2.18929 − 0.78848I −9.38930 + 3.30417I
u = 0.472540 + 0.928709I
−0.19704 + 2.19503I 0
u = 0.472540 − 0.928709I
−0.19704 − 2.19503I 0
u = −0.777679 + 0.521809I
3.79637 − 7.20850I −1.29301 + 5.78914I
u = −0.777679 − 0.521809I
3.79637 + 7.20850I −1.29301 − 5.78914I
u = 0.790583 + 0.491775I
8.97318 + 0.79076I 3.03187 − 3.00040I
u = 0.790583 − 0.491775I
8.97318 − 0.79076I 3.03187 + 3.00040I
u = 0.776695 + 0.512527I
6.49253 + 2.31855I 1.93099 − 2.22263I
u = 0.776695 − 0.512527I
6.49253 − 2.31855I 1.93099 + 2.22263I
u = −0.794225 + 0.480848I
8.91071 + 3.99166I 2.81554 − 3.57592I
u = −0.794225 − 0.480848I
8.91071 − 3.99166I 2.81554 + 3.57592I
u = 0.799974 + 0.452152I
3.40222 − 10.36420I −1.86089 + 6.02560I
u = 0.799974 − 0.452152I
3.40222 + 10.36420I −1.86089 − 6.02560I
u = −0.795010 + 0.457768I
6.18261 + 5.44195I 1.37667 − 2.61754I
u = −0.795010 − 0.457768I
6.18261 − 5.44195I 1.37667 + 2.61754I
u = −0.539580 + 0.740555I
−2.19284 − 5.95136I −3.06972 + 7.35183I
u = −0.539580 − 0.740555I
−2.19284 + 5.95136I −3.06972 − 7.35183I
u = 0.078728 + 1.082670I
−3.31194 − 0.08407I 0
u = 0.078728 − 1.082670I
−3.31194 + 0.08407I 0
u = −0.758214 + 0.509308I
2.23994 + 0.99895I −3.29257 − 0.53289I
u = −0.758214 − 0.509308I
2.23994 − 0.99895I −3.29257 + 0.53289I
u = 0.782931 + 0.451118I
1.90919 − 1.95514I −3.75115 + 0.I
u = 0.782931 − 0.451118I
1.90919 + 1.95514I −3.75115 + 0.I
u = −0.057574 + 1.102150I
0.80009 + 3.56647I 0
u = −0.057574 − 1.102150I
0.80009 − 3.56647I 0
u = −0.011598 + 1.103820I
3.36202 + 2.32895I 0
u = −0.011598 − 1.103820I
3.36202 − 2.32895I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.330330 + 1.053940I
−4.29872 − 0.60827I 0
u = −0.330330 − 1.053940I
−4.29872 + 0.60827I 0
u = 0.315571 + 1.069460I
−7.52343 − 3.77517I 0
u = 0.315571 − 1.069460I
−7.52343 + 3.77517I 0
u = 0.066591 + 1.113330I
−1.99034 − 8.40432I 0
u = 0.066591 − 1.113330I
−1.99034 + 8.40432I 0
u = 0.518854 + 0.988102I
0.41468 + 2.88353I 0
u = 0.518854 − 0.988102I
0.41468 − 2.88353I 0
u = −0.430212 + 1.031220I
−3.49022 − 3.24568I 0
u = −0.430212 − 1.031220I
−3.49022 + 3.24568I 0
u = 0.345422 + 1.071560I
−7.79780 + 4.70521I 0
u = 0.345422 − 1.071560I
−7.79780 − 4.70521I 0
u = 0.472065 + 0.706972I
0.43948 + 1.74919I 0.70667 − 4.05874I
u = 0.472065 − 0.706972I
0.43948 − 1.74919I 0.70667 + 4.05874I
u = −0.530932 + 1.032320I
−0.41303 − 6.78330I 0
u = −0.530932 − 1.032320I
−0.41303 + 6.78330I 0
u = −0.498801 + 1.079610I
−3.17706 − 6.37439I 0
u = −0.498801 − 1.079610I
−3.17706 + 6.37439I 0
u = 0.484264 + 1.086440I
−6.87950 + 2.43282I 0
u = 0.484264 − 1.086440I
−6.87950 − 2.43282I 0
u = 0.503668 + 1.090740I
−6.28401 + 10.93530I 0
u = 0.503668 − 1.090740I
−6.28401 − 10.93530I 0
u = −0.615780 + 1.056650I
0.60926 − 6.20761I 0
u = −0.615780 − 1.056650I
0.60926 + 6.20761I 0
u = −0.631557 + 1.055390I
2.20395 + 1.89316I 0
u = −0.631557 − 1.055390I
2.20395 − 1.89316I 0
u = 0.627875 + 1.060360I
4.85794 + 2.98135I 0
u = 0.627875 − 1.060360I
4.85794 − 2.98135I 0
u = 0.628251 + 1.075530I
7.22967 + 4.54653I 0
u = 0.628251 − 1.075530I
7.22967 − 4.54653I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.626429 + 1.081980I
7.11532 − 9.33149I 0
u = −0.626429 − 1.081980I
7.11532 + 9.33149I 0
u = 0.612337 + 1.091520I
0.00350 + 7.21255I 0
u = 0.612337 − 1.091520I
0.00350 − 7.21255I 0
u = 0.516957 + 0.538342I
1.69269 + 1.37789I 2.70355 − 4.03268I
u = 0.516957 − 0.538342I
1.69269 − 1.37789I 2.70355 + 4.03268I
u = −0.619167 + 1.092530I
4.28876 − 10.75590I 0
u = −0.619167 − 1.092530I
4.28876 + 10.75590I 0
u = 0.619393 + 1.096430I
1.4791 + 15.6911I 0
u = 0.619393 − 1.096430I
1.4791 − 15.6911I 0
u = −0.560028 + 0.413582I
1.30119 + 2.38830I 0.66864 − 5.36145I
u = −0.560028 − 0.413582I
1.30119 − 2.38830I 0.66864 + 5.36145I
u = 0.624420 + 0.239874I
−3.92703 − 6.58068I −5.74395 + 6.54636I
u = 0.624420 − 0.239874I
−3.92703 + 6.58068I −5.74395 − 6.54636I
u = −0.582840 + 0.243162I
−0.90156 + 2.12687I −2.58208 − 3.56451I
u = −0.582840 − 0.243162I
−0.90156 − 2.12687I −2.58208 + 3.56451I
u = 0.590316 + 0.185482I
−4.44704 + 1.71932I −7.28622 − 0.52322I
u = 0.590316 − 0.185482I
−4.44704 − 1.71932I −7.28622 + 0.52322I
u = −0.396331
−1.15940 −8.74740
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
79
+ 35u
78
+ ··· + 8u
2
− 1
c
2
, c
6
u
79
− u
78
+ ··· + 4u
3
+ 1
c
3
u
79
+ u
78
+ ··· + 9u + 2
c
4
, c
10
u
79
− u
78
+ ··· − 2u
4
+ 1
c
5
, c
11
u
79
− 3u
78
+ ··· − 445u + 88
c
7
, c
8
, c
12
u
79
− 5u
78
+ ··· − 24u + 1
c
9
u
79
+ 41u
78
+ ··· − 4u
2
+ 1
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
79
+ 19y
78
+ ··· + 16y −1
c
2
, c
6
y
79
+ 35y
78
+ ··· + 8y
2
− 1
c
3
y
79
+ 3y
78
+ ··· − 139y −4
c
4
, c
10
y
79
− 41y
78
+ ··· + 4y
2
− 1
c
5
, c
11
y
79
+ 51y
78
+ ··· + 140825y −7744
c
7
, c
8
, c
12
y
79
+ 79y
78
+ ··· + 72y −1
c
9
y
79
− 5y
78
+ ··· + 8y −1
9
