12a
0773
(K12a
0773
)
A knot diagram
1
Linearized knot diagam
3 8 10 12 11 9 2 7 6 1 5 4
Solving Sequence
2,7
8 3 9 1 6 10 4 11 5 12
c
7
c
2
c
8
c
1
c
6
c
9
c
3
c
10
c
5
c
12
c
4
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
45
+ u
44
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 45 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
45
+ u
44
+ · · · + u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
−u
2
+ 1
u
2
a
1
=
u
3
u
5
− u
3
+ u
a
6
=
u
4
− u
2
+ 1
−u
4
a
10
=
−u
6
+ u
4
− 2u
2
+ 1
u
6
+ u
2
a
4
=
u
15
− 2u
13
+ 6u
11
− 8u
9
+ 10u
7
− 8u
5
+ 4u
3
− 2u
−u
15
+ u
13
− 4u
11
+ 3u
9
− 4u
7
+ 2u
5
− 2u
3
+ u
a
11
=
−u
14
+ u
12
− 4u
10
+ 3u
8
− 4u
6
+ 2u
4
− 2u
2
+ 1
−u
16
+ 2u
14
− 6u
12
+ 8u
10
− 10u
8
+ 8u
6
− 4u
4
+ 2u
2
a
5
=
u
34
− 3u
32
+ ··· + u
2
+ 1
u
36
− 4u
34
+ ··· − 18u
6
+ 3u
4
a
12
=
−u
35
+ 4u
33
+ ··· + 18u
5
− 3u
3
u
35
− 3u
33
+ ··· + u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
44
+ 20u
42
+ ··· − 4u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
c
9
u
45
+ 9u
44
+ ··· − u + 1
c
2
, c
7
u
45
+ u
44
+ ··· + u + 1
c
3
u
45
+ u
44
+ ··· + 21u + 1
c
4
, c
5
, c
11
c
12
u
45
+ u
44
+ ··· + 3u + 1
c
10
u
45
− 11u
44
+ ··· − 3u − 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
8
c
9
y
45
+ 55y
44
+ ··· + 7y −1
c
2
, c
7
y
45
− 9y
44
+ ··· − y −1
c
3
y
45
− y
44
+ ··· + 191y −1
c
4
, c
5
, c
11
c
12
y
45
+ 51y
44
+ ··· − y −1
c
10
y
45
+ 3y
44
+ ··· + 507y −9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.842523 + 0.539612I
1.63617 − 3.33410I −0.33334 + 4.44336I
u = 0.842523 − 0.539612I
1.63617 + 3.33410I −0.33334 − 4.44336I
u = −0.745790 + 0.649514I
−3.25288 + 2.39871I −2.89131 − 3.55564I
u = −0.745790 − 0.649514I
−3.25288 − 2.39871I −2.89131 + 3.55564I
u = −0.893450 + 0.533806I
0.35918 + 6.76103I −4.58151 − 10.24409I
u = −0.893450 − 0.533806I
0.35918 − 6.76103I −4.58151 + 10.24409I
u = 0.882706 + 0.368441I
−9.18323 − 0.52895I −10.64212 + 3.60551I
u = 0.882706 − 0.368441I
−9.18323 + 0.52895I −10.64212 − 3.60551I
u = 0.924753 + 0.528045I
−7.25615 − 8.99421I −7.47706 + 8.23216I
u = 0.924753 − 0.528045I
−7.25615 + 8.99421I −7.47706 − 8.23216I
u = −0.915632 + 0.085731I
−10.66890 + 4.29803I −13.41929 − 4.05209I
u = −0.915632 − 0.085731I
−10.66890 − 4.29803I −13.41929 + 4.05209I
u = −0.798279 + 0.412042I
−1.42195 + 1.48989I −9.20204 − 3.10031I
u = −0.798279 − 0.412042I
−1.42195 − 1.48989I −9.20204 + 3.10031I
u = 0.622618 + 0.607896I
2.34985 − 1.00131I 2.25214 + 3.75135I
u = 0.622618 − 0.607896I
2.34985 + 1.00131I 2.25214 − 3.75135I
u = 0.860336 + 0.082675I
−2.96104 − 2.56413I −12.15035 + 6.37098I
u = 0.860336 − 0.082675I
−2.96104 + 2.56413I −12.15035 − 6.37098I
u = 0.500299 + 0.676887I
−5.89698 + 4.51199I −3.83830 − 2.27659I
u = 0.500299 − 0.676887I
−5.89698 − 4.51199I −3.83830 + 2.27659I
u = −0.545239 + 0.640437I
1.47015 − 2.35216I −0.76426 + 3.93836I
u = −0.545239 − 0.640437I
1.47015 + 2.35216I −0.76426 − 3.93836I
u = −0.753905
−1.22216 −7.16390
u = −0.913783 + 0.849175I
−2.09514 + 3.15874I −6.19428 − 2.57138I
u = −0.913783 − 0.849175I
−2.09514 − 3.15874I −6.19428 + 2.57138I
u = 0.923803 + 0.877811I
6.39657 − 3.24843I −4.00000 + 2.33788I
u = 0.923803 − 0.877811I
6.39657 + 3.24843I −4.00000 − 2.33788I
u = −0.888807 + 0.915163I
2.17300 − 5.40200I −4.00000 + 2.07857I
u = −0.888807 − 0.915163I
2.17300 + 5.40200I −4.00000 − 2.07857I
u = 0.897839 + 0.910766I
9.68761 + 2.81350I 0. − 3.36569I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.897839 − 0.910766I
9.68761 − 2.81350I 0. + 3.36569I
u = −0.908434 + 0.905373I
10.78900 + 1.09718I 0. − 2.47582I
u = −0.908434 − 0.905373I
10.78900 − 1.09718I 0. + 2.47582I
u = 0.932398 + 0.899940I
5.98919 − 3.31737I −4.00000 + 2.40847I
u = 0.932398 − 0.899940I
5.98919 + 3.31737I −4.00000 − 2.40847I
u = −0.951494 + 0.884176I
10.64970 + 5.50488I 0
u = −0.951494 − 0.884176I
10.64970 − 5.50488I 0
u = 0.961169 + 0.879776I
9.48304 − 9.41748I 0. + 8.04677I
u = 0.961169 − 0.879776I
9.48304 + 9.41748I 0. − 8.04677I
u = −0.968830 + 0.875878I
1.91452 + 12.00600I 0. − 6.72542I
u = −0.968830 − 0.875878I
1.91452 − 12.00600I 0. + 6.72542I
u = 0.192606 + 0.558254I
−7.18221 − 2.67775I −4.03487 + 2.63740I
u = 0.192606 − 0.558254I
−7.18221 + 2.67775I −4.03487 − 2.63740I
u = −0.134361 + 0.422733I
−0.031442 + 1.214490I −0.60670 − 5.55927I
u = −0.134361 − 0.422733I
−0.031442 − 1.214490I −0.60670 + 5.55927I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
c
9
u
45
+ 9u
44
+ ··· − u + 1
c
2
, c
7
u
45
+ u
44
+ ··· + u + 1
c
3
u
45
+ u
44
+ ··· + 21u + 1
c
4
, c
5
, c
11
c
12
u
45
+ u
44
+ ··· + 3u + 1
c
10
u
45
− 11u
44
+ ··· − 3u − 3
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
8
c
9
y
45
+ 55y
44
+ ··· + 7y −1
c
2
, c
7
y
45
− 9y
44
+ ··· − y −1
c
3
y
45
− y
44
+ ··· + 191y −1
c
4
, c
5
, c
11
c
12
y
45
+ 51y
44
+ ··· − y −1
c
10
y
45
+ 3y
44
+ ··· + 507y −9
8
