12a
1163
(K12a
1163
)
A knot diagram
1
Linearized knot diagam
4 9 8 11 12 1 10 3 2 7 6 5
Solving Sequence
6,11
12 5 1 7 4 2 10 8 3 9
c
11
c
5
c
12
c
6
c
4
c
1
c
10
c
7
c
3
c
9
c
2
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
51
− u
50
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 51 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
51
− u
50
+ · · · + 2u − 1i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
5
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
7
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
4
=
u
3
+ 2u
u
3
+ u
a
2
=
−u
10
− 5u
8
− 8u
6
− 3u
4
+ 3u
2
+ 1
−u
10
− 4u
8
− 5u
6
+ 3u
2
a
10
=
−u
12
− 5u
10
− 9u
8
− 6u
6
+ u
2
+ 1
−u
14
− 6u
12
− 13u
10
− 10u
8
+ 2u
6
+ 4u
4
− u
2
a
8
=
−u
19
− 8u
17
− 26u
15
− 42u
13
− 31u
11
− 2u
9
+ 10u
7
+ 4u
5
− u
3
− 2u
−u
21
− 9u
19
+ ··· − u
3
+ u
a
3
=
u
43
+ 18u
41
+ ··· − 7u
3
+ 2u
u
45
+ 19u
43
+ ··· + 5u
3
+ u
a
9
=
u
34
+ 15u
32
+ ··· + 5u
2
+ 1
u
34
+ 14u
32
+ ··· + 16u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
50
+ 4u
49
+ ··· + 20u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
10
u
51
− 7u
50
+ ··· + 112u − 17
c
2
, c
3
, c
8
c
9
u
51
+ u
50
+ ··· + 3u
2
+ 1
c
4
, c
6
u
51
− u
50
+ ··· + 3u
2
+ 1
c
5
, c
11
, c
12
u
51
+ u
50
+ ··· + 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
10
y
51
+ 47y
50
+ ··· + 202y −289
c
2
, c
3
, c
8
c
9
y
51
+ 55y
50
+ ··· − 6y −1
c
4
, c
6
y
51
− 25y
50
+ ··· − 6y −1
c
5
, c
11
, c
12
y
51
+ 43y
50
+ ··· − 6y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.249709 + 0.948226I
4.63631 − 2.12088I −1.01844 + 2.80811I
u = −0.249709 − 0.948226I
4.63631 + 2.12088I −1.01844 − 2.80811I
u = 0.295729 + 0.994644I
−2.13539 + 4.89833I −5.01649 − 2.19451I
u = 0.295729 − 0.994644I
−2.13539 − 4.89833I −5.01649 + 2.19451I
u = 0.230603 + 0.853532I
4.74743 − 1.96048I −0.34668 + 4.23406I
u = 0.230603 − 0.853532I
4.74743 + 1.96048I −0.34668 − 4.23406I
u = −0.273056 + 0.774265I
−1.78828 + 4.72311I −4.06394 − 4.26663I
u = −0.273056 − 0.774265I
−1.78828 − 4.72311I −4.06394 + 4.26663I
u = 0.777766 + 0.178377I
−4.65007 − 8.93459I −8.10474 + 6.18574I
u = 0.777766 − 0.178377I
−4.65007 + 8.93459I −8.10474 − 6.18574I
u = −0.761639 + 0.184556I
2.23741 + 6.02041I −4.49356 − 6.91985I
u = −0.761639 − 0.184556I
2.23741 − 6.02041I −4.49356 + 6.91985I
u = 0.775098 + 0.060463I
−11.25330 − 3.44491I −12.79521 + 3.55577I
u = 0.775098 − 0.060463I
−11.25330 + 3.44491I −12.79521 − 3.55577I
u = 0.742257 + 0.192170I
2.53020 − 1.80186I −3.57173 + 0.69342I
u = 0.742257 − 0.192170I
2.53020 + 1.80186I −3.57173 − 0.69342I
u = 0.318281 + 1.201370I
−7.76752 − 0.51963I 0
u = 0.318281 − 1.201370I
−7.76752 + 0.51963I 0
u = −0.275754 + 1.221110I
−0.186542 + 1.326290I 0
u = −0.275754 − 1.221110I
−0.186542 − 1.326290I 0
u = −0.716310 + 0.207468I
−3.73927 − 1.03700I −7.10850 − 0.87605I
u = −0.716310 − 0.207468I
−3.73927 + 1.03700I −7.10850 + 0.87605I
u = 0.063850 + 1.258910I
4.32614 − 1.52805I 0
u = 0.063850 − 1.258910I
4.32614 + 1.52805I 0
u = −0.731823 + 0.057552I
−3.72646 + 2.32596I −11.41052 − 5.70564I
u = −0.731823 − 0.057552I
−3.72646 − 2.32596I −11.41052 + 5.70564I
u = 0.267337 + 1.286100I
2.27908 − 3.39012I 0
u = 0.267337 − 1.286100I
2.27908 + 3.39012I 0
u = −0.145806 + 1.317740I
−1.58295 + 3.13834I 0
u = −0.145806 − 1.317740I
−1.58295 − 3.13834I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.671685
−1.74026 −4.25130
u = −0.306268 + 1.301300I
0.52039 + 6.08284I 0
u = −0.306268 − 1.301300I
0.52039 − 6.08284I 0
u = 0.332711 + 1.301130I
−7.00145 − 7.44226I 0
u = 0.332711 − 1.301130I
−7.00145 + 7.44226I 0
u = −0.297050 + 1.372640I
1.25075 + 2.64872I 0
u = −0.297050 − 1.372640I
1.25075 − 2.64872I 0
u = 0.309777 + 1.371410I
7.47174 − 5.62076I 0
u = 0.309777 − 1.371410I
7.47174 + 5.62076I 0
u = −0.319107 + 1.370980I
7.15390 + 9.93639I 0
u = −0.319107 − 1.370980I
7.15390 − 9.93639I 0
u = 0.327378 + 1.370270I
0.24340 − 12.93330I 0
u = 0.327378 − 1.370270I
0.24340 + 12.93330I 0
u = 0.00618 + 1.42442I
11.54180 − 2.18033I 0
u = 0.00618 − 1.42442I
11.54180 + 2.18033I 0
u = −0.01946 + 1.42477I
4.94539 + 5.22241I 0
u = −0.01946 − 1.42477I
4.94539 − 5.22241I 0
u = −0.374516 + 0.344098I
−6.57378 + 1.34480I −7.53020 − 4.73780I
u = −0.374516 − 0.344098I
−6.57378 − 1.34480I −7.53020 + 4.73780I
u = 0.187694 + 0.267286I
−0.141288 − 0.746703I −4.42303 + 9.26587I
u = 0.187694 − 0.267286I
−0.141288 + 0.746703I −4.42303 − 9.26587I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
10
u
51
− 7u
50
+ ··· + 112u − 17
c
2
, c
3
, c
8
c
9
u
51
+ u
50
+ ··· + 3u
2
+ 1
c
4
, c
6
u
51
− u
50
+ ··· + 3u
2
+ 1
c
5
, c
11
, c
12
u
51
+ u
50
+ ··· + 2u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
10
y
51
+ 47y
50
+ ··· + 202y −289
c
2
, c
3
, c
8
c
9
y
51
+ 55y
50
+ ··· − 6y −1
c
4
, c
6
y
51
− 25y
50
+ ··· − 6y −1
c
5
, c
11
, c
12
y
51
+ 43y
50
+ ··· − 6y −1
8
