12a
1128
(K12a
1128
)
A knot diagram
1
Linearized knot diagam
4 8 9 10 11 12 2 3 1 5 6 7
Solving Sequence
6,11
12 7 1 5 10 4 2 9 3 8
c
11
c
6
c
12
c
5
c
10
c
4
c
1
c
9
c
3
c
8
c
2
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
29
− u
28
+ ··· + u − 1i
* 1 irreducible components of dim
C
= 0, with total 29 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
29
− u
28
+ · · · + u − 1i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
7
=
u
−u
3
+ u
a
1
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
−u
u
a
10
=
−u
2
+ 1
u
2
a
4
=
u
3
− 2u
−u
3
+ u
a
2
=
−u
10
+ 7u
8
− 16u
6
+ 13u
4
− 3u
2
+ 1
u
10
− 6u
8
+ 11u
6
− 6u
4
− u
2
a
9
=
u
8
− 5u
6
+ 7u
4
− 4u
2
+ 1
−u
10
+ 6u
8
− 11u
6
+ 6u
4
+ u
2
a
3
=
u
21
− 14u
19
+ ··· − 6u
3
− u
−u
23
+ 15u
21
+ ··· + 3u
5
+ u
a
8
=
u
23
− 16u
21
+ ··· − 44u
5
+ 6u
3
−u
23
+ 15u
21
+ ··· + 3u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
26
+ 76u
24
− 624u
22
+ 2900u
20
− 4u
19
− 8396u
18
+ 56u
17
+
15708u
16
− 320u
15
− 19072u
14
+ 960u
13
+ 14724u
12
− 1620u
11
− 6940u
10
+ 1528u
9
+
1900u
8
− 752u
7
− 256u
6
+ 180u
5
− 28u
4
− 36u
3
+ 8u
2
+ 4u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
29
− 7u
28
+ ··· − 7u + 1
c
2
, c
3
, c
7
c
8
u
29
+ u
28
+ ··· + u − 1
c
4
, c
5
, c
6
c
10
, c
11
, c
12
u
29
− u
28
+ ··· + u − 1
c
9
u
29
− 5u
28
+ ··· + 17u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
29
+ 3y
28
+ ··· + 67y −1
c
2
, c
3
, c
7
c
8
y
29
− 33y
28
+ ··· + 3y −1
c
4
, c
5
, c
6
c
10
, c
11
, c
12
y
29
− 41y
28
+ ··· + 3y −1
c
9
y
29
− y
28
+ ··· + 239y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.07968
2.46262 2.59660
u = −0.840545 + 0.145144I
−5.25732 + 0.07846I 2.69491 + 1.17577I
u = −0.840545 − 0.145144I
−5.25732 − 0.07846I 2.69491 − 1.17577I
u = −1.205760 + 0.116422I
6.35623 − 1.67361I 9.89817 + 0.46541I
u = −1.205760 − 0.116422I
6.35623 + 1.67361I 9.89817 − 0.46541I
u = 1.202640 + 0.175266I
5.26333 + 5.33299I 6.65607 − 6.84513I
u = 1.202640 − 0.175266I
5.26333 − 5.33299I 6.65607 + 6.84513I
u = −1.199740 + 0.218974I
−2.23245 − 7.72857I 3.61909 + 5.37469I
u = −1.199740 − 0.218974I
−2.23245 + 7.72857I 3.61909 − 5.37469I
u = 1.26442
1.39387 5.96400
u = 0.471072 + 0.447454I
−7.58667 + 5.43585I −0.17849 − 6.76696I
u = 0.471072 − 0.447454I
−7.58667 − 5.43585I −0.17849 + 6.76696I
u = −0.467285 + 0.371692I
−0.11770 − 3.45863I 2.80280 + 9.42983I
u = −0.467285 − 0.371692I
−0.11770 + 3.45863I 2.80280 − 9.42983I
u = 0.182355 + 0.485286I
−8.43922 − 2.34125I −3.35682 − 0.17846I
u = 0.182355 − 0.485286I
−8.43922 + 2.34125I −3.35682 + 0.17846I
u = 0.466672 + 0.213238I
0.927707 + 0.489193I 8.47168 − 2.23458I
u = 0.466672 − 0.213238I
0.927707 − 0.489193I 8.47168 + 2.23458I
u = −0.153276 + 0.375440I
−1.021340 + 0.906585I −2.70117 − 1.63465I
u = −0.153276 − 0.375440I
−1.021340 − 0.906585I −2.70117 + 1.63465I
u = 1.73522
4.28136 2.00000
u = −1.76786
12.9166 2.00000
u = 1.78372 + 0.05527I
8.64020 + 8.93823I 0. − 4.29230I
u = 1.78372 − 0.05527I
8.64020 − 8.93823I 0. + 4.29230I
u = −1.78538 + 0.04379I
16.1866 − 6.3008I 0. + 5.54756I
u = −1.78538 − 0.04379I
16.1866 + 6.3008I 0. − 5.54756I
u = 1.78638 + 0.03003I
17.3230 + 2.3306I 0
u = 1.78638 − 0.03003I
17.3230 − 2.3306I 0
u = −1.79318
12.6221 5.86870
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
29
− 7u
28
+ ··· − 7u + 1
c
2
, c
3
, c
7
c
8
u
29
+ u
28
+ ··· + u − 1
c
4
, c
5
, c
6
c
10
, c
11
, c
12
u
29
− u
28
+ ··· + u − 1
c
9
u
29
− 5u
28
+ ··· + 17u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
29
+ 3y
28
+ ··· + 67y −1
c
2
, c
3
, c
7
c
8
y
29
− 33y
28
+ ··· + 3y −1
c
4
, c
5
, c
6
c
10
, c
11
, c
12
y
29
− 41y
28
+ ··· + 3y −1
c
9
y
29
− y
28
+ ··· + 239y −1
7
