12a
0762
(K12a
0762
)
A knot diagram
1
Linearized knot diagam
3 8 10 11 12 1 9 2 7 4 5 6
Solving Sequence
2,9
8 3 1 7 10 4 11 6 12 5
c
8
c
2
c
1
c
7
c
9
c
3
c
10
c
6
c
12
c
5
c
4
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
25
− u
24
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 25 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
25
− u
24
+ · · · − u − 1i
(i) Arc colorings
a
2
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
7
=
u
2
+ 1
u
2
a
10
=
u
4
+ u
2
+ 1
u
4
a
4
=
−u
11
− 2u
9
− 4u
7
− 4u
5
− 3u
3
−u
11
− u
9
− 2u
7
− u
5
+ u
3
+ u
a
11
=
−u
18
− 3u
16
− 8u
14
− 13u
12
− 17u
10
− 15u
8
− 10u
6
− 2u
4
+ u
2
+ 1
−u
18
− 2u
16
− 5u
14
− 6u
12
− 5u
10
− 2u
8
+ 2u
6
+ 4u
4
+ u
2
a
6
=
−u
10
− u
8
− 2u
6
− u
4
+ u
2
+ 1
−u
12
− 2u
10
− 4u
8
− 4u
6
− 3u
4
a
12
=
−u
17
− 2u
15
− 5u
13
− 6u
11
− 5u
9
− 2u
7
+ 2u
5
+ 4u
3
+ u
−u
19
− 3u
17
− 8u
15
− 13u
13
− 17u
11
− 15u
9
− 10u
7
− 2u
5
+ u
3
+ u
a
5
=
u
24
+ 3u
22
+ ··· − 7u
4
+ 1
u
24
− u
23
+ ··· + 2u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
24
+12u
22
+4u
21
+40u
20
+12u
19
+76u
18
+36u
17
+132u
16
+68u
15
+168u
14
+104u
13
+
184u
12
+ 128u
11
+ 144u
10
+ 116u
9
+ 96u
8
+ 76u
7
+ 24u
6
+ 32u
5
−8u
3
−12u
2
−12u −14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
9
u
25
+ 7u
24
+ ··· + u − 1
c
2
, c
8
u
25
− u
24
+ ··· − u − 1
c
3
, c
4
, c
5
c
6
, c
10
, c
11
c
12
u
25
− u
24
+ ··· − 3u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
y
25
+ 23y
24
+ ··· + 53y −1
c
2
, c
8
y
25
+ 7y
24
+ ··· + y −1
c
3
, c
4
, c
5
c
6
, c
10
, c
11
c
12
y
25
− 37y
24
+ ··· + y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.265781 + 0.997248I
−10.12290 + 2.99473I −17.9259 − 4.0117I
u = 0.265781 − 0.997248I
−10.12290 − 2.99473I −17.9259 + 4.0117I
u = −0.273882 + 1.054670I
17.4097 − 3.3423I −17.7803 + 3.3269I
u = −0.273882 − 1.054670I
17.4097 + 3.3423I −17.7803 − 3.3269I
u = −0.246006 + 0.873993I
−3.15716 − 2.26268I −17.3905 + 6.2101I
u = −0.246006 − 0.873993I
−3.15716 + 2.26268I −17.3905 − 6.2101I
u = −0.830816 + 0.777643I
−3.05026 + 1.70594I −11.67057 − 0.75196I
u = −0.830816 − 0.777643I
−3.05026 − 1.70594I −11.67057 + 0.75196I
u = 0.865156 + 0.751311I
−14.5343 − 2.5689I −11.95129 + 0.13381I
u = 0.865156 − 0.751311I
−14.5343 + 2.5689I −11.95129 − 0.13381I
u = 0.799748 + 0.834653I
3.10996 + 0.09524I −9.28181 + 2.24962I
u = 0.799748 − 0.834653I
3.10996 − 0.09524I −9.28181 − 2.24962I
u = −0.789348 + 0.887317I
4.84212 − 2.96582I −4.58372 + 3.07678I
u = −0.789348 − 0.887317I
4.84212 + 2.96582I −4.58372 − 3.07678I
u = 0.775933 + 0.933111I
2.80794 + 5.82631I −10.19251 − 7.46016I
u = 0.775933 − 0.933111I
2.80794 − 5.82631I −10.19251 + 7.46016I
u = −0.771220 + 0.977956I
−3.66358 − 7.69842I −12.72418 + 5.77785I
u = −0.771220 − 0.977956I
−3.66358 + 7.69842I −12.72418 − 5.77785I
u = 0.774392 + 1.005890I
−15.3222 + 8.6670I −13.19072 − 4.94641I
u = 0.774392 − 1.005890I
−15.3222 − 8.6670I −13.19072 + 4.94641I
u = −0.728653
−18.6276 −11.9440
u = 0.172656 + 0.645298I
−0.420243 + 0.852863I −9.01002 − 7.64857I
u = 0.172656 − 0.645298I
−0.420243 − 0.852863I −9.01002 + 7.64857I
u = 0.636642
−7.02137 −11.7190
u = −0.392781
−0.881262 −10.9350
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
9
u
25
+ 7u
24
+ ··· + u − 1
c
2
, c
8
u
25
− u
24
+ ··· − u − 1
c
3
, c
4
, c
5
c
6
, c
10
, c
11
c
12
u
25
− u
24
+ ··· − 3u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
y
25
+ 23y
24
+ ··· + 53y −1
c
2
, c
8
y
25
+ 7y
24
+ ··· + y −1
c
3
, c
4
, c
5
c
6
, c
10
, c
11
c
12
y
25
− 37y
24
+ ··· + y −1
7
