12a
1039
(K12a
1039
)
A knot diagram
1
Linearized knot diagam
4 7 8 11 12 9 3 2 1 6 5 10
Solving Sequence
4,8
3 7 2 9 1 10 6 11 12 5
c
3
c
7
c
2
c
8
c
1
c
9
c
6
c
10
c
12
c
5
c
4
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
68
− u
67
+ ··· + 3u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 68 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
68
− u
67
+ · · · + 3u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
7
=
−u
−u
3
+ u
a
2
=
−u
2
+ 1
−u
4
+ 2u
2
a
9
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
1
=
−u
4
+ u
2
+ 1
−u
4
+ 2u
2
a
10
=
u
15
− 6u
13
+ 12u
11
− 6u
9
− 6u
7
+ 4u
5
+ 2u
u
15
− 7u
13
+ 18u
11
− 19u
9
+ 6u
7
− 2u
5
+ 4u
3
+ u
a
6
=
−u
9
+ 4u
7
− 5u
5
+ 2u
3
− u
−u
11
+ 5u
9
− 8u
7
+ 3u
5
+ u
3
+ u
a
11
=
u
35
− 16u
33
+ ··· − 3u
3
+ 2u
u
37
− 17u
35
+ ··· + 7u
3
+ u
a
12
=
−u
26
+ 11u
24
+ ··· + 3u
2
+ 1
−u
26
+ 12u
24
+ ··· + 4u
4
+ 3u
2
a
5
=
−u
63
+ 28u
61
+ ··· + 22u
5
+ 12u
3
−u
63
+ 29u
61
+ ··· + 4u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
66
+ 124u
64
+ ··· + 16u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
68
− 11u
67
+ ··· − 1692u + 113
c
2
, c
3
, c
7
u
68
+ u
67
+ ··· + 3u
2
+ 1
c
4
, c
5
, c
11
u
68
− u
67
+ ··· + 3u
2
+ 1
c
8
u
68
− 3u
67
+ ··· + 630u − 369
c
9
, c
12
u
68
+ 11u
67
+ ··· + 1692u + 113
c
10
u
68
+ 3u
67
+ ··· − 630u − 369
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
9
c
12
y
68
+ 49y
67
+ ··· + 20218y + 12769
c
2
, c
3
, c
4
c
5
, c
7
, c
11
y
68
− 63y
67
+ ··· + 6y + 1
c
8
, c
10
y
68
− 19y
67
+ ··· − 2666250y + 136161
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.16639
−2.36439 0
u = 1.185360 + 0.209451I
−6.83305 − 1.72993I 0
u = 1.185360 − 0.209451I
−6.83305 + 1.72993I 0
u = −0.365893 + 0.690572I
−5.83372 − 10.83810I −3.95689 + 8.43769I
u = −0.365893 − 0.690572I
−5.83372 + 10.83810I −3.95689 − 8.43769I
u = −1.208360 + 0.195557I
−0.669905 − 1.153560I 0
u = −1.208360 − 0.195557I
−0.669905 + 1.153560I 0
u = 0.366622 + 0.678680I
7.42138I 0. − 8.76802I
u = 0.366622 − 0.678680I
− 7.42138I 0. + 8.76802I
u = −0.411460 + 0.633737I
0.45656 − 5.12674I 0.57871 + 7.03241I
u = −0.411460 − 0.633737I
0.45656 + 5.12674I 0.57871 − 7.03241I
u = −0.353617 + 0.662232I
−0.67977 − 3.43697I −1.83810 + 2.79608I
u = −0.353617 − 0.662232I
−0.67977 + 3.43697I −1.83810 − 2.79608I
u = 1.231400 + 0.212602I
−0.45656 + 5.12674I 0
u = 1.231400 − 0.212602I
−0.45656 − 5.12674I 0
u = 0.330337 + 0.672943I
−7.00321 + 0.97426I −5.71997 − 2.85709I
u = 0.330337 − 0.672943I
−7.00321 − 0.97426I −5.71997 + 2.85709I
u = −0.548441 + 0.510750I
−5.09005 + 6.77785I −2.21904 − 2.56386I
u = −0.548441 − 0.510750I
−5.09005 − 6.77785I −2.21904 + 2.56386I
u = −1.231440 + 0.231517I
−6.47567 − 8.30107I 0
u = −1.231440 − 0.231517I
−6.47567 + 8.30107I 0
u = 0.427107 + 0.604623I
4.25225 + 1.96489I 6.41876 − 3.80214I
u = 0.427107 − 0.604623I
4.25225 − 1.96489I 6.41876 + 3.80214I
u = −0.457025 + 0.579336I
0.669905 + 1.153560I 1.403435 − 0.101236I
u = −0.457025 − 0.579336I
0.669905 − 1.153560I 1.403435 + 0.101236I
u = 0.524039 + 0.507598I
0.67977 − 3.43697I 1.83810 + 2.79608I
u = 0.524039 − 0.507598I
0.67977 + 3.43697I 1.83810 − 2.79608I
u = −1.28430
2.97683 0
u = 0.540694 + 0.417882I
−6.07300 + 2.79125I −3.29801 − 3.53193I
u = 0.540694 − 0.417882I
−6.07300 − 2.79125I −3.29801 + 3.53193I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.484269 + 0.469339I
− 0.351863I 0. + 3.89168I
u = −0.484269 − 0.469339I
0.351863I 0. − 3.89168I
u = 0.026103 + 0.672070I
−10.31710 + 4.99618I −9.53537 − 3.59644I
u = 0.026103 − 0.672070I
−10.31710 − 4.99618I −9.53537 + 3.59644I
u = 1.341290 + 0.078014I
4.79218 + 2.27303I 0
u = 1.341290 − 0.078014I
4.79218 − 2.27303I 0
u = −0.016190 + 0.650435I
−4.25225 − 1.96489I −6.41876 + 3.80214I
u = −0.016190 − 0.650435I
−4.25225 + 1.96489I −6.41876 − 3.80214I
u = −1.36044
2.36439 0
u = −1.354250 + 0.153282I
− 4.85572I 0
u = −1.354250 − 0.153282I
4.85572I 0
u = 0.168296 + 0.562791I
−4.79218 + 2.27303I −7.53878 − 5.43774I
u = 0.168296 − 0.562791I
−4.79218 − 2.27303I −7.53878 + 5.43774I
u = −1.41500 + 0.15765I
− 4.77953I 0
u = −1.41500 − 0.15765I
4.77953I 0
u = −1.43315 + 0.25654I
−1.34747 − 4.36482I 0
u = −1.43315 − 0.25654I
−1.34747 + 4.36482I 0
u = 1.44513 + 0.18530I
6.07300 + 2.79125I 0
u = 1.44513 − 0.18530I
6.07300 − 2.79125I 0
u = 1.44230 + 0.25142I
5.09005 + 6.77785I 0
u = 1.44230 − 0.25142I
5.09005 − 6.77785I 0
u = −1.44844 + 0.25675I
5.83372 − 10.83810I 0
u = −1.44844 − 0.25675I
5.83372 + 10.83810I 0
u = −1.46054 + 0.17675I
7.00321 + 0.97426I 0
u = −1.46054 − 0.17675I
7.00321 − 0.97426I 0
u = 1.44937 + 0.26160I
14.3130I 0
u = 1.44937 − 0.26160I
− 14.3130I 0
u = −1.45871 + 0.22229I
10.31710 − 4.99618I 0
u = −1.45871 − 0.22229I
10.31710 + 4.99618I 0
u = 1.46621 + 0.16916I
1.34747 − 4.36482I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.46621 − 0.16916I
1.34747 + 4.36482I 0
u = 1.46180 + 0.20937I
6.83305 + 1.72993I 0
u = 1.46180 − 0.20937I
6.83305 − 1.72993I 0
u = 1.45834 + 0.23374I
6.47567 + 8.30107I 0
u = 1.45834 − 0.23374I
6.47567 − 8.30107I 0
u = 0.454374
−2.97683 0.0821020
u = −0.205634 + 0.349087I
− 0.817350I 0. + 8.35638I
u = −0.205634 − 0.349087I
0.817350I 0. − 8.35638I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
68
− 11u
67
+ ··· − 1692u + 113
c
2
, c
3
, c
7
u
68
+ u
67
+ ··· + 3u
2
+ 1
c
4
, c
5
, c
11
u
68
− u
67
+ ··· + 3u
2
+ 1
c
8
u
68
− 3u
67
+ ··· + 630u − 369
c
9
, c
12
u
68
+ 11u
67
+ ··· + 1692u + 113
c
10
u
68
+ 3u
67
+ ··· − 630u − 369
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
9
c
12
y
68
+ 49y
67
+ ··· + 20218y + 12769
c
2
, c
3
, c
4
c
5
, c
7
, c
11
y
68
− 63y
67
+ ··· + 6y + 1
c
8
, c
10
y
68
− 19y
67
+ ··· − 2666250y + 136161
9
