12a
0740
(K12a
0740
)
A knot diagram
1
Linearized knot diagam
3 8 9 11 12 10 1 2 7 6 5 4
Solving Sequence
6,12
5 11 4 1 10 7 8 9 3 2
c
5
c
11
c
4
c
12
c
10
c
6
c
7
c
9
c
3
c
2
c
1
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
56
+ u
55
+ ··· − 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 56 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
56
+ u
55
+ · · · − 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
5
=
1
−u
2
a
11
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
1
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
10
=
−u
3
+ 2u
−u
3
+ u
a
7
=
u
6
− 3u
4
+ 2u
2
+ 1
u
6
− 2u
4
+ u
2
a
8
=
−u
18
+ 7u
16
− 20u
14
+ 27u
12
− 11u
10
− 13u
8
+ 16u
6
− 6u
4
+ u
2
+ 1
u
20
− 8u
18
+ 26u
16
− 40u
14
+ 19u
12
+ 24u
10
− 30u
8
+ 2u
6
+ 5u
4
+ 2u
2
a
9
=
−u
9
+ 4u
7
− 5u
5
+ 3u
−u
9
+ 3u
7
− 3u
5
+ u
a
3
=
u
22
− 9u
20
+ ··· − 4u
2
+ 1
u
22
− 8u
20
+ ··· − 4u
4
− 3u
2
a
2
=
−u
51
+ 20u
49
+ ··· + 11u
3
− 2u
−u
51
+ 19u
49
+ ··· + 5u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
53
+ 80u
51
+ ··· − 12u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
56
+ 29u
55
+ ··· − 10u
2
+ 1
c
2
, c
8
u
56
− u
55
+ ··· − 2u
3
− 1
c
3
, c
7
u
56
+ u
55
+ ··· + 80u − 53
c
4
, c
5
, c
11
u
56
+ u
55
+ ··· − 2u − 1
c
6
, c
9
, c
10
c
12
u
56
− 3u
55
+ ··· − 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
56
− 3y
55
+ ··· − 20y + 1
c
2
, c
8
y
56
+ 29y
55
+ ··· − 10y
2
+ 1
c
3
, c
7
y
56
− 35y
55
+ ··· − 20180y + 2809
c
4
, c
5
, c
11
y
56
− 43y
55
+ ··· + 30y
2
+ 1
c
6
, c
9
, c
10
c
12
y
56
+ 65y
55
+ ··· + 20y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.966138 + 0.146675I
−4.03618 + 3.76547I −9.86305 − 3.31528I
u = 0.966138 − 0.146675I
−4.03618 − 3.76547I −9.86305 + 3.31528I
u = −0.005719 + 0.906711I
11.65310 + 2.42579I −0.94991 − 3.21386I
u = −0.005719 − 0.906711I
11.65310 − 2.42579I −0.94991 + 3.21386I
u = 0.036344 + 0.901122I
6.27142 − 9.00482I −5.29022 + 5.83508I
u = 0.036344 − 0.901122I
6.27142 + 9.00482I −5.29022 − 5.83508I
u = −1.090050 + 0.140449I
−1.55041 + 0.38680I −5.72495 + 0.I
u = −1.090050 − 0.140449I
−1.55041 − 0.38680I −5.72495 + 0.I
u = −0.028384 + 0.898900I
8.99836 + 4.05002I −2.11311 − 2.32433I
u = −0.028384 − 0.898900I
8.99836 − 4.05002I −2.11311 + 2.32433I
u = 0.028330 + 0.883702I
4.64419 − 0.64348I −7.26111 − 0.24240I
u = 0.028330 − 0.883702I
4.64419 + 0.64348I −7.26111 + 0.24240I
u = −1.167310 + 0.233432I
−0.432854 + 1.119920I 0
u = −1.167310 − 0.233432I
−0.432854 − 1.119920I 0
u = 1.244770 + 0.102397I
−4.72176 − 2.16923I 0
u = 1.244770 − 0.102397I
−4.72176 + 2.16923I 0
u = 1.225110 + 0.251359I
−0.95561 − 5.19909I 0
u = 1.225110 − 0.251359I
−0.95561 + 5.19909I 0
u = 1.30697
−6.22222 0
u = 1.294490 + 0.219824I
−3.63173 − 5.28884I 0
u = 1.294490 − 0.219824I
−3.63173 + 5.28884I 0
u = −1.306120 + 0.197397I
−7.41440 + 1.49252I 0
u = −1.306120 − 0.197397I
−7.41440 − 1.49252I 0
u = 1.253840 + 0.421699I
0.85056 − 4.02651I 0
u = 1.253840 − 0.421699I
0.85056 + 4.02651I 0
u = −1.324320 + 0.015856I
−9.57385 + 4.23364I 0
u = −1.324320 − 0.015856I
−9.57385 − 4.23364I 0
u = 1.250890 + 0.441220I
2.51555 + 4.21199I 0
u = 1.250890 − 0.441220I
2.51555 − 4.21199I 0
u = −1.310570 + 0.227530I
−6.63163 + 9.90909I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.310570 − 0.227530I
−6.63163 − 9.90909I 0
u = −1.257710 + 0.436717I
5.19296 + 0.72097I 0
u = −1.257710 − 0.436717I
5.19296 − 0.72097I 0
u = −1.279070 + 0.437088I
7.70069 + 2.37410I 0
u = −1.279070 − 0.437088I
7.70069 − 2.37410I 0
u = 0.199264 + 0.611623I
−1.94679 − 6.93022I −6.93561 + 8.02369I
u = 0.199264 − 0.611623I
−1.94679 + 6.93022I −6.93561 − 8.02369I
u = 1.288170 + 0.434128I
7.63163 − 7.21669I 0
u = 1.288170 − 0.434128I
7.63163 + 7.21669I 0
u = −1.300160 + 0.412494I
0.50431 + 5.28588I 0
u = −1.300160 − 0.412494I
0.50431 − 5.28588I 0
u = 1.303070 + 0.422656I
4.84936 − 8.77757I 0
u = 1.303070 − 0.422656I
4.84936 + 8.77757I 0
u = −0.042518 + 0.626099I
2.87687 + 2.02638I −0.63182 − 4.64721I
u = −0.042518 − 0.626099I
2.87687 − 2.02638I −0.63182 + 4.64721I
u = −1.308980 + 0.422388I
2.07579 + 13.73950I 0
u = −1.308980 − 0.422388I
2.07579 − 13.73950I 0
u = −0.166435 + 0.582590I
0.87541 + 2.42282I −3.19232 − 4.86886I
u = −0.166435 − 0.582590I
0.87541 − 2.42282I −3.19232 + 4.86886I
u = 0.581831 + 0.132630I
−4.09488 − 3.93251I −12.13433 + 4.90398I
u = 0.581831 − 0.132630I
−4.09488 + 3.93251I −12.13433 − 4.90398I
u = 0.224976 + 0.537140I
−2.70624 + 1.11644I −8.57012 + 1.60454I
u = 0.224976 − 0.537140I
−2.70624 − 1.11644I −8.57012 − 1.60454I
u = −0.459240
−1.08734 −10.0590
u = −0.233743 + 0.256345I
−0.484744 + 0.884850I −8.86461 − 7.46301I
u = −0.233743 − 0.256345I
−0.484744 − 0.884850I −8.86461 + 7.46301I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
56
+ 29u
55
+ ··· − 10u
2
+ 1
c
2
, c
8
u
56
− u
55
+ ··· − 2u
3
− 1
c
3
, c
7
u
56
+ u
55
+ ··· + 80u − 53
c
4
, c
5
, c
11
u
56
+ u
55
+ ··· − 2u − 1
c
6
, c
9
, c
10
c
12
u
56
− 3u
55
+ ··· − 4u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
56
− 3y
55
+ ··· − 20y + 1
c
2
, c
8
y
56
+ 29y
55
+ ··· − 10y
2
+ 1
c
3
, c
7
y
56
− 35y
55
+ ··· − 20180y + 2809
c
4
, c
5
, c
11
y
56
− 43y
55
+ ··· + 30y
2
+ 1
c
6
, c
9
, c
10
c
12
y
56
+ 65y
55
+ ··· + 20y + 1
8
