12a
1162
(K12a
1162
)
A knot diagram
1
Linearized knot diagam
4 9 8 11 12 1 10 3 2 7 5 6
Solving Sequence
5,12
6 1 7 11 4 2 10 8 3 9
c
5
c
12
c
6
c
11
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
34
− u
33
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 34 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
34
− u
33
+ · · · − u − 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
u
2
a
1
=
−u
−u
3
+ u
a
7
=
−u
2
+ 1
−u
4
+ 2u
2
a
11
=
u
u
a
4
=
−u
2
+ 1
−u
2
a
2
=
u
7
− 4u
5
+ 4u
3
− 2u
u
7
− 3u
5
+ u
a
10
=
−u
7
+ 4u
5
− 4u
3
+ 2u
−u
9
+ 5u
7
− 7u
5
+ 2u
3
+ u
a
8
=
−u
12
+ 7u
10
− 17u
8
+ 18u
6
− 10u
4
+ u
2
+ 1
−u
14
+ 8u
12
− 23u
10
+ 28u
8
− 12u
6
− 2u
4
+ 3u
2
a
3
=
−u
28
+ 17u
26
+ ··· + 3u
2
+ 1
−u
30
+ 18u
28
+ ··· + 12u
4
− u
2
a
9
=
u
23
− 14u
21
+ ··· − 12u
3
+ 2u
u
23
− 13u
21
+ ··· + 6u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
30
− 76u
28
+ 632u
26
− 4u
25
− 3020u
24
+ 64u
23
+ 9160u
22
− 436u
21
− 18396u
20
+
1648u
19
+ 24724u
18
− 3780u
17
− 21696u
16
+ 5412u
15
+ 11000u
14
− 4760u
13
− 1160u
12
+
2280u
11
−2344u
10
−168u
9
+ 1456u
8
−424u
7
−192u
6
+ 192u
5
−112u
4
+ 32u
2
−16u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
10
u
34
− 5u
33
+ ··· − 37u + 11
c
2
, c
3
, c
8
c
9
u
34
+ u
33
+ ··· − u − 1
c
4
, c
5
, c
6
c
11
, c
12
u
34
− u
33
+ ··· − u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
10
y
34
+ 29y
33
+ ··· − 1171y + 121
c
2
, c
3
, c
8
c
9
y
34
+ 37y
33
+ ··· + 5y + 1
c
4
, c
5
, c
6
c
11
, c
12
y
34
− 43y
33
+ ··· + 5y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.991821 + 0.158095I
−10.68960 + 3.15183I −14.0763 − 3.9724I
u = −0.991821 − 0.158095I
−10.68960 − 3.15183I −14.0763 + 3.9724I
u = −0.893573 + 0.396504I
−4.49049 + 8.32995I −9.15739 − 6.65948I
u = −0.893573 − 0.396504I
−4.49049 − 8.32995I −9.15739 + 6.65948I
u = 0.859035 + 0.393675I
2.35629 − 5.47047I −5.42904 + 7.39488I
u = 0.859035 − 0.393675I
2.35629 + 5.47047I −5.42904 − 7.39488I
u = −0.818764 + 0.392887I
2.60490 + 1.31090I −4.52445 − 0.97294I
u = −0.818764 − 0.392887I
2.60490 − 1.31090I −4.52445 + 0.97294I
u = 0.893463 + 0.130044I
−3.31682 − 2.12721I −12.9145 + 6.3416I
u = 0.893463 − 0.130044I
−3.31682 + 2.12721I −12.9145 − 6.3416I
u = 0.766255 + 0.403391I
−3.72832 + 1.46235I −8.04381 + 1.15427I
u = 0.766255 − 0.403391I
−3.72832 − 1.46235I −8.04381 − 1.15427I
u = −0.769926
−1.46282 −5.15730
u = 0.058238 + 0.615568I
−1.59411 − 4.91155I −4.11375 + 3.54526I
u = 0.058238 − 0.615568I
−1.59411 + 4.91155I −4.11375 − 3.54526I
u = −0.019163 + 0.609431I
5.01871 + 2.08023I −0.25628 − 3.52395I
u = −0.019163 − 0.609431I
5.01871 − 2.08023I −0.25628 + 3.52395I
u = 0.311005 + 0.396451I
−6.63940 − 1.35507I −7.90199 + 4.63231I
u = 0.311005 − 0.396451I
−6.63940 + 1.35507I −7.90199 − 4.63231I
u = −1.63888 + 0.08443I
−12.00830 + 0.25970I 0
u = −1.63888 − 0.08443I
−12.00830 − 0.25970I 0
u = 1.65843 + 0.09430I
−5.99222 − 3.10866I 0
u = 1.65843 − 0.09430I
−5.99222 + 3.10866I 0
u = 1.66496
−10.1351 0
u = −1.67097 + 0.10038I
−6.45085 + 7.34504I 0
u = −1.67097 − 0.10038I
−6.45085 − 7.34504I 0
u = −0.165695 + 0.272869I
−0.148667 + 0.754720I −4.59527 − 9.11142I
u = −0.165695 − 0.272869I
−0.148667 − 0.754720I −4.59527 + 9.11142I
u = −1.68383 + 0.02823I
−12.43350 + 2.70866I 0
u = −1.68383 − 0.02823I
−12.43350 − 2.70866I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.68188 + 0.10424I
−13.4764 − 10.2661I 0
u = 1.68188 − 0.10424I
−13.4764 + 10.2661I 0
u = 1.70687 + 0.03573I
19.2149 − 3.8937I 0
u = 1.70687 − 0.03573I
19.2149 + 3.8937I 0
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
10
u
34
− 5u
33
+ ··· − 37u + 11
c
2
, c
3
, c
8
c
9
u
34
+ u
33
+ ··· − u − 1
c
4
, c
5
, c
6
c
11
, c
12
u
34
− u
33
+ ··· − u − 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
10
y
34
+ 29y
33
+ ··· − 1171y + 121
c
2
, c
3
, c
8
c
9
y
34
+ 37y
33
+ ··· + 5y + 1
c
4
, c
5
, c
6
c
11
, c
12
y
34
− 43y
33
+ ··· + 5y + 1
8
