12a
0197
(K12a
0197
)
A knot diagram
1
Linearized knot diagam
3 5 10 6 2 1 12 11 4 9 8 7
Solving Sequence
4,9
10 11 3 8 12 7 1 6 5 2
c
9
c
10
c
3
c
8
c
11
c
7
c
12
c
6
c
4
c
2
c
1
, c
5
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
4
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
11
=
u
2
+ 1
u
2
a
3
=
u
u
3
+ u
a
8
=
u
4
+ u
2
+ 1
u
4
a
12
=
u
6
+ u
4
+ 2u
2
+ 1
u
6
+ u
2
a
7
=
u
8
+ u
6
+ 3u
4
+ 2u
2
+ 1
u
8
+ 2u
4
a
1
=
u
10
+ u
8
+ 4u
6
+ 3u
4
+ 3u
2
+ 1
u
10
+ 3u
6
+ u
2
a
6
=
u
12
+ u
10
+ 5u
8
+ 4u
6
+ 6u
4
+ 3u
2
+ 1
u
12
+ 4u
8
+ 3u
4
a
5
=
−u
25
− 2u
23
+ ··· − 6u
3
− u
−u
25
− u
23
+ ··· − 3u
5
+ u
a
2
=
u
14
+ u
12
+ 6u
10
+ 5u
8
+ 10u
6
+ 6u
4
+ 4u
2
+ 1
u
16
+ 2u
14
+ 6u
12
+ 10u
10
+ 10u
8
+ 12u
6
+ 4u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
32
+4u
31
+12u
30
+8u
29
+64u
28
+52u
27
+144u
26
+88u
25
+396u
24
+268u
23
+676u
22
+
376u
21
+ 1216u
20
+ 696u
19
+ 1564u
18
+ 784u
17
+ 1956u
16
+ 948u
15
+ 1836u
14
+ 812u
13
+
1576u
12
+620u
11
+992u
10
+360u
9
+528u
8
+132u
7
+176u
6
+40u
5
+40u
4
−8u
3
+12u
2
+8u+2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
34
+ 13u
33
+ ··· + 5u + 1
c
2
, c
5
u
34
+ u
33
+ ··· − 3u + 1
c
3
, c
9
u
34
− u
33
+ ··· + u + 1
c
6
, c
7
, c
8
c
10
, c
11
, c
12
u
34
− 5u
33
+ ··· − 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
34
+ 17y
33
+ ··· + 97y + 1
c
2
, c
5
y
34
+ 13y
33
+ ··· + 5y + 1
c
3
, c
9
y
34
+ 5y
33
+ ··· + 5y + 1
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
34
+ 49y
33
+ ··· + 25y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.407066 + 0.834658I
1.03103 + 6.41382I 3.82648 − 9.99401I
u = −0.407066 − 0.834658I
1.03103 − 6.41382I 3.82648 + 9.99401I
u = −0.760333 + 0.772672I
−4.35750 + 1.50466I 0.22640 − 2.73870I
u = −0.760333 − 0.772672I
−4.35750 − 1.50466I 0.22640 + 2.73870I
u = 0.802505 + 0.764339I
−5.87304 + 3.61528I −2.19692 − 2.52505I
u = 0.802505 − 0.764339I
−5.87304 − 3.61528I −2.19692 + 2.52505I
u = 0.348058 + 0.805715I
1.73732 − 1.33000I 6.22240 + 4.49160I
u = 0.348058 − 0.805715I
1.73732 + 1.33000I 6.22240 − 4.49160I
u = −0.718616 + 0.868268I
−4.04046 + 3.96737I 1.07736 − 3.54418I
u = −0.718616 − 0.868268I
−4.04046 − 3.96737I 1.07736 + 3.54418I
u = −0.532857 + 0.661540I
−2.87697 + 1.94550I −4.75114 − 5.05594I
u = −0.532857 − 0.661540I
−2.87697 − 1.94550I −4.75114 + 5.05594I
u = 0.786286 + 0.843735I
−9.58813 − 2.89200I −5.67849 + 3.04986I
u = 0.786286 − 0.843735I
−9.58813 + 2.89200I −5.67849 − 3.04986I
u = 0.733686 + 0.898055I
−5.42158 − 9.27208I −0.93638 + 8.29994I
u = 0.733686 − 0.898055I
−5.42158 + 9.27208I −0.93638 − 8.29994I
u = 0.034944 + 0.814547I
3.24779 − 2.53240I 10.48060 + 3.91593I
u = 0.034944 − 0.814547I
3.24779 + 2.53240I 10.48060 − 3.91593I
u = −0.560898 + 0.384252I
−0.40745 − 2.89261I −2.01184 + 2.94776I
u = −0.560898 − 0.384252I
−0.40745 + 2.89261I −2.01184 − 2.94776I
u = 0.943944 + 0.946247I
−15.2642 − 1.6043I 0.05765 + 2.13250I
u = 0.943944 − 0.946247I
−15.2642 + 1.6043I 0.05765 − 2.13250I
u = −0.951432 + 0.943931I
−17.0241 − 3.9437I −2.23878 + 2.32500I
u = −0.951432 − 0.943931I
−17.0241 + 3.9437I −2.23878 − 2.32500I
u = 0.933375 + 0.963881I
−15.2051 − 5.2894I 0.15464 + 2.30279I
u = 0.933375 − 0.963881I
−15.2051 + 5.2894I 0.15464 − 2.30279I
u = −0.934696 + 0.971112I
−16.9325 + 10.8664I −2.05453 − 6.71778I
u = −0.934696 − 0.971112I
−16.9325 − 10.8664I −2.05453 + 6.71778I
u = −0.946814 + 0.960125I
18.2073 + 3.4743I −5.57472 − 2.21410I
u = −0.946814 − 0.960125I
18.2073 − 3.4743I −5.57472 + 2.21410I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.258906 + 0.569344I
0.245296 − 0.924586I 4.90419 + 7.15131I
u = 0.258906 − 0.569344I
0.245296 + 0.924586I 4.90419 − 7.15131I
u = 0.471008 + 0.235567I
0.14514 − 1.57341I −1.50693 + 3.59818I
u = 0.471008 − 0.235567I
0.14514 + 1.57341I −1.50693 − 3.59818I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
u
34
+ 13u
33
+ ··· + 5u + 1
c
2
, c
5
u
34
+ u
33
+ ··· − 3u + 1
c
3
, c
9
u
34
− u
33
+ ··· + u + 1
c
6
, c
7
, c
8
c
10
, c
11
, c
12
u
34
− 5u
33
+ ··· − 5u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
34
+ 17y
33
+ ··· + 97y + 1
c
2
, c
5
y
34
+ 13y
33
+ ··· + 5y + 1
c
3
, c
9
y
34
+ 5y
33
+ ··· + 5y + 1
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
34
+ 49y
33
+ ··· + 25y + 1
8
