11a
243
(K11a
243
)
A knot diagram
1
Linearized knot diagam
7 1 11 10 9 8 2 6 3 4 5
Solving Sequence
2,8
7 1 3 6 9 10 5 4 11
c
7
c
1
c
2
c
6
c
8
c
9
c
5
c
4
c
11
c
3
, c
10
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
2
=
0
u
a
8
=
1
0
a
7
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
3
u
5
− u
3
+ u
a
6
=
−u
2
+ 1
−u
2
a
9
=
u
4
− u
2
+ 1
u
4
a
10
=
−u
12
+ u
10
− 3u
8
+ 2u
6
− u
2
+ 1
u
14
− 2u
12
+ 5u
10
− 6u
8
+ 6u
6
− 2u
4
+ u
2
a
5
=
−u
6
+ u
4
− 2u
2
+ 1
−u
6
− u
2
a
4
=
−u
32
+ 3u
30
+ ··· − 4u
2
+ 1
−u
33
− u
32
+ ··· + u + 1
a
11
=
−u
15
+ 2u
13
− 6u
11
+ 8u
9
− 10u
7
+ 8u
5
− 4u
3
+ 2u
−u
15
+ u
13
− 4u
11
+ 3u
9
− 4u
7
+ 2u
5
− 2u
3
+ u
a
11
=
−u
15
+ 2u
13
− 6u
11
+ 8u
9
− 10u
7
+ 8u
5
− 4u
3
+ 2u
−u
15
+ u
13
− 4u
11
+ 3u
9
− 4u
7
+ 2u
5
− 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
33
−16u
31
−4u
30
+68u
29
+12u
28
−180u
27
−52u
26
+420u
25
+112u
24
−788u
23
−244u
22
+
1248u
21
+ 376u
20
−1696u
19
−508u
18
+ 1916u
17
+ 528u
16
−1876u
15
−436u
14
+ 1504u
13
+
248u
12
−1040u
11
−76u
10
+584u
9
−16u
8
−276u
7
+32u
6
+108u
5
−24u
4
−28u
3
+12u
2
+12u−14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
34
+ u
33
+ ··· − u − 1
c
2
, c
5
, c
6
c
8
u
34
+ 7u
33
+ ··· + 7u + 1
c
3
, c
4
, c
10
u
34
− u
33
+ ··· − 3u − 1
c
9
, c
11
u
34
+ u
33
+ ··· − 11u − 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
34
− 7y
33
+ ··· − 7y + 1
c
2
, c
5
, c
6
c
8
y
34
+ 41y
33
+ ··· + y + 1
c
3
, c
4
, c
10
y
34
+ 29y
33
+ ··· − 7y + 1
c
9
, c
11
y
34
− 15y
33
+ ··· − 25y + 4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.747104 + 0.637416I
6.64470 + 2.36489I −2.86883 − 3.72968I
u = −0.747104 − 0.637416I
6.64470 − 2.36489I −2.86883 + 3.72968I
u = −0.899925 + 0.475897I
−2.14151 + 4.62376I −13.8382 − 7.0838I
u = −0.899925 − 0.475897I
−2.14151 − 4.62376I −13.8382 + 7.0838I
u = 0.872014 + 0.400496I
0.949146 − 0.978585I −10.88963 + 3.28439I
u = 0.872014 − 0.400496I
0.949146 + 0.978585I −10.88963 − 3.28439I
u = 0.922322 + 0.514518I
2.40379 − 8.43362I −8.56504 + 8.66068I
u = 0.922322 − 0.514518I
2.40379 + 8.43362I −8.56504 − 8.66068I
u = −0.911159 + 0.064557I
−0.80027 + 3.72913I −14.4528 − 4.1895I
u = −0.911159 − 0.064557I
−0.80027 − 3.72913I −14.4528 + 4.1895I
u = 0.901185
−4.70685 −19.4900
u = 0.703635 + 0.475487I
1.07563 − 1.83024I −6.47079 + 5.97936I
u = 0.703635 − 0.475487I
1.07563 + 1.83024I −6.47079 − 5.97936I
u = 0.484387 + 0.660768I
3.79773 + 4.05189I −4.65777 − 2.65947I
u = 0.484387 − 0.660768I
3.79773 − 4.05189I −4.65777 + 2.65947I
u = −0.905647 + 0.876658I
8.74108 + 3.00465I −6.23462 − 3.51022I
u = −0.905647 − 0.876658I
8.74108 − 3.00465I −6.23462 + 3.51022I
u = 0.887193 + 0.895874I
6.61353 + 1.01180I −9.12967 − 1.18783I
u = 0.887193 − 0.895874I
6.61353 − 1.01180I −9.12967 + 1.18783I
u = −0.885998 + 0.911204I
11.67770 − 4.89843I −4.67803 + 2.35929I
u = −0.885998 − 0.911204I
11.67770 + 4.89843I −4.67803 − 2.35929I
u = −0.933946 + 0.863515I
8.64990 + 3.44136I −6.50419 − 1.50666I
u = −0.933946 − 0.863515I
8.64990 − 3.44136I −6.50419 + 1.50666I
u = −0.440591 + 0.564184I
−0.754026 − 0.647677I −10.09307 + 0.88782I
u = −0.440591 − 0.564184I
−0.754026 + 0.647677I −10.09307 − 0.88782I
u = 0.957008 + 0.864633I
6.39073 − 7.51888I −9.58479 + 5.88933I
u = 0.957008 − 0.864633I
6.39073 + 7.51888I −9.58479 − 5.88933I
u = 0.933149 + 0.900837I
15.8663 − 3.3207I −2.12280 + 2.39131I
u = 0.933149 − 0.900837I
15.8663 + 3.3207I −2.12280 − 2.39131I
u = −0.967526 + 0.871929I
11.4151 + 11.4767I −5.20067 − 7.04203I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.967526 − 0.871929I
11.4151 − 11.4767I −5.20067 + 7.04203I
u = 0.226712 + 0.537212I
2.73574 − 2.31248I −4.68504 + 3.18940I
u = 0.226712 − 0.537212I
2.73574 + 2.31248I −4.68504 − 3.18940I
u = −0.490234
−0.620230 −16.5580
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
34
+ u
33
+ ··· − u − 1
c
2
, c
5
, c
6
c
8
u
34
+ 7u
33
+ ··· + 7u + 1
c
3
, c
4
, c
10
u
34
− u
33
+ ··· − 3u − 1
c
9
, c
11
u
34
+ u
33
+ ··· − 11u − 2
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
34
− 7y
33
+ ··· − 7y + 1
c
2
, c
5
, c
6
c
8
y
34
+ 41y
33
+ ··· + y + 1
c
3
, c
4
, c
10
y
34
+ 29y
33
+ ··· − 7y + 1
c
9
, c
11
y
34
− 15y
33
+ ··· − 25y + 4
8
