11a
236
(K11a
236
)
A knot diagram
1
Linearized knot diagam
7 1 11 10 9 8 2 3 4 5 6
Solving Sequence
2,7
8 1 3 9 6 5 11 4 10
c
7
c
1
c
2
c
8
c
6
c
5
c
11
c
3
c
10
c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
48
− 2u
47
+ ··· − 4u + 1i
I
u
2
= hu + 1i
* 2 irreducible components of dim
C
= 0, with total 49 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
48
− 2u
47
+ · · · − 4u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
9
=
−u
8
+ u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
+ 2u
2
a
6
=
−u
2
+ 1
−u
4
a
5
=
−u
20
+ 3u
18
− 7u
16
+ 10u
14
− 10u
12
+ 7u
10
− u
8
− 2u
6
+ 3u
4
− 3u
2
+ 1
−u
20
+ 4u
18
− 10u
16
+ 18u
14
− 23u
12
+ 24u
10
− 18u
8
+ 10u
6
− 5u
4
a
11
=
−u
7
+ 2u
5
− 2u
3
+ 2u
−u
9
+ u
7
− u
5
+ u
a
4
=
−u
19
+ 4u
17
− 10u
15
+ 18u
13
− 23u
11
+ 24u
9
− 18u
7
+ 10u
5
− 5u
3
−u
21
+ 3u
19
− 7u
17
+ 10u
15
− 10u
13
+ 7u
11
− u
9
− 2u
7
+ 3u
5
− 3u
3
+ u
a
10
=
−2u
47
+ 3u
46
+ ··· − 4u + 2
−u
47
+ 3u
46
+ ··· − 6u + 2
a
10
=
−2u
47
+ 3u
46
+ ··· − 4u + 2
−u
47
+ 3u
46
+ ··· − 6u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 8u
47
− 12u
46
+ ··· + 28u − 26
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
48
+ 2u
47
+ ··· + 4u + 1
c
2
, c
6
u
48
+ 16u
47
+ ··· + 8u + 1
c
3
, c
5
u
48
− 3u
47
+ ··· − 20u
2
+ 1
c
4
, c
9
, c
10
u
48
+ 2u
47
+ ··· + 4u + 1
c
8
, c
11
u
48
− 14u
46
+ ··· + 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
48
− 16y
47
+ ··· − 8y + 1
c
2
, c
6
y
48
+ 32y
47
+ ··· − 8y + 1
c
3
, c
5
y
48
+ 27y
47
+ ··· − 40y + 1
c
4
, c
9
, c
10
y
48
− 40y
47
+ ··· − 8y + 1
c
8
, c
11
y
48
− 28y
47
+ ··· + 72y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.882555 + 0.461026I
−3.01031 − 4.88758I −15.6251 + 6.5404I
u = 0.882555 − 0.461026I
−3.01031 + 4.88758I −15.6251 − 6.5404I
u = 0.665767 + 0.762214I
0.632478 + 0.108144I −9.55124 + 0.86883I
u = 0.665767 − 0.762214I
0.632478 − 0.108144I −9.55124 − 0.86883I
u = −0.639372 + 0.784790I
3.51281 − 4.08944I −6.57921 + 3.06594I
u = −0.639372 − 0.784790I
3.51281 + 4.08944I −6.57921 − 3.06594I
u = 0.624433 + 0.797000I
−1.18842 + 8.10290I −11.33189 − 4.69039I
u = 0.624433 − 0.797000I
−1.18842 − 8.10290I −11.33189 + 4.69039I
u = −0.785703 + 0.584322I
1.37338 + 2.15146I −8.25248 − 5.45590I
u = −0.785703 − 0.584322I
1.37338 − 2.15146I −8.25248 + 5.45590I
u = −1.02158
−4.93269 −18.1530
u = 0.644420 + 0.678291I
0.048446 + 0.560613I −11.68780 − 1.95261I
u = 0.644420 − 0.678291I
0.048446 − 0.560613I −11.68780 + 1.95261I
u = 1.070420 + 0.070047I
−2.46715 − 3.58742I −13.8838 + 4.2943I
u = 1.070420 − 0.070047I
−2.46715 + 3.58742I −13.8838 − 4.2943I
u = −0.921125
−4.91974 −18.6280
u = −0.555627 + 0.727194I
−5.98604 − 1.18604I −15.5397 + 0.4606I
u = −0.555627 − 0.727194I
−5.98604 + 1.18604I −15.5397 − 0.4606I
u = −1.093390 + 0.071584I
−7.29017 + 7.41299I −18.4799 − 5.5389I
u = −1.093390 − 0.071584I
−7.29017 − 7.41299I −18.4799 + 5.5389I
u = 1.09915
−11.4368 −21.8600
u = −0.841196 + 0.750320I
3.16432 − 1.24428I −8.04097 + 0.56162I
u = −0.841196 − 0.750320I
3.16432 + 1.24428I −8.04097 − 0.56162I
u = 0.863763 + 0.744913I
6.99140 − 2.82021I −3.95134 + 3.08292I
u = 0.863763 − 0.744913I
6.99140 + 2.82021I −3.95134 − 3.08292I
u = −0.977993 + 0.605871I
0.66805 + 2.46888I −10.26548 − 1.31520I
u = −0.977993 − 0.605871I
0.66805 − 2.46888I −10.26548 + 1.31520I
u = −0.885079 + 0.741658I
3.03130 + 6.89085I −8.49212 − 6.46442I
u = −0.885079 − 0.741658I
3.03130 − 6.89085I −8.49212 + 6.46442I
u = 1.009840 + 0.589266I
−4.16473 + 0.96747I −15.6034 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.009840 − 0.589266I
−4.16473 − 0.96747I −15.6034 + 0.I
u = 0.996479 + 0.655041I
−0.98972 − 5.75638I −13.3076 + 6.8650I
u = 0.996479 − 0.655041I
−0.98972 + 5.75638I −13.3076 − 6.8650I
u = −1.031620 + 0.650416I
−7.35665 + 6.46067I −17.5687 − 5.3712I
u = −1.031620 − 0.650416I
−7.35665 − 6.46067I −17.5687 + 5.3712I
u = 1.006860 + 0.688557I
−0.39402 − 5.62399I −11.59767 + 4.05733I
u = 1.006860 − 0.688557I
−0.39402 + 5.62399I −11.59767 − 4.05733I
u = −1.024260 + 0.692231I
2.35847 + 9.67537I −8.68198 − 7.82216I
u = −1.024260 − 0.692231I
2.35847 − 9.67537I −8.68198 + 7.82216I
u = 1.033900 + 0.692265I
−2.41639 − 13.71870I −13.3452 + 9.2783I
u = 1.033900 − 0.692265I
−2.41639 + 13.71870I −13.3452 − 9.2783I
u = 0.376949 + 0.637932I
−2.56451 − 5.60912I −12.01724 + 5.48028I
u = 0.376949 − 0.637932I
−2.56451 + 5.60912I −12.01724 − 5.48028I
u = −0.339798 + 0.564531I
1.97900 + 1.93404I −6.47322 − 4.04899I
u = −0.339798 − 0.564531I
1.97900 − 1.93404I −6.47322 + 4.04899I
u = 0.209593 + 0.518446I
−1.32155 + 1.52053I −9.58208 − 0.33085I
u = 0.209593 − 0.518446I
−1.32155 − 1.52053I −9.58208 + 0.33085I
u = 0.421695
−0.568709 −17.6430
6
II. I
u
2
= hu + 1i
(i) Arc colorings
a
2
=
0
−1
a
7
=
1
0
a
8
=
1
1
a
1
=
−1
−1
a
3
=
1
0
a
9
=
0
1
a
6
=
0
−1
a
5
=
0
−1
a
11
=
−1
0
a
4
=
1
0
a
10
=
−1
1
a
10
=
−1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −18
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
7
c
8
, c
9
, c
10
c
11
u − 1
c
2
, c
6
u + 1
c
3
, c
5
u
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
7
, c
8
c
9
, c
10
, c
11
y −1
c
3
, c
5
y
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
−4.93480 −18.0000
10
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
(u − 1)(u
48
+ 2u
47
+ ··· + 4u + 1)
c
2
, c
6
(u + 1)(u
48
+ 16u
47
+ ··· + 8u + 1)
c
3
, c
5
u(u
48
− 3u
47
+ ··· − 20u
2
+ 1)
c
4
, c
9
, c
10
(u − 1)(u
48
+ 2u
47
+ ··· + 4u + 1)
c
8
, c
11
(u − 1)(u
48
− 14u
46
+ ··· + 4u + 1)
11
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y −1)(y
48
− 16y
47
+ ··· − 8y + 1)
c
2
, c
6
(y −1)(y
48
+ 32y
47
+ ··· − 8y + 1)
c
3
, c
5
y(y
48
+ 27y
47
+ ··· − 40y + 1)
c
4
, c
9
, c
10
(y −1)(y
48
− 40y
47
+ ··· − 8y + 1)
c
8
, c
11
(y −1)(y
48
− 28y
47
+ ··· + 72y + 1)
12
