11a
204
(K11a
204
)
A knot diagram
1
Linearized knot diagam
6 1 10 9 8 2 11 3 4 5 7
Solving Sequence
2,7
6 1 3 11 8 9 5 4 10
c
6
c
1
c
2
c
11
c
7
c
8
c
5
c
4
c
10
c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
50
− u
49
+ ··· + u − 1i
* 1 irreducible components of dim
C
= 0, with total 50 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
50
− u
49
+ · · · + u − 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
3
u
5
− u
3
+ u
a
11
=
u
3
−u
3
+ u
a
8
=
u
6
− u
4
+ 1
−u
6
+ 2u
4
− u
2
a
9
=
−u
14
+ 3u
12
− 4u
10
+ u
8
+ 2u
6
− 2u
4
+ 1
u
16
− 4u
14
+ 8u
12
− 8u
10
+ 4u
8
a
5
=
−u
14
+ 3u
12
− 4u
10
+ u
8
+ 2u
6
− 2u
4
+ 1
u
14
− 4u
12
+ 7u
10
− 6u
8
+ 2u
6
− u
2
a
4
=
−u
44
+ 11u
42
+ ··· − u
2
+ 1
u
46
− 12u
44
+ ··· + 2u
6
− u
2
a
10
=
−u
25
+ 6u
23
+ ··· − 3u
5
+ u
u
25
− 7u
23
+ ··· − 2u
3
+ u
a
10
=
−u
25
+ 6u
23
+ ··· − 3u
5
+ u
u
25
− 7u
23
+ ··· − 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
48
+ 52u
46
+ ··· + 8u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
50
− u
49
+ ··· + u − 1
c
2
u
50
+ 27u
49
+ ··· + 3u + 1
c
3
, c
4
, c
9
u
50
+ u
49
+ ··· − 3u − 1
c
5
u
50
− 7u
49
+ ··· − 111u + 37
c
7
, c
11
u
50
− 3u
49
+ ··· + u + 1
c
8
, c
10
u
50
− u
49
+ ··· − 45u − 17
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
50
− 27y
49
+ ··· − 3y + 1
c
2
y
50
− 7y
49
+ ··· − 7y + 1
c
3
, c
4
, c
9
y
50
+ 41y
49
+ ··· − 3y + 1
c
5
y
50
− 11y
49
+ ··· − 28823y + 1369
c
7
, c
11
y
50
+ 41y
49
+ ··· − 111y + 1
c
8
, c
10
y
50
− 35y
49
+ ··· + 457y + 289
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.898377 + 0.505512I
−2.14014 + 4.60582I −9.82761 − 7.01636I
u = −0.898377 − 0.505512I
−2.14014 − 4.60582I −9.82761 + 7.01636I
u = 0.886274 + 0.537129I
2.36766 − 8.44259I −4.56565 + 8.69974I
u = 0.886274 − 0.537129I
2.36766 + 8.44259I −4.56565 − 8.69974I
u = 0.940835 + 0.435517I
1.03261 − 1.03580I −6.91855 + 2.91618I
u = 0.940835 − 0.435517I
1.03261 + 1.03580I −6.91855 − 2.91618I
u = 1.04249
−5.57110 −16.4420
u = −1.048370 + 0.049358I
−1.64759 + 4.00369I −11.91063 − 3.67666I
u = −1.048370 − 0.049358I
−1.64759 − 4.00369I −11.91063 + 3.67666I
u = −0.764066 + 0.531630I
6.63211 + 2.15686I 0.57370 − 3.89945I
u = −0.764066 − 0.531630I
6.63211 − 2.15686I 0.57370 + 3.89945I
u = 0.774496 + 0.423862I
0.95587 − 1.83688I −2.97268 + 5.52059I
u = 0.774496 − 0.423862I
0.95587 + 1.83688I −2.97268 − 5.52059I
u = 0.131214 + 0.816301I
−1.25862 + 8.74450I −6.26482 − 5.70892I
u = 0.131214 − 0.816301I
−1.25862 − 8.74450I −6.26482 + 5.70892I
u = −0.113334 + 0.813002I
−5.75677 − 4.53837I −10.90083 + 3.52404I
u = −0.113334 − 0.813002I
−5.75677 + 4.53837I −10.90083 − 3.52404I
u = 0.600001 + 0.552718I
3.16690 + 4.05720I −2.39559 − 2.41761I
u = 0.600001 − 0.552718I
3.16690 − 4.05720I −2.39559 + 2.41761I
u = 0.088090 + 0.807114I
−2.52256 + 0.29931I −7.87191 + 0.33424I
u = 0.088090 − 0.807114I
−2.52256 − 0.29931I −7.87191 − 0.33424I
u = 1.124710 + 0.394492I
0.834215 − 0.681511I −6.55623 + 0.I
u = 1.124710 − 0.394492I
0.834215 + 0.681511I −6.55623 + 0.I
u = −1.169100 + 0.434672I
−4.41097 + 2.59787I −11.45875 + 0.I
u = −1.169100 − 0.434672I
−4.41097 − 2.59787I −11.45875 + 0.I
u = −1.157340 + 0.497610I
1.58916 + 7.35454I 0
u = −1.157340 − 0.497610I
1.58916 − 7.35454I 0
u = −0.542490 + 0.497935I
−1.186550 − 0.458750I −7.63805 + 0.36311I
u = −0.542490 − 0.497935I
−1.186550 + 0.458750I −7.63805 − 0.36311I
u = 1.173630 + 0.470826I
−4.14754 − 5.79334I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.173630 − 0.470826I
−4.14754 + 5.79334I 0
u = −0.173744 + 0.706786I
4.42834 − 2.79951I −1.47445 + 3.26453I
u = −0.173744 − 0.706786I
4.42834 + 2.79951I −1.47445 − 3.26453I
u = −1.219870 + 0.382444I
−5.33475 − 4.67917I 0
u = −1.219870 − 0.382444I
−5.33475 + 4.67917I 0
u = 1.219490 + 0.394041I
−9.75574 + 0.40809I 0
u = 1.219490 − 0.394041I
−9.75574 − 0.40809I 0
u = −1.217770 + 0.408433I
−6.41473 + 3.90979I 0
u = −1.217770 − 0.408433I
−6.41473 − 3.90979I 0
u = 0.065064 + 0.701160I
−1.00563 + 1.42365I −7.09664 − 4.59801I
u = 0.065064 − 0.701160I
−1.00563 − 1.42365I −7.09664 + 4.59801I
u = 1.203910 + 0.493230I
−5.81092 − 5.03608I 0
u = 1.203910 − 0.493230I
−5.81092 + 5.03608I 0
u = −1.202290 + 0.504191I
−8.97338 + 9.35305I 0
u = −1.202290 − 0.504191I
−8.97338 − 9.35305I 0
u = 1.200010 + 0.511632I
−4.4198 − 13.6080I 0
u = 1.200010 − 0.511632I
−4.4198 + 13.6080I 0
u = 0.406824 + 0.539325I
2.56296 − 2.88378I −2.70702 + 3.08785I
u = 0.406824 − 0.539325I
2.56296 + 2.88378I −2.70702 − 3.08785I
u = −0.658085
−0.823669 −13.0660
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
50
− u
49
+ ··· + u − 1
c
2
u
50
+ 27u
49
+ ··· + 3u + 1
c
3
, c
4
, c
9
u
50
+ u
49
+ ··· − 3u − 1
c
5
u
50
− 7u
49
+ ··· − 111u + 37
c
7
, c
11
u
50
− 3u
49
+ ··· + u + 1
c
8
, c
10
u
50
− u
49
+ ··· − 45u − 17
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
50
− 27y
49
+ ··· − 3y + 1
c
2
y
50
− 7y
49
+ ··· − 7y + 1
c
3
, c
4
, c
9
y
50
+ 41y
49
+ ··· − 3y + 1
c
5
y
50
− 11y
49
+ ··· − 28823y + 1369
c
7
, c
11
y
50
+ 41y
49
+ ··· − 111y + 1
c
8
, c
10
y
50
− 35y
49
+ ··· + 457y + 289
8
