11a
45
(K11a
45
)
A knot diagram
1
Linearized knot diagam
4 1 7 2 10 9 3 11 6 5 8
Solving Sequence
5,10
6
2,11
4 1 9 7 3 8
c
5
c
10
c
4
c
1
c
9
c
6
c
3
c
8
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
43
+ u
42
+ ··· + b + 1, −u
46
− 2u
45
+ ··· + a − 2, u
47
+ 2u
46
+ ··· + 4u + 1i
I
u
2
= hb + 1, −u
3
− u
2
+ a − 3u, u
4
+ u
3
+ 3u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 51 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
43
+u
42
+· · ·+b+1, −u
46
−2u
45
+· · ·+a−2, u
47
+2u
46
+· · ·+4u+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
−u
2
a
2
=
u
46
+ 2u
45
+ ··· + u + 2
−u
43
− u
42
+ ··· − 9u
3
− 1
a
11
=
u
u
a
4
=
u
46
+ 2u
45
+ ··· − u + 2
−u
43
− u
42
+ ··· − u − 1
a
1
=
u
9
+ 4u
7
+ 3u
5
− 2u
3
+ u
u
9
+ 5u
7
+ 7u
5
+ 2u
3
+ u
a
9
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
3
=
u
46
+ 2u
45
+ ··· + 3u + 3
u
44
− u
43
+ ··· + u
2
− 1
a
8
=
u
5
+ 2u
3
− u
u
5
+ 3u
3
+ u
a
8
=
u
5
+ 2u
3
− u
u
5
+ 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
46
+ 2u
45
+ ··· − 7u − 9
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
47
− 5u
46
+ ··· − 8u + 1
c
2
u
47
+ 21u
46
+ ··· − 6u + 1
c
3
, c
7
u
47
+ u
46
+ ··· + 40u + 16
c
5
, c
6
, c
9
c
10
u
47
+ 2u
46
+ ··· + 4u + 1
c
8
, c
11
u
47
− 8u
46
+ ··· + 616u − 49
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
47
− 21y
46
+ ··· − 6y −1
c
2
y
47
+ 15y
46
+ ··· − 262y −1
c
3
, c
7
y
47
+ 27y
46
+ ··· − 3264y −256
c
5
, c
6
, c
9
c
10
y
47
+ 52y
46
+ ··· + 12y −1
c
8
, c
11
y
47
+ 32y
46
+ ··· + 287140y −2401
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.604283 + 0.592983I
a = 1.47187 − 1.86934I
b = 1.126700 + 0.685229I
4.37990 − 10.31740I −1.65034 + 8.68510I
u = −0.604283 − 0.592983I
a = 1.47187 + 1.86934I
b = 1.126700 − 0.685229I
4.37990 + 10.31740I −1.65034 − 8.68510I
u = 0.232115 + 0.798027I
a = 2.24071 + 0.38222I
b = 0.974632 − 0.559034I
−1.04927 + 4.94975I −5.93011 − 7.21371I
u = 0.232115 − 0.798027I
a = 2.24071 − 0.38222I
b = 0.974632 + 0.559034I
−1.04927 − 4.94975I −5.93011 + 7.21371I
u = −0.610300 + 0.553965I
a = −0.902531 − 0.046325I
b = 0.490595 − 0.918525I
6.31726 − 4.42879I 1.23708 + 4.26556I
u = −0.610300 − 0.553965I
a = −0.902531 + 0.046325I
b = 0.490595 + 0.918525I
6.31726 + 4.42879I 1.23708 − 4.26556I
u = 0.564268 + 0.532900I
a = −0.60777 − 2.13982I
b = −0.886230 + 0.571745I
1.15387 + 4.21075I −2.42283 − 6.46620I
u = 0.564268 − 0.532900I
a = −0.60777 + 2.13982I
b = −0.886230 − 0.571745I
1.15387 − 4.21075I −2.42283 + 6.46620I
u = 0.368403 + 0.677743I
a = 0.723270 + 1.043890I
b = 0.725690 + 0.454437I
−0.121886 + 0.686906I −2.62923 − 1.30814I
u = 0.368403 − 0.677743I
a = 0.723270 − 1.043890I
b = 0.725690 − 0.454437I
−0.121886 − 0.686906I −2.62923 + 1.30814I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.631315 + 0.431371I
a = 0.384246 − 0.958542I
b = 0.543018 + 0.899712I
6.67942 + 0.21804I 2.26501 + 2.20975I
u = −0.631315 − 0.431371I
a = 0.384246 + 0.958542I
b = 0.543018 − 0.899712I
6.67942 − 0.21804I 2.26501 − 2.20975I
u = −0.641272 + 0.383119I
a = 0.022026 + 0.485329I
b = 1.094550 − 0.696965I
4.99878 + 6.09831I 0.10454 − 2.74650I
u = −0.641272 − 0.383119I
a = 0.022026 − 0.485329I
b = 1.094550 + 0.696965I
4.99878 − 6.09831I 0.10454 + 2.74650I
u = −0.536843 + 0.494469I
a = −0.97848 + 1.17374I
b = −1.286310 + 0.037305I
−0.20145 − 1.85701I −0.50975 + 4.37782I
u = −0.536843 − 0.494469I
a = −0.97848 − 1.17374I
b = −1.286310 − 0.037305I
−0.20145 + 1.85701I −0.50975 − 4.37782I
u = 0.565661 + 0.444526I
a = 0.741523 + 0.717629I
b = −0.806231 − 0.561068I
1.41432 − 0.32518I −1.284718 − 0.498489I
u = 0.565661 − 0.444526I
a = 0.741523 − 0.717629I
b = −0.806231 + 0.561068I
1.41432 + 0.32518I −1.284718 + 0.498489I
u = −0.073145 + 0.598544I
a = −2.60222 + 1.37444I
b = −1.034680 − 0.259393I
−2.92920 − 0.94552I −11.86909 + 0.58583I
u = −0.073145 − 0.598544I
a = −2.60222 − 1.37444I
b = −1.034680 + 0.259393I
−2.92920 + 0.94552I −11.86909 − 0.58583I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.284667 + 0.487292I
a = 0.588067 + 0.203086I
b = 0.141384 + 0.220781I
−0.038903 + 1.106530I −0.72417 − 6.07516I
u = 0.284667 − 0.487292I
a = 0.588067 − 0.203086I
b = 0.141384 − 0.220781I
−0.038903 − 1.106530I −0.72417 + 6.07516I
u = −0.15656 + 1.43102I
a = 0.964258 − 0.136228I
b = 1.042580 − 0.719852I
−0.77593 + 3.28450I 0
u = −0.15656 − 1.43102I
a = 0.964258 + 0.136228I
b = 1.042580 + 0.719852I
−0.77593 − 3.28450I 0
u = 0.534809 + 0.072952I
a = 0.267834 + 0.634733I
b = 0.841064 − 0.586379I
1.73762 + 2.33285I 1.63431 − 3.88919I
u = 0.534809 − 0.072952I
a = 0.267834 − 0.634733I
b = 0.841064 + 0.586379I
1.73762 − 2.33285I 1.63431 + 3.88919I
u = −0.17342 + 1.46958I
a = 0.892690 − 0.159044I
b = 0.614156 + 0.885412I
0.53093 − 2.62820I 0
u = −0.17342 − 1.46958I
a = 0.892690 + 0.159044I
b = 0.614156 − 0.885412I
0.53093 + 2.62820I 0
u = 0.14450 + 1.50474I
a = 0.086605 + 0.128202I
b = −0.704621 − 0.592796I
−4.99092 + 2.12497I 0
u = 0.14450 − 1.50474I
a = 0.086605 − 0.128202I
b = −0.704621 + 0.592796I
−4.99092 − 2.12497I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.14983 + 1.52897I
a = −2.18209 + 0.88257I
b = −1.313780 + 0.094691I
−6.93429 − 4.28271I 0
u = −0.14983 − 1.52897I
a = −2.18209 − 0.88257I
b = −1.313780 − 0.094691I
−6.93429 + 4.28271I 0
u = 0.04949 + 1.54079I
a = 0.359833 + 0.420302I
b = 0.022840 + 0.536346I
−6.95405 + 2.13733I 0
u = 0.04949 − 1.54079I
a = 0.359833 − 0.420302I
b = 0.022840 − 0.536346I
−6.95405 − 2.13733I 0
u = 0.16493 + 1.53761I
a = −1.47288 − 1.40203I
b = −0.945052 + 0.589157I
−5.72542 + 6.83119I 0
u = 0.16493 − 1.53761I
a = −1.47288 + 1.40203I
b = −0.945052 − 0.589157I
−5.72542 − 6.83119I 0
u = −0.18579 + 1.54140I
a = −0.364549 − 0.727740I
b = 0.443402 − 0.937849I
−0.62096 − 7.31850I 0
u = −0.18579 − 1.54140I
a = −0.364549 + 0.727740I
b = 0.443402 + 0.937849I
−0.62096 + 7.31850I 0
u = −0.01255 + 1.55908I
a = −2.70333 + 0.61165I
b = −1.133330 − 0.334796I
−10.25720 − 1.20723I 0
u = −0.01255 − 1.55908I
a = −2.70333 − 0.61165I
b = −1.133330 + 0.334796I
−10.25720 + 1.20723I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.18591 + 1.55945I
a = 2.26208 − 1.08076I
b = 1.152470 + 0.673628I
−2.78197 − 13.21230I 0
u = −0.18591 − 1.55945I
a = 2.26208 + 1.08076I
b = 1.152470 − 0.673628I
−2.78197 + 13.21230I 0
u = 0.10845 + 1.58073I
a = 1.54084 + 0.82842I
b = 0.782367 + 0.305537I
−7.73076 + 2.45052I 0
u = 0.10845 − 1.58073I
a = 1.54084 − 0.82842I
b = 0.782367 − 0.305537I
−7.73076 − 2.45052I 0
u = 0.04923 + 1.60296I
a = 2.55612 − 0.07351I
b = 1.041330 − 0.500879I
−9.19770 + 5.90087I 0
u = 0.04923 − 1.60296I
a = 2.55612 + 0.07351I
b = 1.041330 + 0.500879I
−9.19770 − 5.90087I 0
u = −0.210582
a = 2.42377
b = −0.853085
−1.24674 −7.85810
9
II. I
u
2
= hb + 1, −u
3
− u
2
+ a − 3u, u
4
+ u
3
+ 3u
2
+ 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
−u
2
a
2
=
u
3
+ u
2
+ 3u
−1
a
11
=
u
u
a
4
=
u
3
+ u
2
+ 3u + 1
−1
a
1
=
−1
0
a
9
=
−u
u
3
+ u
a
7
=
u
2
+ 1
u
3
+ u
2
+ 2u + 1
a
3
=
u
3
+ u
2
+ 3u + 1
−1
a
8
=
u
2
+ 1
u
3
+ u
2
+ 2u + 1
a
8
=
u
2
+ 1
u
3
+ u
2
+ 2u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
3
+ 3u
2
+ 10u − 4
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
c
2
, c
4
(u + 1)
4
c
3
, c
7
u
4
c
5
, c
6
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
8
u
4
+ u
3
+ u
2
+ 1
c
9
, c
10
u
4
− u
3
+ 3u
2
− 2u + 1
c
11
u
4
− u
3
+ u
2
+ 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
4
c
3
, c
7
y
4
c
5
, c
6
, c
9
c
10
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
8
, c
11
y
4
+ y
3
+ 3y
2
+ 2y + 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395123 + 0.506844I
a = −1.04332 + 1.22719I
b = −1.00000
−1.43393 − 1.41510I −7.52507 + 4.18840I
u = −0.395123 − 0.506844I
a = −1.04332 − 1.22719I
b = −1.00000
−1.43393 + 1.41510I −7.52507 − 4.18840I
u = −0.10488 + 1.55249I
a = −1.95668 + 0.64120I
b = −1.00000
−8.43568 − 3.16396I −9.97493 + 3.47609I
u = −0.10488 − 1.55249I
a = −1.95668 − 0.64120I
b = −1.00000
−8.43568 + 3.16396I −9.97493 − 3.47609I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
47
− 5u
46
+ ··· − 8u + 1)
c
2
((u + 1)
4
)(u
47
+ 21u
46
+ ··· − 6u + 1)
c
3
, c
7
u
4
(u
47
+ u
46
+ ··· + 40u + 16)
c
4
((u + 1)
4
)(u
47
− 5u
46
+ ··· − 8u + 1)
c
5
, c
6
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
47
+ 2u
46
+ ··· + 4u + 1)
c
8
(u
4
+ u
3
+ u
2
+ 1)(u
47
− 8u
46
+ ··· + 616u − 49)
c
9
, c
10
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
47
+ 2u
46
+ ··· + 4u + 1)
c
11
(u
4
− u
3
+ u
2
+ 1)(u
47
− 8u
46
+ ··· + 616u − 49)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
4
)(y
47
− 21y
46
+ ··· − 6y −1)
c
2
((y −1)
4
)(y
47
+ 15y
46
+ ··· − 262y −1)
c
3
, c
7
y
4
(y
47
+ 27y
46
+ ··· − 3264y −256)
c
5
, c
6
, c
9
c
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
47
+ 52y
46
+ ··· + 12y −1)
c
8
, c
11
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
47
+ 32y
46
+ ··· + 287140y −2401)
15
