11a
241
(K11a
241
)
A knot diagram
1
Linearized knot diagam
7 1 11 10 8 9 2 6 3 4 5
Solving Sequence
4,10 5,8
6 11 1 3 2 7 9
c
4
c
5
c
10
c
11
c
3
c
2
c
7
c
9
c
1
, c
6
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
49
+ 2u
48
+ ··· + b − 1, −u
49
− 2u
48
+ ··· + a + u, u
50
+ 2u
49
+ ··· + 2u − 1i
I
u
2
= hb − u − 1, u
2
+ a + u + 2, u
3
+ u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 53 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
49
+2u
48
+· · ·+b−1, −u
49
−2u
48
+· · ·+a+u, u
50
+2u
49
+· · ·+2u−1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
8
=
u
49
+ 2u
48
+ ··· + 9u
2
− u
−u
49
− 2u
48
+ ··· − u + 1
a
6
=
u
49
+ 2u
48
+ ··· + 5u
2
+ u
−u
48
− 2u
47
+ ··· − 2u + 1
a
11
=
−u
u
a
1
=
−u
3
− 2u
−u
5
− u
3
+ u
a
3
=
u
2
+ 1
−u
2
a
2
=
−u
10
− 5u
8
− 8u
6
− 3u
4
+ 3u
2
+ 1
−u
12
− 4u
10
− 4u
8
+ 2u
6
+ 3u
4
− 2u
2
a
7
=
u
49
+ 2u
48
+ ··· + 5u − 1
u
49
+ 18u
47
+ ··· − 2u + 1
a
9
=
u
5
+ 2u
3
+ u
−u
5
− u
3
+ u
a
9
=
u
5
+ 2u
3
+ u
−u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
49
+ 2u
48
+ ··· − 5u − 13
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
50
+ u
49
+ ··· + 20u + 8
c
2
u
50
+ 21u
49
+ ··· + 592u + 64
c
3
, c
4
, c
10
u
50
− 2u
49
+ ··· − 2u − 1
c
5
, c
6
, c
8
u
50
− 4u
49
+ ··· − 3u − 1
c
9
, c
11
u
50
+ 2u
49
+ ··· − 92u − 17
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
50
− 21y
49
+ ··· − 592y + 64
c
2
y
50
+ 11y
49
+ ··· − 19712y + 4096
c
3
, c
4
, c
10
y
50
+ 42y
49
+ ··· − 2y + 1
c
5
, c
6
, c
8
y
50
− 44y
49
+ ··· − 3y + 1
c
9
, c
11
y
50
− 30y
49
+ ··· + 70y + 289
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.367759 + 1.080260I
a = 1.274030 − 0.076271I
b = −2.79298 − 1.22823I
−4.88671 − 5.18577I −14.7099 + 2.7132I
u = −0.367759 − 1.080260I
a = 1.274030 + 0.076271I
b = −2.79298 + 1.22823I
−4.88671 + 5.18577I −14.7099 − 2.7132I
u = −0.292411 + 1.122110I
a = 0.063602 + 0.178201I
b = 0.357273 + 0.494914I
0.61352 − 1.42597I −11.17419 + 2.49743I
u = −0.292411 − 1.122110I
a = 0.063602 − 0.178201I
b = 0.357273 − 0.494914I
0.61352 + 1.42597I −11.17419 − 2.49743I
u = −0.835547
a = 3.17253
b = 0.721481
−12.3381 −20.6750
u = −0.815626 + 0.148361I
a = 2.61545 + 1.17715I
b = 0.549537 + 0.451977I
−7.73338 + 9.49487I −17.3734 − 6.5886I
u = −0.815626 − 0.148361I
a = 2.61545 − 1.17715I
b = 0.549537 − 0.451977I
−7.73338 − 9.49487I −17.3734 + 6.5886I
u = 0.304563 + 1.171450I
a = −2.12969 − 0.09359I
b = 4.12999 − 1.54851I
−2.05727 − 0.60926I −13.40155 + 0.I
u = 0.304563 − 1.171450I
a = −2.12969 + 0.09359I
b = 4.12999 + 1.54851I
−2.05727 + 0.60926I −13.40155 + 0.I
u = −0.777098 + 0.128997I
a = −0.922897 + 0.254550I
b = −0.222769 − 0.477721I
−2.36749 + 5.37835I −14.0557 − 6.0904I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.777098 − 0.128997I
a = −0.922897 − 0.254550I
b = −0.222769 + 0.477721I
−2.36749 − 5.37835I −14.0557 + 6.0904I
u = 0.772297 + 0.099116I
a = −3.28933 + 1.31312I
b = −0.788912 + 0.473334I
−5.29863 − 3.31697I −16.7691 + 3.0814I
u = 0.772297 − 0.099116I
a = −3.28933 − 1.31312I
b = −0.788912 − 0.473334I
−5.29863 + 3.31697I −16.7691 − 3.0814I
u = −0.748495 + 0.067917I
a = −1.225140 − 0.393644I
b = 0.168459 + 0.395472I
−4.29681 + 0.76442I −18.3162 − 1.2723I
u = −0.748495 − 0.067917I
a = −1.225140 + 0.393644I
b = 0.168459 − 0.395472I
−4.29681 − 0.76442I −18.3162 + 1.2723I
u = −0.300001 + 1.216560I
a = −0.732766 − 0.843732I
b = 1.18393 + 1.18605I
−0.78921 + 3.02934I 0
u = −0.300001 − 1.216560I
a = −0.732766 + 0.843732I
b = 1.18393 − 1.18605I
−0.78921 − 3.02934I 0
u = 0.396406 + 0.624218I
a = 1.10662 − 1.27223I
b = −0.984367 + 0.603627I
−3.70738 − 5.14926I −14.3632 + 6.3732I
u = 0.396406 − 0.624218I
a = 1.10662 + 1.27223I
b = −0.984367 − 0.603627I
−3.70738 + 5.14926I −14.3632 − 6.3732I
u = 0.214240 + 1.257320I
a = 0.498732 + 0.074085I
b = −1.029970 + 0.417924I
2.72213 − 2.30998I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.214240 − 1.257320I
a = 0.498732 − 0.074085I
b = −1.029970 − 0.417924I
2.72213 + 2.30998I 0
u = 0.625043 + 0.306332I
a = 1.44268 − 0.83843I
b = −0.575863 + 0.474119I
−4.77278 + 1.48125I −17.3142 − 0.2721I
u = 0.625043 − 0.306332I
a = 1.44268 + 0.83843I
b = −0.575863 − 0.474119I
−4.77278 − 1.48125I −17.3142 + 0.2721I
u = −0.380094 + 1.257640I
a = 1.75256 + 1.12877I
b = −2.93137 − 3.26120I
−8.44132 + 4.36522I 0
u = −0.380094 − 1.257640I
a = 1.75256 − 1.12877I
b = −2.93137 + 3.26120I
−8.44132 − 4.36522I 0
u = 0.666165 + 0.120010I
a = 0.966211 + 0.119156I
b = 0.304071 − 0.280867I
−0.711738 − 0.697273I −10.71279 + 1.15101I
u = 0.666165 − 0.120010I
a = 0.966211 − 0.119156I
b = 0.304071 + 0.280867I
−0.711738 + 0.697273I −10.71279 − 1.15101I
u = −0.019632 + 1.351750I
a = 0.23638 − 1.46435I
b = 0.66874 + 2.33992I
3.75475 + 1.24423I 0
u = −0.019632 − 1.351750I
a = 0.23638 + 1.46435I
b = 0.66874 − 2.33992I
3.75475 − 1.24423I 0
u = −0.317517 + 1.315330I
a = 0.122364 − 0.368282I
b = 0.462053 + 0.996285I
0.04307 + 4.61787I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.317517 − 1.315330I
a = 0.122364 + 0.368282I
b = 0.462053 − 0.996285I
0.04307 − 4.61787I 0
u = 0.287032 + 1.337150I
a = 1.037980 − 0.647453I
b = −1.40488 + 1.30184I
3.88325 − 4.20193I 0
u = 0.287032 − 1.337150I
a = 1.037980 + 0.647453I
b = −1.40488 − 1.30184I
3.88325 + 4.20193I 0
u = 0.331579 + 1.330070I
a = −1.69831 + 2.26896I
b = 2.16421 − 5.01806I
−0.80897 − 7.30656I 0
u = 0.331579 − 1.330070I
a = −1.69831 − 2.26896I
b = 2.16421 + 5.01806I
−0.80897 + 7.30656I 0
u = 0.031726 + 1.385860I
a = 0.117801 + 1.234380I
b = −0.25515 − 1.61002I
7.10349 − 2.64910I 0
u = 0.031726 − 1.385860I
a = 0.117801 − 1.234380I
b = −0.25515 + 1.61002I
7.10349 + 2.64910I 0
u = −0.332926 + 1.345880I
a = −0.999826 − 0.769402I
b = 1.25204 + 1.35725I
2.27588 + 9.39250I 0
u = −0.332926 − 1.345880I
a = −0.999826 + 0.769402I
b = 1.25204 − 1.35725I
2.27588 − 9.39250I 0
u = 0.202172 + 0.562210I
a = −0.048043 + 0.695323I
b = 0.026647 + 0.413386I
1.12881 − 2.03777I −7.78527 + 5.62795I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.202172 − 0.562210I
a = −0.048043 − 0.695323I
b = 0.026647 − 0.413386I
1.12881 + 2.03777I −7.78527 − 5.62795I
u = 0.237505 + 1.383800I
a = −0.179690 − 0.698918I
b = −0.46220 + 1.34014I
0.55189 − 1.61966I 0
u = 0.237505 − 1.383800I
a = −0.179690 + 0.698918I
b = −0.46220 − 1.34014I
0.55189 + 1.61966I 0
u = −0.350812 + 1.359940I
a = 1.22082 + 2.12971I
b = −1.48792 − 4.49301I
−2.97930 + 13.70140I 0
u = −0.350812 − 1.359940I
a = 1.22082 − 2.12971I
b = −1.48792 + 4.49301I
−2.97930 − 13.70140I 0
u = 0.06826 + 1.41694I
a = −0.365259 − 1.175510I
b = −0.35719 + 1.98198I
2.73057 − 6.43368I 0
u = 0.06826 − 1.41694I
a = −0.365259 + 1.175510I
b = −0.35719 − 1.98198I
2.73057 + 6.43368I 0
u = −0.166424 + 0.369815I
a = −1.27663 − 2.18999I
b = 1.009330 + 0.248240I
−1.55529 + 0.78493I −9.19094 − 1.36537I
u = −0.166424 − 0.369815I
a = −1.27663 + 2.18999I
b = 1.009330 − 0.248240I
−1.55529 − 0.78493I −9.19094 + 1.36537I
u = 0.299163
a = 0.652170
b = 0.313109
−0.616490 −16.5510
9
II. I
u
2
= hb − u − 1, u
2
+ a + u + 2, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
8
=
−u
2
− u − 2
u + 1
a
6
=
−u
2
− u − 1
u
2
+ u + 1
a
11
=
−u
u
a
1
=
u
2
+ 1
−u
2
a
3
=
u
2
+ 1
−u
2
a
2
=
u
2
+ 1
−u
2
a
7
=
−u
2
− u − 2
u + 1
a
9
=
−1
−u
2
a
9
=
−1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
2
− 4u − 16
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
3
c
3
, c
4
u
3
+ u
2
+ 2u + 1
c
5
, c
6
(u − 1)
3
c
8
(u + 1)
3
c
9
, c
11
u
3
+ u
2
− 1
c
10
u
3
− u
2
+ 2u − 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
y
3
c
3
, c
4
, c
10
y
3
+ 3y
2
+ 2y −1
c
5
, c
6
, c
8
(y −1)
3
c
9
, c
11
y
3
− y
2
+ 2y −1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = −0.122561 − 0.744862I
b = 0.78492 + 1.30714I
1.37919 + 2.82812I −10.15260 − 3.54173I
u = −0.215080 − 1.307140I
a = −0.122561 + 0.744862I
b = 0.78492 − 1.30714I
1.37919 − 2.82812I −10.15260 + 3.54173I
u = −0.569840
a = −1.75488
b = 0.430160
−2.75839 −14.6950
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
3
(u
50
+ u
49
+ ··· + 20u + 8)
c
2
u
3
(u
50
+ 21u
49
+ ··· + 592u + 64)
c
3
, c
4
(u
3
+ u
2
+ 2u + 1)(u
50
− 2u
49
+ ··· − 2u − 1)
c
5
, c
6
((u − 1)
3
)(u
50
− 4u
49
+ ··· − 3u − 1)
c
8
((u + 1)
3
)(u
50
− 4u
49
+ ··· − 3u − 1)
c
9
, c
11
(u
3
+ u
2
− 1)(u
50
+ 2u
49
+ ··· − 92u − 17)
c
10
(u
3
− u
2
+ 2u − 1)(u
50
− 2u
49
+ ··· − 2u − 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
3
(y
50
− 21y
49
+ ··· − 592y + 64)
c
2
y
3
(y
50
+ 11y
49
+ ··· − 19712y + 4096)
c
3
, c
4
, c
10
(y
3
+ 3y
2
+ 2y −1)(y
50
+ 42y
49
+ ··· − 2y + 1)
c
5
, c
6
, c
8
((y −1)
3
)(y
50
− 44y
49
+ ··· − 3y + 1)
c
9
, c
11
(y
3
− y
2
+ 2y −1)(y
50
− 30y
49
+ ··· + 70y + 289)
15
