11a
50
(K11a
50
)
A knot diagram
1
Linearized knot diagam
5 1 7 2 4 10 3 11 6 9 8
Solving Sequence
1,5
2 3 4
6,8
7 11 9 10
c
1
c
2
c
4
c
5
c
7
c
11
c
8
c
10
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2u
46
+ 9u
45
+ ··· + 4b + 5, −u
46
+ 18u
45
+ ··· + 4a − 25, u
47
− 4u
46
+ ··· + 6u − 1i
I
u
2
= h−au + b, a
3
− a
2
u − a
2
+ 2au + 1, u
2
+ u + 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
=
h−2u
46
+9u
45
+· · ·+4b+5, −u
46
+18u
45
+· · ·+4a−25, u
47
−4u
46
+· · ·+6u−1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
4
=
−u
u
3
+ u
a
6
=
−u
3
u
5
+ u
3
+ u
a
8
=
1
4
u
46
−
9
2
u
45
+ ··· − 17u +
25
4
1
2
u
46
−
9
4
u
45
+ ··· +
9
4
u −
5
4
a
7
=
7
4
u
46
−
5
2
u
45
+ ··· + 2u +
7
4
−
9
2
u
46
+
41
4
u
45
+ ··· +
35
4
u −
7
4
a
11
=
−
1
4
u
46
+
3
4
u
45
+ ··· +
13
4
u + 2
1
4
u
46
− u
45
+ ··· −
5
2
u +
1
4
a
9
=
−2u
46
+
15
2
u
45
+ ··· + 20u + 1
−
5
4
u
46
+
13
4
u
45
+ ··· −
11
4
u +
1
2
a
10
=
−
7
4
u
46
+
33
4
u
45
+ ··· +
107
4
u −
1
2
−
5
4
u
46
+
9
4
u
45
+ ··· −
31
4
u +
3
2
a
10
=
−
7
4
u
46
+
33
4
u
45
+ ··· +
107
4
u −
1
2
−
5
4
u
46
+
9
4
u
45
+ ··· −
31
4
u +
3
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −9u
46
+
33
2
u
45
+ ··· − 27u − 4
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
47
+ 4u
46
+ ··· + 6u + 1
c
2
, c
5
u
47
+ 14u
46
+ ··· + 38u − 1
c
3
, c
7
u
47
− u
46
+ ··· + 96u + 64
c
6
, c
9
u
47
+ 3u
46
+ ··· − u + 1
c
8
, c
10
, c
11
u
47
+ 11u
46
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
47
+ 14y
46
+ ··· + 38y −1
c
2
, c
5
y
47
+ 42y
46
+ ··· + 2346y −1
c
3
, c
7
y
47
+ 35y
46
+ ··· − 23552y −4096
c
6
, c
9
y
47
− 11y
46
+ ··· + y −1
c
8
, c
10
, c
11
y
47
+ 53y
46
+ ··· + 41y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.663428 + 0.780790I
a = 1.00646 − 1.05901I
b = −0.205400 + 0.577345I
1.047100 − 0.807076I −4.48198 − 0.15159I
u = −0.663428 − 0.780790I
a = 1.00646 + 1.05901I
b = −0.205400 − 0.577345I
1.047100 + 0.807076I −4.48198 + 0.15159I
u = −0.199822 + 1.009780I
a = −0.834043 − 0.291155I
b = −0.625995 − 0.626906I
−2.01497 − 4.25844I −10.22284 + 8.38293I
u = −0.199822 − 1.009780I
a = −0.834043 + 0.291155I
b = −0.625995 + 0.626906I
−2.01497 + 4.25844I −10.22284 − 8.38293I
u = −0.461388 + 0.956277I
a = 0.665200 + 0.526100I
b = −0.316069 + 0.253513I
−0.63663 − 1.64887I −2.14725 − 2.29266I
u = −0.461388 − 0.956277I
a = 0.665200 − 0.526100I
b = −0.316069 − 0.253513I
−0.63663 + 1.64887I −2.14725 + 2.29266I
u = 0.810606 + 0.776375I
a = 0.565835 + 0.632629I
b = −0.750225 − 1.009350I
4.58669 − 3.21526I −3.05328 + 3.33895I
u = 0.810606 − 0.776375I
a = 0.565835 − 0.632629I
b = −0.750225 + 1.009350I
4.58669 + 3.21526I −3.05328 − 3.33895I
u = −0.656947 + 0.912090I
a = −0.22666 + 1.51107I
b = −0.392245 − 0.675540I
0.63898 − 4.31334I −6.53825 + 6.48689I
u = −0.656947 − 0.912090I
a = −0.22666 − 1.51107I
b = −0.392245 + 0.675540I
0.63898 + 4.31334I −6.53825 − 6.48689I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.867038 + 0.019562I
a = 0.12989 + 1.85582I
b = −0.08456 − 1.60423I
9.34836 − 3.22875I 0.48816 + 2.52460I
u = −0.867038 − 0.019562I
a = 0.12989 − 1.85582I
b = −0.08456 + 1.60423I
9.34836 + 3.22875I 0.48816 − 2.52460I
u = −0.311898 + 0.787865I
a = 0.956078 + 0.122134I
b = 0.1036160 + 0.0693880I
−0.33163 − 1.48922I −3.21291 + 4.41196I
u = −0.311898 − 0.787865I
a = 0.956078 − 0.122134I
b = 0.1036160 − 0.0693880I
−0.33163 + 1.48922I −3.21291 − 4.41196I
u = 0.749711 + 0.881463I
a = 0.133762 − 0.692661I
b = −1.094820 − 0.057901I
1.38780 + 2.84463I −7.00000 − 2.87095I
u = 0.749711 − 0.881463I
a = 0.133762 + 0.692661I
b = −1.094820 + 0.057901I
1.38780 − 2.84463I −7.00000 + 2.87095I
u = −0.026264 + 0.834708I
a = −1.139080 − 0.577019I
b = −0.739974 + 0.342805I
−2.87835 + 0.31776I −14.00580 − 0.89851I
u = −0.026264 − 0.834708I
a = −1.139080 + 0.577019I
b = −0.739974 − 0.342805I
−2.87835 − 0.31776I −14.00580 + 0.89851I
u = 0.830386 + 0.839820I
a = 0.137676 − 0.366174I
b = 0.439191 + 0.593639I
6.59048 + 1.40114I 0. − 2.24691I
u = 0.830386 − 0.839820I
a = 0.137676 + 0.366174I
b = 0.439191 − 0.593639I
6.59048 − 1.40114I 0. + 2.24691I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.927893 + 0.738669I
a = 0.28332 + 1.95602I
b = −0.22878 − 1.70233I
13.7092 − 7.1190I 0. + 3.20529I
u = 0.927893 − 0.738669I
a = 0.28332 − 1.95602I
b = −0.22878 + 1.70233I
13.7092 + 7.1190I 0. − 3.20529I
u = −0.294048 + 1.158780I
a = −1.041500 − 0.000140I
b = −0.17743 − 1.57625I
5.33133 − 7.16658I −4.32444 + 6.19083I
u = −0.294048 − 1.158780I
a = −1.041500 + 0.000140I
b = −0.17743 + 1.57625I
5.33133 + 7.16658I −4.32444 − 6.19083I
u = −0.322894 + 1.152850I
a = 1.126820 + 0.062685I
b = −0.03457 + 1.51727I
5.51392 − 0.84918I −3.71085 + 0.I
u = −0.322894 − 1.152850I
a = 1.126820 − 0.062685I
b = −0.03457 − 1.51727I
5.51392 + 0.84918I −3.71085 + 0.I
u = −0.810352 + 0.881677I
a = 1.20304 − 2.40238I
b = −0.06174 + 1.58029I
8.49103 + 0.19218I −2.01859 + 0.I
u = −0.810352 − 0.881677I
a = 1.20304 + 2.40238I
b = −0.06174 − 1.58029I
8.49103 − 0.19218I −2.01859 + 0.I
u = 0.928006 + 0.759035I
a = −0.06191 − 1.86044I
b = 0.10905 + 1.59219I
14.10940 − 0.53726I 0. − 1.50138I
u = 0.928006 − 0.759035I
a = −0.06191 + 1.86044I
b = 0.10905 − 1.59219I
14.10940 + 0.53726I 0. + 1.50138I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.803055 + 0.903733I
a = −0.99990 + 2.49478I
b = −0.11755 − 1.60103I
8.42204 − 6.23223I 0. + 5.02146I
u = −0.803055 − 0.903733I
a = −0.99990 − 2.49478I
b = −0.11755 + 1.60103I
8.42204 + 6.23223I 0. − 5.02146I
u = 0.797400 + 0.942409I
a = 0.817901 + 0.783072I
b = 0.484733 − 0.494859I
6.27252 + 4.67969I 0
u = 0.797400 − 0.942409I
a = 0.817901 − 0.783072I
b = 0.484733 + 0.494859I
6.27252 − 4.67969I 0
u = 0.760355 + 0.975109I
a = −0.78027 − 1.38920I
b = −0.832040 + 0.941509I
3.97968 + 9.12021I −7.00000 − 8.49829I
u = 0.760355 − 0.975109I
a = −0.78027 + 1.38920I
b = −0.832040 − 0.941509I
3.97968 − 9.12021I −7.00000 + 8.49829I
u = 0.236667 + 0.699953I
a = −2.00141 − 0.89361I
b = −0.27531 + 1.39228I
2.56997 + 3.95764I −7.31001 − 0.68586I
u = 0.236667 − 0.699953I
a = −2.00141 + 0.89361I
b = −0.27531 − 1.39228I
2.56997 − 3.95764I −7.31001 + 0.68586I
u = 0.807992 + 1.034530I
a = 1.69856 + 1.55368I
b = 0.14248 − 1.55761I
13.2416 + 6.9328I 0
u = 0.807992 − 1.034530I
a = 1.69856 − 1.55368I
b = 0.14248 + 1.55761I
13.2416 − 6.9328I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.796590 + 1.043640I
a = −1.65368 − 1.73183I
b = −0.26885 + 1.69481I
12.7501 + 13.4737I 0
u = 0.796590 − 1.043640I
a = −1.65368 + 1.73183I
b = −0.26885 − 1.69481I
12.7501 − 13.4737I 0
u = 0.262896 + 0.609439I
a = 2.19053 + 0.65507I
b = −0.102273 − 1.283390I
2.83383 − 1.80935I −5.60137 + 4.89150I
u = 0.262896 − 0.609439I
a = 2.19053 − 0.65507I
b = −0.102273 + 1.283390I
2.83383 + 1.80935I −5.60137 − 4.89150I
u = −0.563257 + 0.159760I
a = 0.608331 + 0.292239I
b = −0.248810 − 0.689997I
1.45889 − 1.89863I −0.82802 + 4.86862I
u = −0.563257 − 0.159760I
a = 0.608331 − 0.292239I
b = −0.248810 + 0.689997I
1.45889 + 1.89863I −0.82802 − 4.86862I
u = 0.143780
a = 3.43014
b = −0.444877
−0.906933 −11.3950
9
II. I
u
2
= h−au + b, a
3
− a
2
u − a
2
+ 2au + 1, u
2
+ u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u + 1
a
3
=
−u
u + 1
a
4
=
−u
u + 1
a
6
=
−1
0
a
8
=
a
au
a
7
=
a
au
a
11
=
−a
2
u + 1
a
2
u + a
2
a
9
=
−a
2
u − au − a + u + 1
a
2
u + a
2
− au − 1
a
10
=
−2a
2
u − a
2
− a + u + 2
a
2
u + a
2
− au − 1
a
10
=
−2a
2
u − a
2
− a + u + 2
a
2
u + a
2
− au − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5a
2
u + 6a
2
− 5au − a + 7u − 10
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
(u
2
+ u + 1)
3
c
3
, c
7
u
6
c
4
(u
2
− u + 1)
3
c
6
(u
3
+ u
2
− 1)
2
c
8
(u
3
− u
2
+ 2u − 1)
2
c
9
(u
3
− u
2
+ 1)
2
c
10
, c
11
(u
3
+ u
2
+ 2u + 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
3
c
3
, c
7
y
6
c
6
, c
9
(y
3
− y
2
+ 2y −1)
2
c
8
, c
10
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 1.239560 − 0.467306I
b = −0.215080 + 1.307140I
3.02413 − 4.85801I −2.74410 + 7.22587I
u = −0.500000 + 0.866025I
a = −1.024480 + 0.839835I
b = −0.215080 − 1.307140I
3.02413 + 0.79824I −4.03424 + 1.64667I
u = −0.500000 + 0.866025I
a = 0.284920 + 0.493496I
b = −0.569840
−1.11345 − 2.02988I −12.72167 + 5.84990I
u = −0.500000 − 0.866025I
a = 1.239560 + 0.467306I
b = −0.215080 − 1.307140I
3.02413 + 4.85801I −2.74410 − 7.22587I
u = −0.500000 − 0.866025I
a = −1.024480 − 0.839835I
b = −0.215080 + 1.307140I
3.02413 − 0.79824I −4.03424 − 1.64667I
u = −0.500000 − 0.866025I
a = 0.284920 − 0.493496I
b = −0.569840
−1.11345 + 2.02988I −12.72167 − 5.84990I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
3
)(u
47
+ 4u
46
+ ··· + 6u + 1)
c
2
, c
5
((u
2
+ u + 1)
3
)(u
47
+ 14u
46
+ ··· + 38u − 1)
c
3
, c
7
u
6
(u
47
− u
46
+ ··· + 96u + 64)
c
4
((u
2
− u + 1)
3
)(u
47
+ 4u
46
+ ··· + 6u + 1)
c
6
((u
3
+ u
2
− 1)
2
)(u
47
+ 3u
46
+ ··· − u + 1)
c
8
((u
3
− u
2
+ 2u − 1)
2
)(u
47
+ 11u
46
+ ··· + u + 1)
c
9
((u
3
− u
2
+ 1)
2
)(u
47
+ 3u
46
+ ··· − u + 1)
c
10
, c
11
((u
3
+ u
2
+ 2u + 1)
2
)(u
47
+ 11u
46
+ ··· + u + 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
3
)(y
47
+ 14y
46
+ ··· + 38y −1)
c
2
, c
5
((y
2
+ y + 1)
3
)(y
47
+ 42y
46
+ ··· + 2346y −1)
c
3
, c
7
y
6
(y
47
+ 35y
46
+ ··· − 23552y −4096)
c
6
, c
9
((y
3
− y
2
+ 2y −1)
2
)(y
47
− 11y
46
+ ··· + y −1)
c
8
, c
10
, c
11
((y
3
+ 3y
2
+ 2y −1)
2
)(y
47
+ 53y
46
+ ··· + 41y −1)
15
