11n
10
(K11n
10
)
A knot diagram
1
Linearized knot diagam
5 1 8 2 3 10 3 11 6 8 9
Solving Sequence
1,5
2 3 6
4,9
11 8 7 10
c
1
c
2
c
5
c
4
c
11
c
8
c
7
c
10
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h8787304659u
35
− 103954721318u
34
+ ··· + 475816620046b − 403612228244,
− 377185205844u
35
+ 1123281301673u
34
+ ··· + 475816620046a − 327197785091,
u
36
− 3u
35
+ ··· + 2u + 1i
I
u
2
= h−au + b + u, a
2
− au − 3a + 2, u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 40 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
= h8.79 × 10
9
u
35
− 1.04 × 10
11
u
34
+ · · · + 4.76× 10
11
b − 4.04 ×10
11
, −3.77 ×
10
11
u
35
+1.12×10
12
u
34
+· · ·+4.76×10
11
a−3.27×10
11
, u
36
−3u
35
+· · ·+2u+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
6
=
−u
5
− 2u
3
− u
u
5
+ u
3
+ u
a
4
=
−u
u
3
+ u
a
9
=
0.792711u
35
− 2.36074u
34
+ ··· − 7.92555u + 0.687655
−0.0184678u
35
+ 0.218476u
34
+ ··· + 2.06332u + 0.848252
a
11
=
1.81069u
35
− 3.83855u
34
+ ··· − 5.73449u + 0.597631
−1.42613u
35
+ 4.12609u
34
+ ··· + 4.24671u + 1.60699
a
8
=
−1.48252u
35
+ 2.76287u
34
+ ··· + 0.445446u + 2.16820
1.68468u
35
− 5.18476u
34
+ ··· − 5.13324u − 1.48252
a
7
=
−3.01339u
35
+ 5.80035u
34
+ ··· + 3.96183u + 2.75504
3.24321u
35
− 9.22497u
34
+ ··· − 6.94504u − 2.40225
a
10
=
−0.224280u
35
− 0.364289u
34
+ ··· − 6.62538u + 1.26123
1.20451u
35
− 3.50438u
34
+ ··· − 0.486823u − 0.427974
a
10
=
−0.224280u
35
− 0.364289u
34
+ ··· − 6.62538u + 1.26123
1.20451u
35
− 3.50438u
34
+ ··· − 0.486823u − 0.427974
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
132200220423
475816620046
u
35
−
80372153223
237908310023
u
34
+ ··· −
2105018315229
475816620046
u +
2668832099181
237908310023
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
36
+ 3u
35
+ ··· − 2u + 1
c
2
u
36
+ 19u
35
+ ··· − 30u + 1
c
3
, c
7
u
36
+ 3u
35
+ ··· − 80u + 16
c
5
u
36
− 3u
35
+ ··· − 552u + 97
c
6
, c
9
u
36
− 3u
35
+ ··· + 7u
2
− 1
c
8
, c
10
, c
11
u
36
+ 3u
35
+ ··· + 8u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
36
+ 19y
35
+ ··· − 30y + 1
c
2
y
36
− y
35
+ ··· − 1390y + 1
c
3
, c
7
y
36
+ 25y
35
+ ··· + 384y + 256
c
5
y
36
− 21y
35
+ ··· − 232342y + 9409
c
6
, c
9
y
36
− 9y
35
+ ··· − 14y + 1
c
8
, c
10
, c
11
y
36
− 29y
35
+ ··· − 14y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.941953 + 0.318856I
a = 1.90171 − 0.06813I
b = −1.330950 + 0.428412I
1.25207 − 7.91102I 10.72087 + 4.98053I
u = 0.941953 − 0.318856I
a = 1.90171 + 0.06813I
b = −1.330950 − 0.428412I
1.25207 + 7.91102I 10.72087 − 4.98053I
u = −0.578922 + 0.827435I
a = 0.466797 − 0.077681I
b = 0.222633 − 0.152510I
0.57502 − 2.28935I 0.59495 + 6.49088I
u = −0.578922 − 0.827435I
a = 0.466797 + 0.077681I
b = 0.222633 + 0.152510I
0.57502 + 2.28935I 0.59495 − 6.49088I
u = −0.462897 + 0.928342I
a = 0.53466 − 3.01700I
b = 0.991548 − 0.131048I
1.36980 − 2.39965I 20.4935 − 7.9827I
u = −0.462897 − 0.928342I
a = 0.53466 + 3.01700I
b = 0.991548 + 0.131048I
1.36980 + 2.39965I 20.4935 + 7.9827I
u = −0.958743
a = 1.33018
b = −1.21120
5.21748 18.9740
u = 0.390666 + 0.829574I
a = 1.76642 − 1.65948I
b = −1.64687 − 0.04349I
8.65750 + 1.68497I 4.45327 + 6.62838I
u = 0.390666 − 0.829574I
a = 1.76642 + 1.65948I
b = −1.64687 + 0.04349I
8.65750 − 1.68497I 4.45327 − 6.62838I
u = −0.352390 + 1.060720I
a = 0.288497 − 0.584924I
b = −0.100145 − 0.439780I
−1.38239 − 2.67848I 3.33680 + 4.36497I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.352390 − 1.060720I
a = 0.288497 + 0.584924I
b = −0.100145 + 0.439780I
−1.38239 + 2.67848I 3.33680 − 4.36497I
u = 0.836718 + 0.162292I
a = 0.139245 + 0.541740I
b = 0.055080 − 0.891815I
−3.08076 − 3.16131I 6.74911 + 2.73736I
u = 0.836718 − 0.162292I
a = 0.139245 − 0.541740I
b = 0.055080 + 0.891815I
−3.08076 + 3.16131I 6.74911 − 2.73736I
u = −0.429143 + 0.677623I
a = −2.71700 + 1.40590I
b = 1.153580 + 0.008712I
2.13722 − 1.37641I 5.40609 + 5.14317I
u = −0.429143 − 0.677623I
a = −2.71700 − 1.40590I
b = 1.153580 − 0.008712I
2.13722 + 1.37641I 5.40609 − 5.14317I
u = 0.418004 + 1.152660I
a = −0.330548 + 0.337367I
b = 1.222910 − 0.619715I
−2.79850 + 2.36350I 5.53508 − 2.60014I
u = 0.418004 − 1.152660I
a = −0.330548 − 0.337367I
b = 1.222910 + 0.619715I
−2.79850 − 2.36350I 5.53508 + 2.60014I
u = −0.917196 + 0.828372I
a = 1.65210 + 0.46733I
b = −1.186090 + 0.089252I
4.37030 − 3.28706I 16.3776 + 6.4044I
u = −0.917196 − 0.828372I
a = 1.65210 − 0.46733I
b = −1.186090 − 0.089252I
4.37030 + 3.28706I 16.3776 − 6.4044I
u = 0.482228 + 1.156400I
a = −1.53682 + 1.54127I
b = 1.42553 + 0.42860I
−2.33330 + 5.78583I 6.12375 − 4.54634I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.482228 − 1.156400I
a = −1.53682 − 1.54127I
b = 1.42553 − 0.42860I
−2.33330 − 5.78583I 6.12375 + 4.54634I
u = 0.355005 + 1.235300I
a = 0.736458 − 0.433010I
b = −0.170722 − 0.941275I
−7.38923 + 0.84480I 2.27275 − 0.94603I
u = 0.355005 − 1.235300I
a = 0.736458 + 0.433010I
b = −0.170722 + 0.941275I
−7.38923 − 0.84480I 2.27275 + 0.94603I
u = 0.528429 + 1.198920I
a = −0.764889 + 0.265751I
b = 0.118707 + 1.039180I
−6.16236 + 8.15772I 4.34763 − 5.90259I
u = 0.528429 − 1.198920I
a = −0.764889 − 0.265751I
b = 0.118707 − 1.039180I
−6.16236 − 8.15772I 4.34763 + 5.90259I
u = 0.191310 + 1.304130I
a = 0.267608 + 0.045241I
b = −1.157150 + 0.494867I
−4.36779 − 4.25736I 4.95189 + 4.14577I
u = 0.191310 − 1.304130I
a = 0.267608 − 0.045241I
b = −1.157150 − 0.494867I
−4.36779 + 4.25736I 4.95189 − 4.14577I
u = 0.667019 + 0.112397I
a = −2.55104 − 0.08549I
b = 1.252170 − 0.381251I
0.59829 − 1.41278I 9.58916 + 0.83279I
u = 0.667019 − 0.112397I
a = −2.55104 + 0.08549I
b = 1.252170 + 0.381251I
0.59829 + 1.41278I 9.58916 − 0.83279I
u = −0.076900 + 0.656111I
a = −0.25086 + 1.59937I
b = 0.571894 + 0.426603I
0.502483 + 0.088457I 8.19922 − 0.63999I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.076900 − 0.656111I
a = −0.25086 − 1.59937I
b = 0.571894 − 0.426603I
0.502483 − 0.088457I 8.19922 + 0.63999I
u = 0.616178 + 1.196580I
a = 1.49880 − 1.41745I
b = −1.39338 − 0.48591I
−1.43022 + 13.58250I 8.11529 − 8.04740I
u = 0.616178 − 1.196580I
a = 1.49880 + 1.41745I
b = −1.39338 + 0.48591I
−1.43022 − 13.58250I 8.11529 + 8.04740I
u = −0.548564 + 1.246830I
a = 0.708615 + 0.979572I
b = −1.132080 + 0.226075I
1.52668 − 5.32517I 10.19862 + 8.96318I
u = −0.548564 − 1.246830I
a = 0.708615 − 0.979572I
b = −1.132080 − 0.226075I
1.52668 + 5.32517I 10.19862 − 8.96318I
u = −0.164250
a = 3.05031
b = 0.417861
0.823260 12.0950
8
II. I
u
2
= h−au + b + u, a
2
− au − 3a + 2, 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
6
=
−1
0
a
4
=
−u
u + 1
a
9
=
a
au − u
a
11
=
au − a − 2u + 1
−au + u + 1
a
8
=
−a − u
−au + u + 1
a
7
=
−a − u
−au + u + 1
a
10
=
au + a − u
au − u
a
10
=
au + a − u
au − u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3au + 6a − 2u + 10
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
(u
2
+ u + 1)
2
c
3
, c
7
u
4
c
4
(u
2
− u + 1)
2
c
6
, c
8
(u
2
− u − 1)
2
c
9
, c
10
, c
11
(u
2
+ u − 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
2
c
3
, c
7
y
4
c
6
, c
8
, c
9
c
10
, c
11
(y
2
− 3y + 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = 0.690983 − 0.535233I
b = 0.618034
0.98696 − 2.02988I 15.5000 − 2.3454I
u = −0.500000 + 0.866025I
a = 1.80902 + 1.40126I
b = −1.61803
8.88264 − 2.02988I 15.5000 + 9.2736I
u = −0.500000 − 0.866025I
a = 0.690983 + 0.535233I
b = 0.618034
0.98696 + 2.02988I 15.5000 + 2.3454I
u = −0.500000 − 0.866025I
a = 1.80902 − 1.40126I
b = −1.61803
8.88264 + 2.02988I 15.5000 − 9.2736I
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
2
)(u
36
+ 3u
35
+ ··· − 2u + 1)
c
2
((u
2
+ u + 1)
2
)(u
36
+ 19u
35
+ ··· − 30u + 1)
c
3
, c
7
u
4
(u
36
+ 3u
35
+ ··· − 80u + 16)
c
4
((u
2
− u + 1)
2
)(u
36
+ 3u
35
+ ··· − 2u + 1)
c
5
((u
2
+ u + 1)
2
)(u
36
− 3u
35
+ ··· − 552u + 97)
c
6
((u
2
− u − 1)
2
)(u
36
− 3u
35
+ ··· + 7u
2
− 1)
c
8
((u
2
− u − 1)
2
)(u
36
+ 3u
35
+ ··· + 8u − 1)
c
9
((u
2
+ u − 1)
2
)(u
36
− 3u
35
+ ··· + 7u
2
− 1)
c
10
, c
11
((u
2
+ u − 1)
2
)(u
36
+ 3u
35
+ ··· + 8u − 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
2
)(y
36
+ 19y
35
+ ··· − 30y + 1)
c
2
((y
2
+ y + 1)
2
)(y
36
− y
35
+ ··· − 1390y + 1)
c
3
, c
7
y
4
(y
36
+ 25y
35
+ ··· + 384y + 256)
c
5
((y
2
+ y + 1)
2
)(y
36
− 21y
35
+ ··· − 232342y + 9409)
c
6
, c
9
((y
2
− 3y + 1)
2
)(y
36
− 9y
35
+ ··· − 14y + 1)
c
8
, c
10
, c
11
((y
2
− 3y + 1)
2
)(y
36
− 29y
35
+ ··· − 14y + 1)
14
