11n
17
(K11n
17
)
A knot diagram
1
Linearized knot diagam
5 1 9 2 3 11 10 3 6 7 9
Solving Sequence
6,11 3,7
5 10 9 4 1 2 8
c
6
c
5
c
10
c
9
c
3
c
11
c
2
c
8
c
1
, c
4
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
28
− 2u
27
+ ··· + 2b − 3, −3u
28
+ 8u
27
+ ··· + 2a + 12, u
29
− 3u
28
+ ··· − 4u + 1i
I
u
2
= h−au + b, −u
2
a + a
2
− au + 2u
2
− 2a + u + 3, u
3
+ u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 35 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
28
−2u
27
+· · ·+2b−3, −3u
28
+8u
27
+· · ·+2a+12, u
29
−3u
28
+· · ·−4u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
3
2
u
28
− 4u
27
+ ··· + 8u − 6
−
1
2
u
28
+ u
27
+ ··· − 8u
2
+
3
2
a
7
=
1
−u
2
a
5
=
−
1
2
u
28
+ u
27
+ ··· − 6u + 1
1
2
u
28
− u
27
+ ··· + 2u −
1
2
a
10
=
−u
u
3
+ u
a
9
=
−u
3
− 2u
u
3
+ u
a
4
=
1
2
u
28
− 2u
27
+ ··· + 6u − 6
1
2
u
28
− u
27
+ ··· + u +
3
2
a
1
=
u
7
+ 4u
5
+ 4u
3
−u
7
− 3u
5
− 2u
3
+ u
a
2
=
3u
28
− 7u
27
+ ··· + 11u −
13
2
−
5
2
u
28
+ 7u
27
+ ··· − 6u +
7
2
a
8
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
u
2
+ 1
−u
4
− 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
28
+
7
2
u
27
+ ··· −
33
2
u +
19
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
29
+ 4u
28
+ ··· + u − 1
c
2
u
29
+ 18u
28
+ ··· + 9u − 1
c
3
, c
8
u
29
− u
28
+ ··· − 32u − 64
c
5
u
29
− 4u
28
+ ··· + 7u − 1
c
6
, c
7
, c
10
u
29
+ 3u
28
+ ··· − 4u − 1
c
9
u
29
− 3u
28
+ ··· − 244u − 73
c
11
u
29
+ 3u
28
+ ··· + 8u
2
− 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
29
+ 18y
28
+ ··· + 9y −1
c
2
y
29
− 10y
28
+ ··· + 425y −1
c
3
, c
8
y
29
+ 35y
28
+ ··· − 31744y −4096
c
5
y
29
− 38y
28
+ ··· + 9y −1
c
6
, c
7
, c
10
y
29
+ 29y
28
+ ··· + 16y −1
c
9
y
29
+ 17y
28
+ ··· + 23912y −5329
c
11
y
29
+ 37y
28
+ ··· + 16y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.691423 + 0.598710I
a = 1.37569 − 1.31340I
b = −1.73753 + 0.08448I
−8.85458 − 2.60938I 2.88623 + 0.30936I
u = 0.691423 − 0.598710I
a = 1.37569 + 1.31340I
b = −1.73753 − 0.08448I
−8.85458 + 2.60938I 2.88623 − 0.30936I
u = 0.770996 + 0.462752I
a = 1.67161 − 1.26096I
b = −1.87232 + 0.19865I
−8.40111 + 7.50786I 3.89559 − 5.68378I
u = 0.770996 − 0.462752I
a = 1.67161 + 1.26096I
b = −1.87232 − 0.19865I
−8.40111 − 7.50786I 3.89559 + 5.68378I
u = 0.690364 + 0.493803I
a = −1.54905 + 1.40959I
b = 1.76547 − 0.20820I
−4.66644 + 2.28896I 6.38324 − 2.89322I
u = 0.690364 − 0.493803I
a = −1.54905 − 1.40959I
b = 1.76547 + 0.20820I
−4.66644 − 2.28896I 6.38324 + 2.89322I
u = −0.171803 + 1.253430I
a = −0.337041 + 0.105101I
b = 0.073833 + 0.440514I
−2.92626 − 2.06352I 3.82434 + 4.59366I
u = −0.171803 − 1.253430I
a = −0.337041 − 0.105101I
b = 0.073833 − 0.440514I
−2.92626 + 2.06352I 3.82434 − 4.59366I
u = −0.674782 + 0.131684I
a = −0.108599 − 0.371194I
b = −0.122161 − 0.236174I
0.280276 − 0.752914I 5.99242 + 0.52273I
u = −0.674782 − 0.131684I
a = −0.108599 + 0.371194I
b = −0.122161 + 0.236174I
0.280276 + 0.752914I 5.99242 − 0.52273I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.019678 + 1.322720I
a = −0.737573 − 0.279772I
b = −0.384574 + 0.970095I
−3.02767 − 1.44830I 4.95474 + 3.01169I
u = −0.019678 − 1.322720I
a = −0.737573 + 0.279772I
b = −0.384574 − 0.970095I
−3.02767 + 1.44830I 4.95474 − 3.01169I
u = −0.297090 + 1.319120I
a = 0.044330 − 0.313521I
b = −0.400401 − 0.151621I
−4.26542 − 4.32252I −0.05495 + 2.76648I
u = −0.297090 − 1.319120I
a = 0.044330 + 0.313521I
b = −0.400401 + 0.151621I
−4.26542 + 4.32252I −0.05495 − 2.76648I
u = 0.070374 + 1.382890I
a = 0.882690 + 0.761515I
b = 0.99097 − 1.27426I
−4.31077 + 3.55507I 1.62564 − 2.30473I
u = 0.070374 − 1.382890I
a = 0.882690 − 0.761515I
b = 0.99097 + 1.27426I
−4.31077 − 3.55507I 1.62564 + 2.30473I
u = −0.300475 + 0.478492I
a = 0.156143 + 0.882607I
b = 0.469237 + 0.190488I
−1.43996 − 2.11719I 2.79129 + 5.41296I
u = −0.300475 − 0.478492I
a = 0.156143 − 0.882607I
b = 0.469237 − 0.190488I
−1.43996 + 2.11719I 2.79129 − 5.41296I
u = −0.11472 + 1.46953I
a = 0.292500 + 0.496633I
b = 0.763375 − 0.372865I
−7.73410 − 3.73497I 0. + 3.25156I
u = −0.11472 − 1.46953I
a = 0.292500 − 0.496633I
b = 0.763375 + 0.372865I
−7.73410 + 3.73497I 0. − 3.25156I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.24380 + 1.50275I
a = 0.103696 + 1.362120I
b = 2.02164 − 0.48792I
−11.15070 + 5.70562I 3.18778 − 2.80294I
u = 0.24380 − 1.50275I
a = 0.103696 − 1.362120I
b = 2.02164 + 0.48792I
−11.15070 − 5.70562I 3.18778 + 2.80294I
u = 0.28209 + 1.50525I
a = 0.024600 − 1.383480I
b = −2.08942 + 0.35324I
−14.7787 + 11.3588I 0.97389 − 5.82372I
u = 0.28209 − 1.50525I
a = 0.024600 + 1.383480I
b = −2.08942 − 0.35324I
−14.7787 − 11.3588I 0.97389 + 5.82372I
u = 0.21267 + 1.54249I
a = −0.131402 − 1.205960I
b = −1.83224 + 0.45916I
−15.9085 + 0.6657I 0
u = 0.21267 − 1.54249I
a = −0.131402 + 1.205960I
b = −1.83224 − 0.45916I
−15.9085 − 0.6657I 0
u = −0.417634
a = −0.553347
b = −0.231097
0.741502 13.5070
u = 0.325642 + 0.098864I
a = −0.41093 + 3.39717I
b = 0.469675 − 1.065640I
0.45415 + 2.26174I 0.65884 − 5.12612I
u = 0.325642 − 0.098864I
a = −0.41093 − 3.39717I
b = 0.469675 + 1.065640I
0.45415 − 2.26174I 0.65884 + 5.12612I
7
II. I
u
2
= h−au + b, −u
2
a + a
2
− au + 2u
2
− 2a + u + 3, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
a
au
a
7
=
1
−u
2
a
5
=
−u
2
+ a − u − 1
au + 1
a
10
=
−u
−u
2
− u − 1
a
9
=
u
2
+ 1
−u
2
− u − 1
a
4
=
a
au
a
1
=
−1
0
a
2
=
au + a
au
a
8
=
u
2
+ 1
−u
2
− u − 1
a
8
=
u
2
+ 1
−u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
2
a − 4au + 5u
2
− a + 5u + 12
8
(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
8
u
6
c
4
(u
2
− u + 1)
3
c
6
, c
7
(u
3
+ u
2
+ 2u + 1)
2
c
9
, c
11
(u
3
+ u
2
− 1)
2
c
10
(u
3
− u
2
+ 2u − 1)
2
9
(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
8
y
6
c
6
, c
7
, c
10
(y
3
+ 3y
2
+ 2y −1)
2
c
9
, c
11
(y
3
− y
2
+ 2y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0.706350 + 0.266290I
b = −0.500000 + 0.866025I
−3.02413 − 4.85801I 6.43615 + 6.24253I
u = −0.215080 + 1.307140I
a = −0.583789 + 0.478572I
b = −0.500000 − 0.866025I
−3.02413 − 0.79824I 2.88198 − 0.84592I
u = −0.215080 − 1.307140I
a = 0.706350 − 0.266290I
b = −0.500000 − 0.866025I
−3.02413 + 4.85801I 6.43615 − 6.24253I
u = −0.215080 − 1.307140I
a = −0.583789 − 0.478572I
b = −0.500000 + 0.866025I
−3.02413 + 0.79824I 2.88198 + 0.84592I
u = −0.569840
a = 0.87744 + 1.51977I
b = −0.500000 − 0.866025I
1.11345 − 2.02988I 12.18187 + 2.43783I
u = −0.569840
a = 0.87744 − 1.51977I
b = −0.500000 + 0.866025I
1.11345 + 2.02988I 12.18187 − 2.43783I
11
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
3
)(u
29
+ 4u
28
+ ··· + u − 1)
c
2
((u
2
+ u + 1)
3
)(u
29
+ 18u
28
+ ··· + 9u − 1)
c
3
, c
8
u
6
(u
29
− u
28
+ ··· − 32u − 64)
c
4
((u
2
− u + 1)
3
)(u
29
+ 4u
28
+ ··· + u − 1)
c
5
((u
2
+ u + 1)
3
)(u
29
− 4u
28
+ ··· + 7u − 1)
c
6
, c
7
((u
3
+ u
2
+ 2u + 1)
2
)(u
29
+ 3u
28
+ ··· − 4u − 1)
c
9
((u
3
+ u
2
− 1)
2
)(u
29
− 3u
28
+ ··· − 244u − 73)
c
10
((u
3
− u
2
+ 2u − 1)
2
)(u
29
+ 3u
28
+ ··· − 4u − 1)
c
11
((u
3
+ u
2
− 1)
2
)(u
29
+ 3u
28
+ ··· + 8u
2
− 1)
12
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
3
)(y
29
+ 18y
28
+ ··· + 9y −1)
c
2
((y
2
+ y + 1)
3
)(y
29
− 10y
28
+ ··· + 425y −1)
c
3
, c
8
y
6
(y
29
+ 35y
28
+ ··· − 31744y −4096)
c
5
((y
2
+ y + 1)
3
)(y
29
− 38y
28
+ ··· + 9y −1)
c
6
, c
7
, c
10
((y
3
+ 3y
2
+ 2y −1)
2
)(y
29
+ 29y
28
+ ··· + 16y −1)
c
9
((y
3
− y
2
+ 2y −1)
2
)(y
29
+ 17y
28
+ ··· + 23912y −5329)
c
11
((y
3
− y
2
+ 2y −1)
2
)(y
29
+ 37y
28
+ ··· + 16y −1)
13
