11n
143
(K11n
143
)
A knot diagram
1
Linearized knot diagam
6 1 9 11 10 2 11 6 4 8 4
Solving Sequence
4,10
9
1,3
2 11 5 6 7 8
c
9
c
3
c
2
c
11
c
4
c
5
c
6
c
8
c
1
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h27169327131u
12
− 4728521972u
11
+ ··· + 163375109309b + 102043710068,
46748483168u
12
− 1185808565u
11
+ ··· + 163375109309a − 246903703505,
u
13
− u
12
− 16u
11
+ 13u
10
+ 93u
9
− 90u
8
+ 85u
7
− 4u
6
+ 11u
5
− 20u
4
+ 2u
2
+ u − 1i
I
u
2
= h3u
8
− 5u
6
− u
5
− 7u
4
− 6u
3
+ b − 3u + 2, −2u
8
+ u
7
+ 3u
6
− u
5
+ 4u
4
+ 3u
3
− u
2
+ a + 2u − 1,
u
9
− u
7
− 3u
5
− 3u
4
− 2u
3
− 3u
2
− u − 1i
* 2 irreducible components of dim
C
= 0, with total 22 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
= h2.72 × 10
10
u
12
− 4.73 × 10
9
u
11
+ · · · + 1.63 × 10
11
b + 1.02 × 10
11
, 4.67 ×
10
10
u
12
−1.19×10
9
u
11
+· · ·+1.63×10
11
a−2.47×10
11
, u
13
−u
12
+· · ·+u−1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
u
2
a
1
=
−0.286142u
12
+ 0.00725820u
11
+ ··· + 0.326465u + 1.51127
−0.166300u
12
+ 0.0289427u
11
+ ··· − 0.0380012u − 0.624598
a
3
=
−u
−u
3
+ u
a
2
=
−1.45178u
12
+ 1.36239u
11
+ ··· − 1.27398u − 1.38184
−0.0325056u
12
+ 0.182051u
11
+ ··· − 1.79766u − 0.0596779
a
11
=
−0.286142u
12
+ 0.00725820u
11
+ ··· + 0.326465u + 1.51127
−0.0919107u
12
+ 0.0169286u
11
+ ··· − 0.0307430u − 0.345714
a
5
=
1.39226u
12
− 1.21256u
11
+ ··· − 1.08841u + 1.29245
0.0595160u
12
− 0.149831u
11
+ ··· + 2.36239u + 0.0893943
a
6
=
1.45178u
12
− 1.36239u
11
+ ··· + 1.27398u + 1.38184
0.0595160u
12
− 0.149831u
11
+ ··· + 2.36239u + 0.0893943
a
7
=
0.286142u
12
− 0.00725820u
11
+ ··· − 0.326465u − 1.51127
0.0289310u
12
+ 0.00713908u
11
+ ··· + 0.000702000u + 0.287036
a
8
=
0.0893943u
12
− 0.0298782u
11
+ ··· − 0.0699394u + 2.45178
−0.0903148u
12
+ 0.0234848u
11
+ ··· + 0.0298782u + 0.0595160
a
8
=
0.0893943u
12
− 0.0298782u
11
+ ··· − 0.0699394u + 2.45178
−0.0903148u
12
+ 0.0234848u
11
+ ··· + 0.0298782u + 0.0595160
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
425649841644
163375109309
u
12
+
257561868150
163375109309
u
11
+ ··· +
821280596494
163375109309
u −
283918679660
163375109309
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
13
− 11u
12
+ ··· − 48u + 16
c
2
u
13
+ 7u
12
+ ··· − 640u + 256
c
3
, c
8
, c
9
u
13
+ u
12
+ ··· + u + 1
c
4
, c
11
u
13
− 3u
12
+ ··· − 2u + 1
c
5
u
13
− 14u
11
+ ··· + 13u + 6
c
7
, c
10
u
13
− 3u
12
+ ··· + 3u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
13
− 7y
12
+ ··· − 640y −256
c
2
y
13
+ 69y
12
+ ··· − 106496y −65536
c
3
, c
8
, c
9
y
13
− 33y
12
+ ··· + 5y −1
c
4
, c
11
y
13
+ 27y
12
+ ··· − 34y −1
c
5
y
13
− 28y
12
+ ··· − 83y −36
c
7
, c
10
y
13
+ y
12
+ ··· − y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.444507 + 0.873153I
a = 0.145964 + 0.210434I
b = −0.10255 − 2.20008I
−5.13656 + 3.94627I 0.021726 + 1.151779I
u = 0.444507 − 0.873153I
a = 0.145964 − 0.210434I
b = −0.10255 + 2.20008I
−5.13656 − 3.94627I 0.021726 − 1.151779I
u = −0.278059 + 0.532845I
a = 0.482522 − 0.330538I
b = −0.243913 + 0.386628I
−0.112278 − 1.172770I −1.56848 + 5.39486I
u = −0.278059 − 0.532845I
a = 0.482522 + 0.330538I
b = −0.243913 − 0.386628I
−0.112278 + 1.172770I −1.56848 − 5.39486I
u = 0.581027
a = 1.33008
b = 0.743719
−1.77301 −4.59260
u = −0.395821 + 0.255747I
a = 1.63033 − 1.89256I
b = −0.681021 − 0.928853I
3.39477 − 1.45394I 0.239284 + 0.384387I
u = −0.395821 − 0.255747I
a = 1.63033 + 1.89256I
b = −0.681021 + 0.928853I
3.39477 + 1.45394I 0.239284 − 0.384387I
u = 0.364118 + 0.280685I
a = 2.64015 + 1.42143I
b = −0.470210 + 1.143350I
3.10631 − 4.18292I 3.50367 + 6.73830I
u = 0.364118 − 0.280685I
a = 2.64015 − 1.42143I
b = −0.470210 − 1.143350I
3.10631 + 4.18292I 3.50367 − 6.73830I
u = −3.02519 + 1.05130I
a = 0.060075 + 0.847736I
b = 6.04324 + 4.26131I
16.1187 − 1.6452I −0.771905 + 0.029863I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −3.02519 − 1.05130I
a = 0.060075 − 0.847736I
b = 6.04324 − 4.26131I
16.1187 + 1.6452I −0.771905 − 0.029863I
u = 3.09993 + 0.83578I
a = −0.124080 + 0.900887I
b = −5.91741 + 5.22009I
16.4142 + 9.3138I −0.62797 − 3.85299I
u = 3.09993 − 0.83578I
a = −0.124080 − 0.900887I
b = −5.91741 − 5.22009I
16.4142 − 9.3138I −0.62797 + 3.85299I
6
II. I
u
2
= h3u
8
− 5u
6
− u
5
− 7u
4
− 6u
3
+ b − 3u + 2, −2u
8
+ u
7
+ · · · + a −
1, u
9
− u
7
− 3u
5
− 3u
4
− 2u
3
− 3u
2
− u − 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
u
2
a
1
=
2u
8
− u
7
− 3u
6
+ u
5
− 4u
4
− 3u
3
+ u
2
− 2u + 1
−3u
8
+ 5u
6
+ u
5
+ 7u
4
+ 6u
3
+ 3u − 2
a
3
=
−u
−u
3
+ u
a
2
=
−u
7
+ 2u
5
+ u
3
+ 3u
2
+ 1
−3u
8
+ 5u
6
+ u
5
+ 7u
4
+ 6u
3
+ 2u − 2
a
11
=
2u
8
− u
7
− 3u
6
+ u
5
− 4u
4
− 3u
3
+ u
2
− 2u + 1
−2u
8
+ 3u
6
+ u
5
+ 5u
4
+ 4u
3
+ 2u − 1
a
5
=
2u
7
− 4u
5
− 3u
3
− 5u
2
− 2
−u
7
+ 2u
5
+ 2u
3
+ 2u
2
+ 1
a
6
=
u
7
− 2u
5
− u
3
− 3u
2
− 1
−u
7
+ 2u
5
+ 2u
3
+ 2u
2
+ 1
a
7
=
−2u
8
+ u
7
+ 3u
6
− u
5
+ 4u
4
+ 3u
3
− u
2
+ 2u − 1
3u
8
+ u
7
− 4u
6
− 3u
5
− 9u
4
− 8u
3
− 3u
2
− 4u + 1
a
8
=
−u
8
+ 2u
6
+ u
4
+ 3u
3
+ u + 1
u
8
− 2u
6
− 2u
4
− 2u
3
+ u
2
− u
a
8
=
−u
8
+ 2u
6
+ u
4
+ 3u
3
+ u + 1
u
8
− 2u
6
− 2u
4
− 2u
3
+ u
2
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −11u
8
− 6u
7
+ 11u
6
+ 15u
5
+ 36u
4
+ 40u
3
+ 29u
2
+ 19u + 4
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
+ u
8
− 3u
7
− 5u
6
+ 2u
5
+ 8u
4
+ u
3
− 4u
2
− u + 1
c
2
u
9
+ 7u
8
+ 23u
7
+ 51u
6
+ 84u
5
+ 96u
4
+ 71u
3
+ 34u
2
+ 9u + 1
c
3
, c
8
u
9
− u
7
− 3u
5
+ 3u
4
− 2u
3
+ 3u
2
− u + 1
c
4
u
9
+ 2u
8
+ 3u
7
+ 3u
6
+ u
5
+ u
4
+ u
3
− 2u
2
+ 1
c
5
u
9
+ u
8
+ 2u
5
+ 5u
4
+ 4u
3
+ 3u
2
+ 2u + 1
c
6
u
9
− u
8
− 3u
7
+ 5u
6
+ 2u
5
− 8u
4
+ u
3
+ 4u
2
− u − 1
c
7
u
9
− 4u
8
+ 8u
7
− 8u
6
+ 4u
5
+ u
4
− 3u
3
+ 4u
2
− 3u + 1
c
9
u
9
− u
7
− 3u
5
− 3u
4
− 2u
3
− 3u
2
− u − 1
c
10
u
9
+ 4u
8
+ 8u
7
+ 8u
6
+ 4u
5
− u
4
− 3u
3
− 4u
2
− 3u − 1
c
11
u
9
− 2u
8
+ 3u
7
− 3u
6
+ u
5
− u
4
+ u
3
+ 2u
2
− 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
9
− 7y
8
+ 23y
7
− 51y
6
+ 84y
5
− 96y
4
+ 71y
3
− 34y
2
+ 9y −1
c
2
y
9
− 3y
8
− 17y
7
+ 61y
6
+ 72y
5
− 356y
4
− 77y
3
− 70y
2
+ 13y −1
c
3
, c
8
, c
9
y
9
− 2y
8
− 5y
7
+ 2y
6
+ 11y
5
+ 5y
4
− 8y
3
− 11y
2
− 5y −1
c
4
, c
11
y
9
+ 2y
8
− y
7
− 5y
6
+ 9y
5
+ 9y
4
− y
3
− 6y
2
+ 4y −1
c
5
y
9
− y
8
+ 4y
7
− 2y
6
+ 2y
5
− 11y
4
− 6y
3
− 3y
2
− 2y −1
c
7
, c
10
y
9
+ 8y
7
+ 2y
6
+ 10y
5
− y
4
− 7y
3
+ y −1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.187026 + 0.975482I
a = 1.49016 − 0.14200I
b = −1.04647 + 1.04626I
2.30462 − 3.49273I −2.36810 + 1.84153I
u = 0.187026 − 0.975482I
a = 1.49016 + 0.14200I
b = −1.04647 − 1.04626I
2.30462 + 3.49273I −2.36810 − 1.84153I
u = 0.371524 + 0.883251I
a = 0.023313 + 0.680902I
b = −0.23136 − 2.96704I
−5.46047 + 4.24647I −14.3219 − 11.0959I
u = 0.371524 − 0.883251I
a = 0.023313 − 0.680902I
b = −0.23136 + 2.96704I
−5.46047 − 4.24647I −14.3219 + 11.0959I
u = −1.182340 + 0.166435I
a = 0.381598 − 0.765916I
b = −0.406219 − 0.959782I
4.76964 − 2.24591I 6.27523 + 4.01918I
u = −1.182340 − 0.166435I
a = 0.381598 + 0.765916I
b = −0.406219 + 0.959782I
4.76964 + 2.24591I 6.27523 − 4.01918I
u = −0.245900 + 0.620274I
a = −0.08889 − 1.83830I
b = −0.76587 + 2.09421I
−2.24646 − 2.97681I 0.11269 + 3.28969I
u = −0.245900 − 0.620274I
a = −0.08889 + 1.83830I
b = −0.76587 − 2.09421I
−2.24646 + 2.97681I 0.11269 − 3.28969I
u = 1.73938
a = 0.387642
b = 1.89983
1.26533 −2.39580
10
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
9
+ u
8
− 3u
7
− 5u
6
+ 2u
5
+ 8u
4
+ u
3
− 4u
2
− u + 1)
· (u
13
− 11u
12
+ ··· − 48u + 16)
c
2
(u
9
+ 7u
8
+ 23u
7
+ 51u
6
+ 84u
5
+ 96u
4
+ 71u
3
+ 34u
2
+ 9u + 1)
· (u
13
+ 7u
12
+ ··· − 640u + 256)
c
3
, c
8
(u
9
− u
7
+ ··· − u + 1)(u
13
+ u
12
+ ··· + u + 1)
c
4
(u
9
+ 2u
8
+ ··· − 2u
2
+ 1)(u
13
− 3u
12
+ ··· − 2u + 1)
c
5
(u
9
+ u
8
+ ··· + 2u + 1)(u
13
− 14u
11
+ ··· + 13u + 6)
c
6
(u
9
− u
8
− 3u
7
+ 5u
6
+ 2u
5
− 8u
4
+ u
3
+ 4u
2
− u − 1)
· (u
13
− 11u
12
+ ··· − 48u + 16)
c
7
(u
9
− 4u
8
+ 8u
7
− 8u
6
+ 4u
5
+ u
4
− 3u
3
+ 4u
2
− 3u + 1)
· (u
13
− 3u
12
+ ··· + 3u − 1)
c
9
(u
9
− u
7
+ ··· − u − 1)(u
13
+ u
12
+ ··· + u + 1)
c
10
(u
9
+ 4u
8
+ 8u
7
+ 8u
6
+ 4u
5
− u
4
− 3u
3
− 4u
2
− 3u − 1)
· (u
13
− 3u
12
+ ··· + 3u − 1)
c
11
(u
9
− 2u
8
+ ··· + 2u
2
− 1)(u
13
− 3u
12
+ ··· − 2u + 1)
11
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
9
− 7y
8
+ 23y
7
− 51y
6
+ 84y
5
− 96y
4
+ 71y
3
− 34y
2
+ 9y −1)
· (y
13
− 7y
12
+ ··· − 640y −256)
c
2
(y
9
− 3y
8
− 17y
7
+ 61y
6
+ 72y
5
− 356y
4
− 77y
3
− 70y
2
+ 13y −1)
· (y
13
+ 69y
12
+ ··· − 106496y −65536)
c
3
, c
8
, c
9
(y
9
− 2y
8
− 5y
7
+ 2y
6
+ 11y
5
+ 5y
4
− 8y
3
− 11y
2
− 5y −1)
· (y
13
− 33y
12
+ ··· + 5y −1)
c
4
, c
11
(y
9
+ 2y
8
− y
7
− 5y
6
+ 9y
5
+ 9y
4
− y
3
− 6y
2
+ 4y −1)
· (y
13
+ 27y
12
+ ··· − 34y −1)
c
5
(y
9
− y
8
+ 4y
7
− 2y
6
+ 2y
5
− 11y
4
− 6y
3
− 3y
2
− 2y −1)
· (y
13
− 28y
12
+ ··· − 83y −36)
c
7
, c
10
(y
9
+ 8y
7
+ ··· + y −1)(y
13
+ y
12
+ ··· − y −1)
12
