11n
47
(K11n
47
)
A knot diagram
1
Linearized knot diagam
4 1 7 2 11 10 4 6 1 8 9
Solving Sequence
1,4
2
5,9
10 11 6 7 3 8
c
1
c
4
c
9
c
11
c
5
c
6
c
3
c
8
c
2
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h7.57271 × 10
25
u
34
+ 6.48827 × 10
26
u
33
+ ··· + 7.97336 × 10
26
b − 7.26255 × 10
26
,
− 1.64269 × 10
25
u
34
− 1.05850 × 10
26
u
33
+ ··· + 2.49168 × 10
25
a − 1.38382 × 10
26
, u
35
+ 8u
34
+ ··· + 9u + 1i
I
u
2
= hb
6
− b
5
− b
4
+ 2b
3
− b + 1, a − 1, u − 1i
I
u
3
= hb + 1, 2u
2
+ a + 4u + 4, u
3
+ u
2
− 1i
* 3 irreducible components of dim
C
= 0, with total 44 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
= h7.57×10
25
u
34
+6.49×10
26
u
33
+· · ·+7.97×10
26
b−7.26×10
26
, −1.64×
10
25
u
34
−1.06×10
26
u
33
+· · ·+2.49×10
25
a−1.38×10
26
, u
35
+8u
34
+· · ·+9u+1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
9
=
0.659269u
34
+ 4.24813u
33
+ ··· + 120.228u + 5.55377
−0.0949751u
34
− 0.813743u
33
+ ··· + 1.09979u + 0.910851
a
10
=
0.754244u
34
+ 5.06188u
33
+ ··· + 119.128u + 4.64292
−0.0949751u
34
− 0.813743u
33
+ ··· + 1.09979u + 0.910851
a
11
=
−0.894280u
34
− 6.14049u
33
+ ··· − 123.987u − 2.97552
−0.0130827u
34
− 0.0126909u
33
+ ··· − 5.06131u − 1.20991
a
6
=
1.77774u
34
+ 17.8440u
33
+ ··· + 23.8681u − 10.0326
−0.414794u
34
− 1.96166u
33
+ ··· + 6.00083u + 0.386377
a
7
=
0.135945u
34
+ 1.32830u
33
+ ··· + 28.8699u − 0.0316372
0.201606u
34
+ 1.17050u
33
+ ··· + 2.73205u + 0.337551
a
3
=
−u
2
+ 1
u
2
a
8
=
0.135945u
34
+ 1.32830u
33
+ ··· + 28.8699u − 0.0316372
−0.239495u
34
− 1.52839u
33
+ ··· + 0.429444u + 0.0968115
a
8
=
0.135945u
34
+ 1.32830u
33
+ ··· + 28.8699u − 0.0316372
−0.239495u
34
− 1.52839u
33
+ ··· + 0.429444u + 0.0968115
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
3378359165600571190629683677
398668191729252960111215152
u
34
−
15526399702733176499705931937
199334095864626480055607576
u
33
+ ··· +
65474135371669423713349877783
398668191729252960111215152
u +
2429897091838954454446349621
199334095864626480055607576
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
35
− 8u
34
+ ··· + 9u − 1
c
2
u
35
+ 42u
34
+ ··· − 129u + 1
c
3
, c
7
u
35
+ 2u
34
+ ··· − 320u − 64
c
5
u
35
− 8u
34
+ ··· + 73u + 31
c
6
u
35
− 4u
34
+ ··· + 1417u + 1219
c
8
u
35
+ 3u
34
+ ··· + 2u + 1
c
9
, c
11
u
35
− 5u
34
+ ··· + 67u − 1
c
10
u
35
+ 6u
34
+ ··· + 124u − 8
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
35
− 42y
34
+ ··· − 129y −1
c
2
y
35
− 90y
34
+ ··· + 6323y −1
c
3
, c
7
y
35
− 36y
34
+ ··· − 20480y −4096
c
5
y
35
− 52y
34
+ ··· + 29509y −961
c
6
y
35
− 4y
34
+ ··· + 25178641y −1485961
c
8
y
35
+ y
34
+ ··· + 14y −1
c
9
, c
11
y
35
− 33y
34
+ ··· + 5091y −1
c
10
y
35
+ 18y
34
+ ··· + 7312y −64
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.964380 + 0.326022I
a = 0.35491 − 1.77356I
b = 1.401850 + 0.174541I
−4.47629 − 0.99972I −15.2464 + 0.4133I
u = 0.964380 − 0.326022I
a = 0.35491 + 1.77356I
b = 1.401850 − 0.174541I
−4.47629 + 0.99972I −15.2464 − 0.4133I
u = 0.679243 + 0.583622I
a = −0.155632 − 1.137360I
b = 0.397949 + 0.909235I
−1.63296 − 3.48211I −7.94104 + 7.54592I
u = 0.679243 − 0.583622I
a = −0.155632 + 1.137360I
b = 0.397949 − 0.909235I
−1.63296 + 3.48211I −7.94104 − 7.54592I
u = −0.990139 + 0.655507I
a = −0.886995 − 0.313990I
b = −0.934664 − 0.185167I
1.54213 + 2.47872I 0. + 5.93000I
u = −0.990139 − 0.655507I
a = −0.886995 + 0.313990I
b = −0.934664 + 0.185167I
1.54213 − 2.47872I 0. − 5.93000I
u = 1.204600 + 0.063415I
a = −0.412107 − 0.706810I
b = 0.628022 − 0.554154I
−3.08874 + 1.42303I −6.41632 − 5.79805I
u = 1.204600 − 0.063415I
a = −0.412107 + 0.706810I
b = 0.628022 + 0.554154I
−3.08874 − 1.42303I −6.41632 + 5.79805I
u = 0.779230
a = −1.08295
b = −0.0140385
−1.12597 −9.35810
u = 0.605532 + 0.380104I
a = −1.67784 − 0.73020I
b = 0.361624 − 0.080090I
−1.46738 − 0.11420I −8.20214 + 0.34884I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.605532 − 0.380104I
a = −1.67784 + 0.73020I
b = 0.361624 + 0.080090I
−1.46738 + 0.11420I −8.20214 − 0.34884I
u = 0.704998
a = 11.0900
b = 1.00991
−2.72892 194.390
u = −0.686181 + 0.154265I
a = −1.246620 − 0.427424I
b = −1.126280 − 0.497250I
−1.08296 − 5.42643I −0.21975 + 3.30530I
u = −0.686181 − 0.154265I
a = −1.246620 + 0.427424I
b = −1.126280 + 0.497250I
−1.08296 + 5.42643I −0.21975 − 3.30530I
u = 0.730316 + 1.119100I
a = −0.576099 + 0.700870I
b = −1.51689 − 0.33803I
−7.84770 − 8.00129I 0
u = 0.730316 − 1.119100I
a = −0.576099 − 0.700870I
b = −1.51689 + 0.33803I
−7.84770 + 8.00129I 0
u = 0.656190 + 1.188230I
a = −0.419118 + 0.434391I
b = −1.47252 + 0.05220I
−7.58070 + 0.56154I 0
u = 0.656190 − 1.188230I
a = −0.419118 − 0.434391I
b = −1.47252 − 0.05220I
−7.58070 − 0.56154I 0
u = −1.63022 + 0.11868I
a = 0.069536 + 0.327596I
b = 0.340175 − 0.686101I
−9.25057 + 1.88240I 0
u = −1.63022 − 0.11868I
a = 0.069536 − 0.327596I
b = 0.340175 + 0.686101I
−9.25057 − 1.88240I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.294421 + 0.137620I
a = −0.647696 − 1.089550I
b = −0.225869 − 0.594231I
1.40601 + 1.20005I 2.74470 − 1.99044I
u = −0.294421 − 0.137620I
a = −0.647696 + 1.089550I
b = −0.225869 + 0.594231I
1.40601 − 1.20005I 2.74470 + 1.99044I
u = −1.68600
a = 2.34569
b = 1.28757
−11.4779 0
u = −1.68299 + 0.18586I
a = 0.383087 − 0.343481I
b = 0.25892 − 1.52764I
−9.90660 + 6.51942I 0
u = −1.68299 − 0.18586I
a = 0.383087 + 0.343481I
b = 0.25892 + 1.52764I
−9.90660 − 6.51942I 0
u = −1.70107 + 0.39786I
a = −1.50913 − 0.63392I
b = −1.58042 + 0.58476I
−15.7071 + 13.7623I 0
u = −1.70107 − 0.39786I
a = −1.50913 + 0.63392I
b = −1.58042 − 0.58476I
−15.7071 − 13.7623I 0
u = 1.74717 + 0.03675I
a = −1.63248 + 0.11344I
b = −1.54159 + 0.19584I
−10.19430 + 4.27290I 0
u = 1.74717 − 0.03675I
a = −1.63248 − 0.11344I
b = −1.54159 − 0.19584I
−10.19430 − 4.27290I 0
u = −1.75068 + 0.06096I
a = 1.46330 + 0.02059I
b = 1.82396 − 0.77537I
−14.4753 + 2.5419I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.75068 − 0.06096I
a = 1.46330 − 0.02059I
b = 1.82396 + 0.77537I
−14.4753 − 2.5419I 0
u = −1.72022 + 0.43828I
a = −1.34465 − 0.58112I
b = −1.49438 + 0.29415I
−15.2163 + 5.6356I 0
u = −1.72022 − 0.43828I
a = −1.34465 + 0.58112I
b = −1.49438 − 0.29415I
−15.2163 − 5.6356I 0
u = −0.0306219 + 0.0974691I
a = −1.93881 + 9.66636I
b = 1.038380 + 0.224787I
−1.92040 − 0.80331I −4.44102 − 0.15082I
u = −0.0306219 − 0.0974691I
a = −1.93881 − 9.66636I
b = 1.038380 − 0.224787I
−1.92040 + 0.80331I −4.44102 + 0.15082I
8
II. I
u
2
= hb
6
− b
5
− b
4
+ 2b
3
− b + 1, a − 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
5
=
−1
0
a
9
=
1
b
a
10
=
−b + 1
b
a
11
=
−b + 1
−b
2
a
6
=
−b
3
+ b
2
− 1
−b
4
a
7
=
0
b
5
− b
4
− 2b
3
+ b
2
+ b − 1
a
3
=
0
1
a
8
=
0
b
5
− b
4
− 2b
3
+ b
2
+ b − 1
a
8
=
0
b
5
− b
4
− 2b
3
+ b
2
+ b − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3b
5
+ b
4
+ b
3
− 2b
2
+ 3b − 7
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
6
c
2
, c
4
(u + 1)
6
c
3
, c
7
u
6
c
5
, c
8
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
6
, c
11
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
9
, c
10
u
6
+ u
5
− u
4
− 2u
3
+ u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
7
y
6
c
5
, c
8
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
c
6
, c
9
, c
10
c
11
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000
b = −1.002190 + 0.295542I
−3.53554 + 0.92430I −12.60470 + 5.55069I
u = 1.00000
a = 1.00000
b = −1.002190 − 0.295542I
−3.53554 − 0.92430I −12.60470 − 5.55069I
u = 1.00000
a = 1.00000
b = 0.428243 + 0.664531I
0.245672 + 0.924305I −5.68949 − 0.25702I
u = 1.00000
a = 1.00000
b = 0.428243 − 0.664531I
0.245672 − 0.924305I −5.68949 + 0.25702I
u = 1.00000
a = 1.00000
b = 1.073950 + 0.558752I
−1.64493 − 5.69302I −11.7058 + 8.3306I
u = 1.00000
a = 1.00000
b = 1.073950 − 0.558752I
−1.64493 + 5.69302I −11.7058 − 8.3306I
12
III. I
u
3
= hb + 1, 2u
2
+ a + 4u + 4, u
3
+ u
2
− 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
u
2
+ u − 1
a
9
=
−2u
2
− 4u − 4
−1
a
10
=
−2u
2
− 4u − 3
−1
a
11
=
−2u
2
− 4u − 3
−1
a
6
=
−7u
2
− 13u − 9
−u − 2
a
7
=
−u
u
2
+ u − 1
a
3
=
−u
2
+ 1
u
2
a
8
=
−u
2u
2
+ u − 2
a
8
=
−u
2u
2
+ u − 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −21u
2
− 53u − 51
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ u
2
− 1
c
2
, c
7
u
3
+ u
2
+ 2u + 1
c
3
u
3
− u
2
+ 2u − 1
c
4
u
3
− u
2
+ 1
c
5
, c
6
u
3
− 2u
2
− 3u − 1
c
8
u
3
− 3u
2
+ 2u + 1
c
9
(u − 1)
3
c
10
u
3
c
11
(u + 1)
3
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
3
− y
2
+ 2y −1
c
2
, c
3
, c
7
y
3
+ 3y
2
+ 2y −1
c
5
, c
6
y
3
− 10y
2
+ 5y −1
c
8
y
3
− 5y
2
+ 10y −1
c
9
, c
11
(y −1)
3
c
10
y
3
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = −0.920404 − 0.365165I
b = −1.00000
1.37919 + 2.82812I −9.0124 − 12.0277I
u = −0.877439 − 0.744862I
a = −0.920404 + 0.365165I
b = −1.00000
1.37919 − 2.82812I −9.0124 + 12.0277I
u = 0.754878
a = −8.15919
b = −1.00000
−2.75839 −102.980
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
3
+ u
2
− 1)(u
35
− 8u
34
+ ··· + 9u − 1)
c
2
((u + 1)
6
)(u
3
+ u
2
+ 2u + 1)(u
35
+ 42u
34
+ ··· − 129u + 1)
c
3
u
6
(u
3
− u
2
+ 2u − 1)(u
35
+ 2u
34
+ ··· − 320u − 64)
c
4
((u + 1)
6
)(u
3
− u
2
+ 1)(u
35
− 8u
34
+ ··· + 9u − 1)
c
5
(u
3
− 2u
2
− 3u − 1)(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
35
− 8u
34
+ ··· + 73u + 31)
c
6
(u
3
− 2u
2
− 3u − 1)(u
6
− u
5
− u
4
+ 2u
3
− u + 1)
· (u
35
− 4u
34
+ ··· + 1417u + 1219)
c
7
u
6
(u
3
+ u
2
+ 2u + 1)(u
35
+ 2u
34
+ ··· − 320u − 64)
c
8
(u
3
− 3u
2
+ 2u + 1)(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
35
+ 3u
34
+ ··· + 2u + 1)
c
9
((u − 1)
3
)(u
6
+ u
5
+ ··· + u + 1)(u
35
− 5u
34
+ ··· + 67u − 1)
c
10
u
3
(u
6
+ u
5
+ ··· + u + 1)(u
35
+ 6u
34
+ ··· + 124u − 8)
c
11
((u + 1)
3
)(u
6
− u
5
+ ··· − u + 1)(u
35
− 5u
34
+ ··· + 67u − 1)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
6
)(y
3
− y
2
+ 2y −1)(y
35
− 42y
34
+ ··· − 129y −1)
c
2
((y −1)
6
)(y
3
+ 3y
2
+ 2y −1)(y
35
− 90y
34
+ ··· + 6323y −1)
c
3
, c
7
y
6
(y
3
+ 3y
2
+ 2y −1)(y
35
− 36y
34
+ ··· − 20480y −4096)
c
5
(y
3
− 10y
2
+ 5y −1)(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
35
− 52y
34
+ ··· + 29509y −961)
c
6
(y
3
− 10y
2
+ 5y −1)(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
35
− 4y
34
+ ··· + 25178641y −1485961)
c
8
(y
3
− 5y
2
+ 10y −1)(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
35
+ y
34
+ ··· + 14y −1)
c
9
, c
11
(y −1)
3
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
35
− 33y
34
+ ··· + 5091y −1)
c
10
y
3
(y
6
− 3y
5
+ ··· − y + 1)(y
35
+ 18y
34
+ ··· + 7312y −64)
18
