11n
41
(K11n
41
)
A knot diagram
1
Linearized knot diagam
4 1 7 2 10 9 4 11 1 8 6
Solving Sequence
1,4
2
5,10
6 9 7 3 11 8
c
1
c
4
c
5
c
9
c
6
c
3
c
11
c
8
c
2
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h5.06381 × 10
26
u
34
+ 3.18576 × 10
27
u
33
+ ··· + 7.97336 × 10
26
b − 1.25386 × 10
26
,
− 4.65925 × 10
25
u
34
+ 3.98163 × 10
24
u
33
+ ··· + 7.97336 × 10
26
a + 6.92161 × 10
26
, u
35
+ 8u
34
+ ··· + 9u + 1i
I
u
2
= h10a
5
− 46a
4
+ 69a
3
+ 18a
2
+ 13b − 31a − 12, a
6
− 5a
5
+ 9a
4
− 2a
3
− 2a
2
− a + 1, u − 1i
I
u
3
= hb, −3u
2
+ a − 5u − 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
= h5.06×10
26
u
34
+3.19×10
27
u
33
+· · ·+7.97×10
26
b−1.25×10
26
, −4.66×
10
25
u
34
+3.98×10
24
u
33
+· · ·+7.97×10
26
a+6.92×10
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
10
=
0.0584352u
34
− 0.00499367u
33
+ ··· + 87.4344u − 0.868092
−0.635091u
34
− 3.99551u
33
+ ··· + 1.26311u + 0.157257
a
6
=
−1.72094u
34
− 17.6948u
33
+ ··· + 67.6060u + 13.1818
−0.291426u
34
− 1.97724u
33
+ ··· − 9.21351u − 0.566549
a
9
=
0.693526u
34
+ 3.99051u
33
+ ··· + 86.1713u − 1.02535
−0.635091u
34
− 3.99551u
33
+ ··· + 1.26311u + 0.157257
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
11
=
−0.242664u
34
− 0.573718u
33
+ ··· − 63.3575u − 0.192908
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
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
− 4u
34
+ ··· + 1417u + 1219
c
6
u
35
− 8u
34
+ ··· + 73u + 31
c
8
, c
10
u
35
− 5u
34
+ ··· + 67u − 1
c
9
u
35
+ 6u
34
+ ··· + 124u − 8
c
11
u
35
+ 3u
34
+ ··· + 2u + 1
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
− 4y
34
+ ··· + 25178641y −1485961
c
6
y
35
− 52y
34
+ ··· + 29509y −961
c
8
, c
10
y
35
− 33y
34
+ ··· + 5091y −1
c
9
y
35
+ 18y
34
+ ··· + 7312y −64
c
11
y
35
+ y
34
+ ··· + 14y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.964380 + 0.326022I
a = −1.34533 − 1.00277I
b = 1.165200 + 0.364382I
−4.47629 − 0.99972I −15.2464 + 0.4133I
u = 0.964380 − 0.326022I
a = −1.34533 + 1.00277I
b = 1.165200 − 0.364382I
−4.47629 + 0.99972I −15.2464 − 0.4133I
u = 0.679243 + 0.583622I
a = 0.692444 − 0.020033I
b = −0.491434 + 1.250360I
−1.63296 − 3.48211I −7.94104 + 7.54592I
u = 0.679243 − 0.583622I
a = 0.692444 + 0.020033I
b = −0.491434 − 1.250360I
−1.63296 + 3.48211I −7.94104 − 7.54592I
u = −0.990139 + 0.655507I
a = −0.328445 − 0.034132I
b = −0.537541 + 0.273251I
1.54213 + 2.47872I 0. + 5.93000I
u = −0.990139 − 0.655507I
a = −0.328445 + 0.034132I
b = −0.537541 − 0.273251I
1.54213 − 2.47872I 0. − 5.93000I
u = 1.204600 + 0.063415I
a = −1.45117 − 1.83159I
b = −0.035022 − 0.979858I
−3.08874 + 1.42303I −6.41632 − 5.79805I
u = 1.204600 − 0.063415I
a = −1.45117 + 1.83159I
b = −0.035022 + 0.979858I
−3.08874 − 1.42303I −6.41632 + 5.79805I
u = 0.779230
a = −0.816856
b = −0.118472
−1.12597 −9.35810
u = 0.605532 + 0.380104I
a = −1.43703 + 0.00546I
b = −0.043259 − 0.568475I
−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 = −1.43703 − 0.00546I
b = −0.043259 + 0.568475I
−1.46738 + 0.11420I −8.20214 − 0.34884I
u = 0.704998
a = 12.6158
b = −0.141812
−2.72892 194.390
u = −0.686181 + 0.154265I
a = 0.838455 − 0.370991I
b = 0.977826 − 0.650468I
−1.08296 − 5.42643I −0.21975 + 3.30530I
u = −0.686181 − 0.154265I
a = 0.838455 + 0.370991I
b = 0.977826 + 0.650468I
−1.08296 + 5.42643I −0.21975 − 3.30530I
u = 0.730316 + 1.119100I
a = −0.586120 − 0.340107I
b = 0.70143 − 1.39478I
−7.84770 − 8.00129I 0
u = 0.730316 − 1.119100I
a = −0.586120 + 0.340107I
b = 0.70143 + 1.39478I
−7.84770 + 8.00129I 0
u = 0.656190 + 1.188230I
a = 0.395829 − 0.005674I
b = 0.109496 + 1.311600I
−7.58070 + 0.56154I 0
u = 0.656190 − 1.188230I
a = 0.395829 + 0.005674I
b = 0.109496 − 1.311600I
−7.58070 − 0.56154I 0
u = −1.63022 + 0.11868I
a = −0.279124 + 1.207660I
b = 0.397690 + 0.969208I
−9.25057 + 1.88240I 0
u = −1.63022 − 0.11868I
a = −0.279124 − 1.207660I
b = 0.397690 − 0.969208I
−9.25057 − 1.88240I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.294421 + 0.137620I
a = −1.30767 − 1.56416I
b = −0.805847 − 0.442462I
1.40601 + 1.20005I 2.74470 − 1.99044I
u = −0.294421 − 0.137620I
a = −1.30767 + 1.56416I
b = −0.805847 + 0.442462I
1.40601 − 1.20005I 2.74470 + 1.99044I
u = −1.68600
a = 0.808929
b = −0.920335
−11.4779 0
u = −1.68299 + 0.18586I
a = −0.18783 − 1.58377I
b = −1.25568 − 1.90551I
−9.90660 + 6.51942I 0
u = −1.68299 − 0.18586I
a = −0.18783 + 1.58377I
b = −1.25568 + 1.90551I
−9.90660 − 6.51942I 0
u = −1.70107 + 0.39786I
a = −0.17360 + 1.42986I
b = 1.20989 + 1.48650I
−15.7071 + 13.7623I 0
u = −1.70107 − 0.39786I
a = −0.17360 − 1.42986I
b = 1.20989 − 1.48650I
−15.7071 − 13.7623I 0
u = 1.74717 + 0.03675I
a = 0.316839 + 1.172530I
b = 0.41033 + 1.45360I
−10.19430 + 4.27290I 0
u = 1.74717 − 0.03675I
a = 0.316839 − 1.172530I
b = 0.41033 − 1.45360I
−10.19430 − 4.27290I 0
u = −1.75068 + 0.06096I
a = 0.777922 − 1.044170I
b = 1.93922 − 1.67518I
−14.4753 + 2.5419I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.75068 − 0.06096I
a = 0.777922 + 1.044170I
b = 1.93922 + 1.67518I
−14.4753 − 2.5419I 0
u = −1.72022 + 0.43828I
a = 0.296229 − 1.018870I
b = −0.61061 − 1.35195I
−15.2163 + 5.6356I 0
u = −1.72022 − 0.43828I
a = 0.296229 + 1.018870I
b = −0.61061 + 1.35195I
−15.2163 − 5.6356I 0
u = −0.0306219 + 0.0974691I
a = −7.02532 + 6.31954I
b = 0.458623 + 0.535266I
−1.92040 − 0.80331I −4.44102 − 0.15082I
u = −0.0306219 − 0.0974691I
a = −7.02532 − 6.31954I
b = 0.458623 − 0.535266I
−1.92040 + 0.80331I −4.44102 + 0.15082I
8
II.
I
u
2
= h10a
5
+ 13b + · · · − 31a − 12, a
6
− 5a
5
+ 9a
4
− 2a
3
− 2a
2
− a + 1, u − 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
1
a
2
=
1
1
a
5
=
−1
0
a
10
=
a
−0.769231a
5
+ 3.53846a
4
+ ··· + 2.38462a + 0.923077
a
6
=
−0.307692a
5
+ 1.61538a
4
+ ··· + 0.153846a − 0.230769
−1.15385a
5
+ 5.30769a
4
+ ··· + 0.0769231a + 2.38462
a
9
=
0.769231a
5
− 3.53846a
4
+ ··· − 1.38462a − 0.923077
−0.769231a
5
+ 3.53846a
4
+ ··· + 2.38462a + 0.923077
a
7
=
0
−2.30769a
5
+ 10.6154a
4
+ ··· + 1.15385a + 2.76923
a
3
=
0
1
a
11
=
a
−2.30769a
5
+ 10.6154a
4
+ ··· + 1.15385a + 2.76923
a
8
=
0
−2.30769a
5
+ 10.6154a
4
+ ··· + 1.15385a + 2.76923
a
8
=
0
−2.30769a
5
+ 10.6154a
4
+ ··· + 1.15385a + 2.76923
(ii) Obstruction class = 1
(iii) Cusp Shapes =
7
13
a
5
−
40
13
a
4
+
112
13
a
3
−
146
13
a
2
+
120
13
a −
115
13
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
9
, c
10
u
6
− u
5
− u
4
+ 2u
3
− u + 1
c
6
, c
11
u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1
c
8
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
, c
9
c
10
y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1
c
6
, c
11
y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.655968 + 0.098281I
b = 1.002190 − 0.295542I
0.245672 − 0.924305I −5.68949 + 0.25702I
u = 1.00000
a = 0.655968 − 0.098281I
b = 1.002190 + 0.295542I
0.245672 + 0.924305I −5.68949 − 0.25702I
u = 1.00000
a = −0.415113 + 0.381252I
b = −1.073950 + 0.558752I
−1.64493 − 5.69302I −11.7058 + 8.3306I
u = 1.00000
a = −0.415113 − 0.381252I
b = −1.073950 − 0.558752I
−1.64493 + 5.69302I −11.7058 − 8.3306I
u = 1.00000
a = 2.25915 + 1.43225I
b = −0.428243 + 0.664531I
−3.53554 + 0.92430I −12.60470 + 5.55069I
u = 1.00000
a = 2.25915 − 1.43225I
b = −0.428243 − 0.664531I
−3.53554 − 0.92430I −12.60470 − 5.55069I
12
III. I
u
3
= hb, −3u
2
+ a − 5u − 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
10
=
3u
2
+ 5u + 4
0
a
6
=
9u
2
+ 15u + 12
u
2
+ u − 1
a
9
=
3u
2
+ 5u + 4
0
a
7
=
−u
u
2
+ u − 1
a
3
=
−u
2
+ 1
u
2
a
11
=
3u
2
+ 6u + 4
−2u
2
− 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 − 1)
3
c
9
u
3
c
10
(u + 1)
3
c
11
u
3
+ 3u
2
+ 2u − 1
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
, c
10
(y −1)
3
c
9
y
3
c
11
y
3
− 5y
2
+ 10y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0.258045 − 0.197115I
b = 0
1.37919 + 2.82812I −9.0124 − 12.0277I
u = −0.877439 − 0.744862I
a = 0.258045 + 0.197115I
b = 0
1.37919 − 2.82812I −9.0124 + 12.0277I
u = 0.754878
a = 9.48391
b = 0
−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
− u
5
− u
4
+ 2u
3
− u + 1)
· (u
35
− 4u
34
+ ··· + 1417u + 1219)
c
6
(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
7
u
6
(u
3
+ u
2
+ 2u + 1)(u
35
+ 2u
34
+ ··· − 320u − 64)
c
8
((u − 1)
3
)(u
6
+ u
5
+ ··· + u + 1)(u
35
− 5u
34
+ ··· + 67u − 1)
c
9
u
3
(u
6
− u
5
+ ··· − u + 1)(u
35
+ 6u
34
+ ··· + 124u − 8)
c
10
((u + 1)
3
)(u
6
− u
5
+ ··· − u + 1)(u
35
− 5u
34
+ ··· + 67u − 1)
c
11
(u
3
+ 3u
2
+ 2u − 1)(u
6
− 3u
5
+ 5u
4
− 4u
3
+ 2u
2
− u + 1)
· (u
35
+ 3u
34
+ ··· + 2u + 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
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
35
− 4y
34
+ ··· + 25178641y −1485961)
c
6
(y
3
− 10y
2
+ 5y −1)(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
35
− 52y
34
+ ··· + 29509y −961)
c
8
, c
10
(y −1)
3
(y
6
− 3y
5
+ 5y
4
− 4y
3
+ 2y
2
− y + 1)
· (y
35
− 33y
34
+ ··· + 5091y −1)
c
9
y
3
(y
6
− 3y
5
+ ··· − y + 1)(y
35
+ 18y
34
+ ··· + 7312y −64)
c
11
(y
3
− 5y
2
+ 10y −1)(y
6
+ y
5
+ 5y
4
+ 6y
2
+ 3y + 1)
· (y
35
+ y
34
+ ··· + 14y −1)
18
