11n
7
(K11n
7
)
A knot diagram
1
Linearized knot diagam
5 1 8 2 3 9 3 11 6 8 10
Solving Sequence
9,11 3,8
4 7 6 5 10 1 2
c
8
c
3
c
7
c
6
c
5
c
10
c
11
c
2
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h2.20194 × 10
21
u
38
+ 4.46582 × 10
22
u
37
+ ··· + 2.15629 × 10
22
b + 5.77763 × 10
22
,
− 5.60651 × 10
22
u
38
− 2.01892 × 10
23
u
37
+ ··· + 2.15629 × 10
22
a + 8.89136 × 10
22
, u
39
+ 3u
38
+ ··· − 5u − 1i
I
u
2
= hu
2
a + b, u
2
a + a
2
+ 2au + 3u
2
+ a + 5u + 4, u
3
+ u
2
− 1i
* 2 irreducible components of dim
C
= 0, with total 45 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
= h2.20×10
21
u
38
+4.47×10
22
u
37
+· · ·+2.16×10
22
b+5.78×10
22
, −5.61×
10
22
u
38
−2.02×10
23
u
37
+· · ·+2.16×10
22
a+8.89×10
22
, u
39
+3u
38
+· · ·−5u−1i
(i) Arc colorings
a
9
=
1
0
a
11
=
0
u
a
3
=
2.60007u
38
+ 9.36292u
37
+ ··· − 11.3955u − 4.12344
−0.102117u
38
− 2.07106u
37
+ ··· − 13.0171u − 2.67943
a
8
=
1
−u
2
a
4
=
2.79441u
38
+ 10.0298u
37
+ ··· − 13.9989u − 5.24015
−0.0584579u
38
− 2.06978u
37
+ ··· − 13.6305u − 2.76324
a
7
=
−0.700760u
38
− 0.594268u
37
+ ··· + 7.97882u − 0.0611499
−1.25362u
38
− 2.81386u
37
+ ··· + 0.0129788u − 0.500639
a
6
=
−1.95438u
38
− 3.40813u
37
+ ··· + 7.99180u − 0.561789
−1.25362u
38
− 2.81386u
37
+ ··· + 0.0129788u − 0.500639
a
5
=
2.47112u
38
+ 9.86388u
37
+ ··· + 8.27156u + 1.66377
−0.721787u
38
− 4.52792u
37
+ ··· − 15.7237u − 2.45051
a
10
=
u
−u
3
+ u
a
1
=
−u
3
u
5
− u
3
+ u
a
2
=
2.46841u
38
+ 9.39037u
37
+ ··· − 9.44573u − 3.72104
−0.0315650u
38
− 2.27311u
37
+ ··· − 14.5271u − 2.54332
a
2
=
2.46841u
38
+ 9.39037u
37
+ ··· − 9.44573u − 3.72104
−0.0315650u
38
− 2.27311u
37
+ ··· − 14.5271u − 2.54332
(ii) Obstruction class = −1
(iii) Cusp Shapes =
95167190231219974262615
10781474718762665439818
u
38
+
642665286688782560331753
21562949437525330879636
u
37
+ ··· +
910083121628952116105487
10781474718762665439818
u +
469851565658388329096693
21562949437525330879636
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
39
+ 4u
38
+ ··· + 10u − 1
c
2
u
39
+ 22u
38
+ ··· + 170u − 1
c
3
, c
7
u
39
+ 3u
38
+ ··· + 160u + 64
c
5
u
39
− 4u
38
+ ··· + 602u − 49
c
6
, c
9
u
39
− 3u
38
+ ··· − 3u + 1
c
8
, c
10
u
39
− 3u
38
+ ··· − 5u + 1
c
11
u
39
+ 23u
38
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
39
+ 22y
38
+ ··· + 170y −1
c
2
y
39
− 6y
38
+ ··· + 31510y −1
c
3
, c
7
y
39
+ 35y
38
+ ··· − 23552y −4096
c
5
y
39
− 34y
38
+ ··· + 391706y −2401
c
6
, c
9
y
39
+ 9y
38
+ ··· + y −1
c
8
, c
10
y
39
− 23y
38
+ ··· + y −1
c
11
y
39
− 11y
38
+ ··· + 117y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.174715 + 0.953666I
a = −0.107736 − 0.141147I
b = −0.224524 + 1.376020I
−5.68977 + 0.80789I −5.63151 − 0.39749I
u = 0.174715 − 0.953666I
a = −0.107736 + 0.141147I
b = −0.224524 − 1.376020I
−5.68977 − 0.80789I −5.63151 + 0.39749I
u = −0.113785 + 1.039480I
a = 0.1112140 + 0.0706545I
b = −0.41499 + 1.53589I
−4.49350 − 8.17612I −3.77298 + 5.44747I
u = −0.113785 − 1.039480I
a = 0.1112140 − 0.0706545I
b = −0.41499 − 1.53589I
−4.49350 + 8.17612I −3.77298 − 5.44747I
u = −0.906304 + 0.258793I
a = −0.59831 + 2.09555I
b = −0.938219 − 0.467153I
0.05191 + 4.16636I −0.57665 − 9.00427I
u = −0.906304 − 0.258793I
a = −0.59831 − 2.09555I
b = −0.938219 + 0.467153I
0.05191 − 4.16636I −0.57665 + 9.00427I
u = 0.913889 + 0.058300I
a = 0.77201 + 4.31604I
b = −0.20598 − 3.29592I
−1.32570 − 2.15384I −38.3073 + 0.3658I
u = 0.913889 − 0.058300I
a = 0.77201 − 4.31604I
b = −0.20598 + 3.29592I
−1.32570 + 2.15384I −38.3073 − 0.3658I
u = 0.814464 + 0.380892I
a = 0.328778 + 0.693706I
b = −0.352686 − 1.052600I
−1.92828 + 0.12066I −7.15424 − 0.12690I
u = 0.814464 − 0.380892I
a = 0.328778 − 0.693706I
b = −0.352686 + 1.052600I
−1.92828 − 0.12066I −7.15424 + 0.12690I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.062003 + 0.891851I
a = 0.073492 − 0.130422I
b = 0.43523 − 1.38427I
−1.45248 − 3.13609I −0.74981 + 2.49452I
u = −0.062003 − 0.891851I
a = 0.073492 + 0.130422I
b = 0.43523 + 1.38427I
−1.45248 + 3.13609I −0.74981 − 2.49452I
u = −0.791534 + 0.793494I
a = −0.286108 + 0.284239I
b = 0.033088 + 0.170270I
2.88333 + 1.52566I −2.95623 − 6.42875I
u = −0.791534 − 0.793494I
a = −0.286108 − 0.284239I
b = 0.033088 − 0.170270I
2.88333 − 1.52566I −2.95623 + 6.42875I
u = −1.105650 + 0.283891I
a = −0.916031 − 0.529536I
b = −0.320477 + 0.011103I
−3.35360 + 5.46941I −6.70822 − 8.69559I
u = −1.105650 − 0.283891I
a = −0.916031 + 0.529536I
b = −0.320477 − 0.011103I
−3.35360 − 5.46941I −6.70822 + 8.69559I
u = 1.155090 + 0.139104I
a = −0.289265 − 1.321470I
b = 0.71983 + 1.54185I
−2.82585 − 1.96097I −4.21009 + 0.40138I
u = 1.155090 − 0.139104I
a = −0.289265 + 1.321470I
b = 0.71983 − 1.54185I
−2.82585 + 1.96097I −4.21009 − 0.40138I
u = 0.833700
a = 0.604067
b = −0.694607
−1.20362 −8.91670
u = −0.952533 + 0.800887I
a = 0.358525 + 0.042382I
b = 0.117335 − 0.110652I
2.42328 + 4.44150I −7.41017 − 1.05267I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.952533 − 0.800887I
a = 0.358525 − 0.042382I
b = 0.117335 + 0.110652I
2.42328 − 4.44150I −7.41017 + 1.05267I
u = −0.670244 + 0.249117I
a = 0.35712 + 1.40517I
b = 0.408266 + 0.138519I
1.33536 + 1.46808I 4.04275 − 4.37387I
u = −0.670244 − 0.249117I
a = 0.35712 − 1.40517I
b = 0.408266 − 0.138519I
1.33536 − 1.46808I 4.04275 + 4.37387I
u = 1.254360 + 0.453217I
a = 1.01660 + 1.37116I
b = 0.06649 − 1.63950I
−5.43179 − 1.52389I 0
u = 1.254360 − 0.453217I
a = 1.01660 − 1.37116I
b = 0.06649 + 1.63950I
−5.43179 + 1.52389I 0
u = −1.261920 + 0.500458I
a = −0.67622 + 1.81078I
b = −0.79327 − 1.68180I
−5.09332 + 8.17367I 0. − 5.17214I
u = −1.261920 − 0.500458I
a = −0.67622 − 1.81078I
b = −0.79327 + 1.68180I
−5.09332 − 8.17367I 0. + 5.17214I
u = −1.317290 + 0.384349I
a = 0.50231 − 1.81838I
b = 0.58706 + 1.52850I
−10.41510 + 3.75787I 0
u = −1.317290 − 0.384349I
a = 0.50231 + 1.81838I
b = 0.58706 − 1.52850I
−10.41510 − 3.75787I 0
u = 1.261720 + 0.574659I
a = −1.09075 − 1.20453I
b = −0.04542 + 1.54404I
−8.99304 − 6.36082I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.261720 − 0.574659I
a = −1.09075 + 1.20453I
b = −0.04542 − 1.54404I
−8.99304 + 6.36082I 0
u = −1.30473 + 0.56143I
a = 0.71828 − 1.70677I
b = 0.73324 + 1.82635I
−8.1954 + 13.8902I 0
u = −1.30473 − 0.56143I
a = 0.71828 + 1.70677I
b = 0.73324 − 1.82635I
−8.1954 − 13.8902I 0
u = 1.37975 + 0.41298I
a = −0.83835 − 1.29118I
b = −0.16526 + 1.61657I
−9.33600 + 3.03011I 0
u = 1.37975 − 0.41298I
a = −0.83835 + 1.29118I
b = −0.16526 − 1.61657I
−9.33600 − 3.03011I 0
u = −0.415565 + 0.222377I
a = 0.82602 − 1.70438I
b = 0.738838 − 0.443010I
1.15178 − 1.50599I 2.56109 + 2.72315I
u = −0.415565 − 0.222377I
a = 0.82602 + 1.70438I
b = 0.738838 + 0.443010I
1.15178 + 1.50599I 2.56109 − 2.72315I
u = 0.030712 + 0.352609I
a = 2.43638 − 1.81010I
b = −0.531247 − 0.445633I
−0.39510 − 2.82136I 0.57403 + 4.29661I
u = 0.030712 − 0.352609I
a = 2.43638 + 1.81010I
b = −0.531247 + 0.445633I
−0.39510 + 2.82136I 0.57403 − 4.29661I
8
II. I
u
2
= hu
2
a + b, u
2
a + a
2
+ 2au + 3u
2
+ a + 5u + 4, u
3
+ u
2
− 1i
(i) Arc colorings
a
9
=
1
0
a
11
=
0
u
a
3
=
a
−u
2
a
a
8
=
1
−u
2
a
4
=
a
−u
2
a
a
7
=
1
−u
2
a
6
=
−u
2
+ 1
−u
2
a
5
=
a + 2u + 2
−u
2
a − u
2
− u − 1
a
10
=
u
u
2
+ u − 1
a
1
=
u
2
− 1
u
2
a
2
=
2u
2
a
−au
a
2
=
2u
2
a
−au
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7u
2
a − 3au + 3u
2
+ 8a + u − 2
9
(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
7
u
6
c
4
(u
2
− u + 1)
3
c
6
(u
3
− u
2
+ 2u − 1)
2
c
8
(u
3
+ u
2
− 1)
2
c
9
, c
11
(u
3
+ u
2
+ 2u + 1)
2
c
10
(u
3
− u
2
+ 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)
3
c
3
, c
7
y
6
c
6
, c
9
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
c
8
, c
10
(y
3
− y
2
+ 2y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0.111778 − 0.558770I
b = 0.706350 + 0.266290I
3.02413 + 4.85801I 2.65209 − 7.50333I
u = −0.877439 + 0.744862I
a = 0.428020 + 0.376187I
b = −0.583789 + 0.478572I
3.02413 + 0.79824I −0.92725 + 3.21674I
u = −0.877439 − 0.744862I
a = 0.111778 + 0.558770I
b = 0.706350 − 0.266290I
3.02413 − 4.85801I 2.65209 + 7.50333I
u = −0.877439 − 0.744862I
a = 0.428020 − 0.376187I
b = −0.583789 − 0.478572I
3.02413 − 0.79824I −0.92725 − 3.21674I
u = 0.754878
a = −1.53980 + 2.66701I
b = 0.87744 − 1.51977I
−1.11345 + 2.02988I −2.22484 + 4.65789I
u = 0.754878
a = −1.53980 − 2.66701I
b = 0.87744 + 1.51977I
−1.11345 − 2.02988I −2.22484 − 4.65789I
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
3
)(u
39
+ 4u
38
+ ··· + 10u − 1)
c
2
((u
2
+ u + 1)
3
)(u
39
+ 22u
38
+ ··· + 170u − 1)
c
3
, c
7
u
6
(u
39
+ 3u
38
+ ··· + 160u + 64)
c
4
((u
2
− u + 1)
3
)(u
39
+ 4u
38
+ ··· + 10u − 1)
c
5
((u
2
+ u + 1)
3
)(u
39
− 4u
38
+ ··· + 602u − 49)
c
6
((u
3
− u
2
+ 2u − 1)
2
)(u
39
− 3u
38
+ ··· − 3u + 1)
c
8
((u
3
+ u
2
− 1)
2
)(u
39
− 3u
38
+ ··· − 5u + 1)
c
9
((u
3
+ u
2
+ 2u + 1)
2
)(u
39
− 3u
38
+ ··· − 3u + 1)
c
10
((u
3
− u
2
+ 1)
2
)(u
39
− 3u
38
+ ··· − 5u + 1)
c
11
((u
3
+ u
2
+ 2u + 1)
2
)(u
39
+ 23u
38
+ ··· + u + 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
3
)(y
39
+ 22y
38
+ ··· + 170y −1)
c
2
((y
2
+ y + 1)
3
)(y
39
− 6y
38
+ ··· + 31510y −1)
c
3
, c
7
y
6
(y
39
+ 35y
38
+ ··· − 23552y −4096)
c
5
((y
2
+ y + 1)
3
)(y
39
− 34y
38
+ ··· + 391706y −2401)
c
6
, c
9
((y
3
+ 3y
2
+ 2y −1)
2
)(y
39
+ 9y
38
+ ··· + y −1)
c
8
, c
10
((y
3
− y
2
+ 2y −1)
2
)(y
39
− 23y
38
+ ··· + y −1)
c
11
((y
3
+ 3y
2
+ 2y −1)
2
)(y
39
− 11y
38
+ ··· + 117y −1)
14
