11a
88
(K11a
88
)
A knot diagram
1
Linearized knot diagam
6 1 10 9 2 3 11 4 5 7 8
Solving Sequence
2,5 6,9
10 1 3 7 4 8 11
c
5
c
9
c
1
c
2
c
6
c
4
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.81735 × 10
18
u
55
− 3.41298 × 10
18
u
54
+ ··· + 7.25836 × 10
18
b − 6.54872 × 10
18
,
8.54661 × 10
18
u
55
− 1.96112 × 10
19
u
54
+ ··· + 7.25836 × 10
18
a − 6.19813 × 10
18
, u
56
− 2u
55
+ ··· − 2u + 1i
I
u
2
= h−au + 3b + a + 2u + 1, a
2
+ 2au − 7u − 7, u
2
+ u + 1i
I
u
3
= hb, a + u, u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 62 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
= h3.82 × 10
18
u
55
− 3.41 × 10
18
u
54
+ · · · + 7.26 × 10
18
b − 6.55 × 10
18
, 8.55 ×
10
18
u
55
−1.96×10
19
u
54
+· · ·+7.26×10
18
a−6.20×10
18
, u
56
−2u
55
+· · ·−2u+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
9
=
−1.17748u
55
+ 2.70188u
54
+ ··· − 7.40789u + 0.853930
−0.525924u
55
+ 0.470213u
54
+ ··· + 0.327275u + 0.902232
a
10
=
−1.70341u
55
+ 3.17209u
54
+ ··· − 7.08061u + 1.75616
−0.525924u
55
+ 0.470213u
54
+ ··· + 0.327275u + 0.902232
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
7
=
−u
6
− u
4
+ 1
u
8
+ 2u
6
+ 2u
4
a
4
=
−0.0147560u
55
+ 0.313638u
54
+ ··· − 6.67639u + 0.916847
0.352209u
55
− 0.918697u
54
+ ··· + 1.18445u + 1.11145
a
8
=
1.10278u
55
− 2.44048u
54
+ ··· + 5.22670u − 1.38381
0.449311u
55
− 0.0110571u
54
+ ··· + 0.457669u − 0.899349
a
11
=
−1.33623u
55
+ 3.16841u
54
+ ··· − 7.38742u + 1.20484
−0.480366u
55
+ 0.160009u
54
+ ··· + 0.210912u + 0.917813
a
11
=
−1.33623u
55
+ 3.16841u
54
+ ··· − 7.38742u + 1.20484
−0.480366u
55
+ 0.160009u
54
+ ··· + 0.210912u + 0.917813
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
10988692710744958139
3629180684127117001
u
55
+
21985136905178948607
3629180684127117001
u
54
+ ··· −
18377034251590244150
3629180684127117001
u +
18266861748021250925
3629180684127117001
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
56
− 2u
55
+ ··· − 2u + 1
c
2
u
56
+ 28u
55
+ ··· + 4u + 1
c
3
u
56
− 3u
55
+ ··· + 276u + 172
c
4
, c
8
, c
9
u
56
+ u
55
+ ··· + 12u + 4
c
6
u
56
+ 2u
55
+ ··· + 1554u + 481
c
7
, c
10
, c
11
u
56
+ 3u
55
+ ··· − 31u + 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
56
+ 28y
55
+ ··· + 4y + 1
c
2
y
56
+ 4y
55
+ ··· + 28y + 1
c
3
y
56
+ 9y
55
+ ··· + 99952y + 29584
c
4
, c
8
, c
9
y
56
− 51y
55
+ ··· + 48y + 16
c
6
y
56
− 20y
55
+ ··· − 456284y + 231361
c
7
, c
10
, c
11
y
56
− 53y
55
+ ··· + 747y + 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.761612 + 0.706746I
a = −2.61065 − 0.67242I
b = 1.324630 − 0.244844I
1.58146 − 5.73177I 1.83404 + 5.79402I
u = −0.761612 − 0.706746I
a = −2.61065 + 0.67242I
b = 1.324630 + 0.244844I
1.58146 + 5.73177I 1.83404 − 5.79402I
u = 0.690346 + 0.801960I
a = 0.481692 + 0.412002I
b = −0.066092 − 0.603875I
−2.82580 + 2.62743I −4.75305 − 4.09062I
u = 0.690346 − 0.801960I
a = 0.481692 − 0.412002I
b = −0.066092 + 0.603875I
−2.82580 − 2.62743I −4.75305 + 4.09062I
u = 0.451244 + 0.989156I
a = 0.050142 − 0.437553I
b = −0.542520 + 0.123434I
−0.57122 + 2.77824I 2.95589 − 4.20688I
u = 0.451244 − 0.989156I
a = 0.050142 + 0.437553I
b = −0.542520 − 0.123434I
−0.57122 − 2.77824I 2.95589 + 4.20688I
u = 0.853869 + 0.316506I
a = −2.36674 − 0.45164I
b = 1.40459 − 0.32683I
−0.70521 − 8.81361I 1.89048 + 4.78995I
u = 0.853869 − 0.316506I
a = −2.36674 + 0.45164I
b = 1.40459 + 0.32683I
−0.70521 + 8.81361I 1.89048 − 4.78995I
u = −0.569045 + 0.945562I
a = −2.02662 − 1.07884I
b = 1.411350 + 0.084042I
5.37458 − 1.80246I 7.34576 + 2.56666I
u = −0.569045 − 0.945562I
a = −2.02662 + 1.07884I
b = 1.411350 − 0.084042I
5.37458 + 1.80246I 7.34576 − 2.56666I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.631832 + 0.630832I
a = 2.75595 + 1.02264I
b = −1.399300 + 0.140066I
6.29507 − 2.91322I 8.51117 + 4.03861I
u = −0.631832 − 0.630832I
a = 2.75595 − 1.02264I
b = −1.399300 − 0.140066I
6.29507 + 2.91322I 8.51117 − 4.03861I
u = −0.829870 + 0.241336I
a = 0.509900 + 0.334719I
b = −0.240288 − 0.794736I
−5.93188 + 4.75475I −2.47991 − 3.65893I
u = −0.829870 − 0.241336I
a = 0.509900 − 0.334719I
b = −0.240288 + 0.794736I
−5.93188 − 4.75475I −2.47991 + 3.65893I
u = 0.374837 + 1.075050I
a = −0.490885 − 0.409888I
b = −1.087140 + 0.111404I
−0.27332 + 2.70620I 0
u = 0.374837 − 1.075050I
a = −0.490885 + 0.409888I
b = −1.087140 − 0.111404I
−0.27332 − 2.70620I 0
u = 0.268445 + 1.111910I
a = 0.146715 − 0.451206I
b = 1.272610 − 0.252980I
0.50238 − 1.98879I 0
u = 0.268445 − 1.111910I
a = 0.146715 + 0.451206I
b = 1.272610 + 0.252980I
0.50238 + 1.98879I 0
u = −0.385295 + 1.082820I
a = −0.468644 − 1.033150I
b = −0.004875 − 0.663333I
−3.45328 − 1.33657I 0
u = −0.385295 − 1.082820I
a = −0.468644 + 1.033150I
b = −0.004875 + 0.663333I
−3.45328 + 1.33657I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.698151 + 0.927977I
a = 1.99746 + 0.91434I
b = −1.275360 − 0.207940I
0.926044 + 0.238949I 0
u = −0.698151 − 0.927977I
a = 1.99746 − 0.91434I
b = −1.275360 + 0.207940I
0.926044 − 0.238949I 0
u = −0.459731 + 1.077510I
a = 1.83760 + 1.09993I
b = −1.55132 − 0.05064I
1.33205 − 3.50361I 0
u = −0.459731 − 1.077510I
a = 1.83760 − 1.09993I
b = −1.55132 + 0.05064I
1.33205 + 3.50361I 0
u = 0.743330 + 0.310940I
a = 2.16703 + 0.83141I
b = −1.369280 + 0.248755I
4.80088 − 4.79415I 6.07434 + 4.15713I
u = 0.743330 − 0.310940I
a = 2.16703 − 0.83141I
b = −1.369280 − 0.248755I
4.80088 + 4.79415I 6.07434 − 4.15713I
u = 0.491299 + 1.104420I
a = 0.51919 − 2.24490I
b = −1.281970 − 0.243617I
0.50012 + 4.58916I 0
u = 0.491299 − 1.104420I
a = 0.51919 + 2.24490I
b = −1.281970 + 0.243617I
0.50012 − 4.58916I 0
u = −0.278365 + 0.729460I
a = 0.896209 − 1.073100I
b = −0.259021 − 0.390087I
−1.99309 − 1.19360I −4.63700 − 2.51647I
u = −0.278365 − 0.729460I
a = 0.896209 + 1.073100I
b = −0.259021 + 0.390087I
−1.99309 + 1.19360I −4.63700 + 2.51647I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.502022 + 1.112160I
a = 0.985384 + 0.850050I
b = −0.199636 + 0.712351I
−2.59517 − 6.04162I 0
u = −0.502022 − 1.112160I
a = 0.985384 − 0.850050I
b = −0.199636 − 0.712351I
−2.59517 + 6.04162I 0
u = 0.764797 + 0.121262I
a = 1.42719 + 0.09783I
b = −0.889806 − 0.402045I
−3.86656 − 0.41270I −0.197348 − 0.929430I
u = 0.764797 − 0.121262I
a = 1.42719 − 0.09783I
b = −0.889806 + 0.402045I
−3.86656 + 0.41270I −0.197348 + 0.929430I
u = 0.218016 + 1.217340I
a = 0.398270 + 0.377014I
b = −1.357810 + 0.368437I
−5.76926 − 5.58643I 0
u = 0.218016 − 1.217340I
a = 0.398270 − 0.377014I
b = −1.357810 − 0.368437I
−5.76926 + 5.58643I 0
u = −0.287537 + 1.214310I
a = 0.204967 + 0.561724I
b = 0.159869 + 0.851956I
−10.53930 + 1.20311I 0
u = −0.287537 − 1.214310I
a = 0.204967 − 0.561724I
b = 0.159869 − 0.851956I
−10.53930 − 1.20311I 0
u = 0.364658 + 1.197690I
a = −0.622424 + 1.025440I
b = 1.042020 + 0.460884I
−7.81847 + 3.46546I 0
u = 0.364658 − 1.197690I
a = −0.622424 − 1.025440I
b = 1.042020 − 0.460884I
−7.81847 − 3.46546I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.553003 + 1.128780I
a = −1.31357 + 2.28219I
b = 1.377580 + 0.293281I
2.40647 + 9.70272I 0
u = 0.553003 − 1.128780I
a = −1.31357 − 2.28219I
b = 1.377580 − 0.293281I
2.40647 − 9.70272I 0
u = 0.501395 + 1.168450I
a = −0.103705 + 0.434801I
b = 0.861654 − 0.536583I
−6.88232 + 5.05308I 0
u = 0.501395 − 1.168450I
a = −0.103705 − 0.434801I
b = 0.861654 + 0.536583I
−6.88232 − 5.05308I 0
u = 0.442137 + 0.560010I
a = −0.812619 + 0.111492I
b = 0.366660 + 0.363322I
0.730759 + 1.016190I 5.20362 − 4.92767I
u = 0.442137 − 0.560010I
a = −0.812619 − 0.111492I
b = 0.366660 − 0.363322I
0.730759 − 1.016190I 5.20362 + 4.92767I
u = −0.554081 + 1.174850I
a = −1.075370 − 0.533382I
b = 0.284145 − 0.839978I
−8.70986 − 9.86105I 0
u = −0.554081 − 1.174850I
a = −1.075370 + 0.533382I
b = 0.284145 + 0.839978I
−8.70986 + 9.86105I 0
u = 0.589077 + 1.163720I
a = 1.67040 − 1.98061I
b = −1.43155 − 0.34420I
−3.2473 + 14.1444I 0
u = 0.589077 − 1.163720I
a = 1.67040 + 1.98061I
b = −1.43155 + 0.34420I
−3.2473 − 14.1444I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.604383 + 0.247576I
a = −0.549400 + 0.155635I
b = 0.196990 + 0.593586I
−0.16557 + 1.66732I 1.05437 − 4.59670I
u = −0.604383 − 0.247576I
a = −0.549400 − 0.155635I
b = 0.196990 − 0.593586I
−0.16557 − 1.66732I 1.05437 + 4.59670I
u = 0.558020 + 0.203304I
a = −1.14181 − 1.13686I
b = 1.302810 − 0.128993I
2.93700 − 0.37083I 3.52953 − 0.41815I
u = 0.558020 − 0.203304I
a = −1.14181 + 1.13686I
b = 1.302810 + 0.128993I
2.93700 + 0.37083I 3.52953 + 0.41815I
u = −0.302548 + 0.409621I
a = −3.46567 − 2.43013I
b = 1.45106 − 0.06557I
3.41711 − 0.18501I 2.17012 − 1.34687I
u = −0.302548 − 0.409621I
a = −3.46567 + 2.43013I
b = 1.45106 + 0.06557I
3.41711 + 0.18501I 2.17012 + 1.34687I
10
II. I
u
2
= h−au + 3b + a + 2u + 1, a
2
+ 2au − 7u − 7, u
2
+ u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u + 1
a
9
=
a
1
3
au −
1
3
a −
2
3
u −
1
3
a
10
=
1
3
au +
2
3
a −
2
3
u −
1
3
1
3
au −
1
3
a −
2
3
u −
1
3
a
1
=
−u
u + 1
a
3
=
−1
0
a
7
=
−u
u + 1
a
4
=
2
3
au +
1
3
a −
7
3
u −
11
3
2
a
8
=
−
1
3
au −
2
3
a +
2
3
u +
1
3
−
1
3
au +
1
3
a +
2
3
u +
1
3
a
11
=
1
3
au +
2
3
a −
5
3
u −
1
3
1
3
au −
1
3
a +
1
3
u +
2
3
a
11
=
1
3
au +
2
3
a −
5
3
u −
1
3
1
3
au −
1
3
a +
1
3
u +
2
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u + 4
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
(u
2
− u + 1)
2
c
2
, c
5
(u
2
+ u + 1)
2
c
3
, c
4
, c
8
c
9
(u
2
− 2)
2
c
7
(u + 1)
4
c
10
, c
11
(u − 1)
4
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
(y
2
+ y + 1)
2
c
3
, c
4
, c
8
c
9
(y −2)
4
c
7
, c
10
, c
11
(y −1)
4
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.62132 − 2.09077I
b = 1.41421
3.28987 − 2.02988I 2.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = 2.62132 + 0.35872I
b = −1.41421
3.28987 − 2.02988I 2.00000 + 3.46410I
u = −0.500000 − 0.866025I
a = −1.62132 + 2.09077I
b = 1.41421
3.28987 + 2.02988I 2.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = 2.62132 − 0.35872I
b = −1.41421
3.28987 + 2.02988I 2.00000 − 3.46410I
14
III. I
u
3
= hb, a + u, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u + 1
a
9
=
−u
0
a
10
=
−u
0
a
1
=
−u
u − 1
a
3
=
1
0
a
7
=
u
−u + 1
a
4
=
1
0
a
8
=
−u
0
a
11
=
−2u
u − 1
a
11
=
−2u
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u + 2
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
2
+ u + 1
c
3
, c
4
, c
8
c
9
u
2
c
5
u
2
− u + 1
c
7
(u − 1)
2
c
10
, c
11
(u + 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
y
2
+ y + 1
c
3
, c
4
, c
8
c
9
y
2
c
7
, c
10
, c
11
(y −1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.500000 − 0.866025I
b = 0
−1.64493 + 2.02988I 0. − 3.46410I
u = 0.500000 − 0.866025I
a = −0.500000 + 0.866025I
b = 0
−1.64493 − 2.02988I 0. + 3.46410I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
56
− 2u
55
+ ··· − 2u + 1)
c
2
((u
2
+ u + 1)
3
)(u
56
+ 28u
55
+ ··· + 4u + 1)
c
3
u
2
(u
2
− 2)
2
(u
56
− 3u
55
+ ··· + 276u + 172)
c
4
, c
8
, c
9
u
2
(u
2
− 2)
2
(u
56
+ u
55
+ ··· + 12u + 4)
c
5
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
56
− 2u
55
+ ··· − 2u + 1)
c
6
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
56
+ 2u
55
+ ··· + 1554u + 481)
c
7
((u − 1)
2
)(u + 1)
4
(u
56
+ 3u
55
+ ··· − 31u + 7)
c
10
, c
11
((u − 1)
4
)(u + 1)
2
(u
56
+ 3u
55
+ ··· − 31u + 7)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
2
+ y + 1)
3
)(y
56
+ 28y
55
+ ··· + 4y + 1)
c
2
((y
2
+ y + 1)
3
)(y
56
+ 4y
55
+ ··· + 28y + 1)
c
3
y
2
(y −2)
4
(y
56
+ 9y
55
+ ··· + 99952y + 29584)
c
4
, c
8
, c
9
y
2
(y −2)
4
(y
56
− 51y
55
+ ··· + 48y + 16)
c
6
((y
2
+ y + 1)
3
)(y
56
− 20y
55
+ ··· − 456284y + 231361)
c
7
, c
10
, c
11
((y −1)
6
)(y
56
− 53y
55
+ ··· + 747y + 49)
20
