11a
86
(K11a
86
)
A knot diagram
1
Linearized knot diagam
6 1 8 9 2 3 11 4 5 7 10
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
= h−1.06825 × 10
16
u
50
+ 1.14118 × 10
17
u
49
+ ··· + 1.72441 × 10
17
b + 1.78982 × 10
17
,
1.65108 × 10
17
u
50
− 3.23686 × 10
17
u
49
+ ··· + 1.72441 × 10
17
a + 6.56927 × 10
17
, u
51
− 2u
50
+ ··· + 2u − 1i
I
u
2
= h−au + b − a − 1, a
2
− 2au + u + 1, u
2
+ u + 1i
I
u
3
= hb, a − u, u
2
− u + 1i
* 3 irreducible components of dim
C
= 0, with total 57 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
= h−1.07×10
16
u
50
+1.14×10
17
u
49
+· · ·+1.72×10
17
b+1.79×10
17
, 1.65×
10
17
u
50
−3.24×10
17
u
49
+· · ·+1.72×10
17
a+6.57×10
17
, u
51
−2u
50
+· · ·+2u−1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
9
=
−0.957478u
50
+ 1.87709u
49
+ ··· + 6.34747u − 3.80958
0.0619485u
50
− 0.661781u
49
+ ··· − 0.419204u − 1.03793
a
10
=
−1.01943u
50
+ 2.53887u
49
+ ··· + 6.76667u − 2.77164
0.0619485u
50
− 0.661781u
49
+ ··· − 0.419204u − 1.03793
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
=
0.197966u
50
+ 0.121740u
49
+ ··· + 6.34202u − 3.22404
0.475917u
50
− 0.906399u
49
+ ··· − 1.37093u − 1.53340
a
8
=
1.37822u
50
− 3.01777u
49
+ ··· − 6.77353u + 2.71826
0.314717u
50
+ 0.217072u
49
+ ··· + 1.51590u + 0.995630
a
11
=
−1.28901u
50
+ 2.47244u
49
+ ··· + 6.66242u − 3.49712
−0.225525u
50
− 0.324327u
49
+ ··· − 0.729101u − 1.01135
a
11
=
−1.28901u
50
+ 2.47244u
49
+ ··· + 6.66242u − 3.49712
−0.225525u
50
− 0.324327u
49
+ ··· − 0.729101u − 1.01135
(ii) Obstruction class = −1
(iii) Cusp Shapes =
159651415798743733
86220451832092937
u
50
−
251339651139007465
86220451832092937
u
49
+ ···−
382063726346780762
86220451832092937
u −
177790526868945837
86220451832092937
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
51
− 2u
50
+ ··· + 2u − 1
c
2
u
51
+ 26u
50
+ ··· − 4u − 1
c
3
, c
4
, c
8
c
9
u
51
− u
50
+ ··· + 12u + 4
c
6
u
51
+ 2u
50
+ ··· + 102u − 289
c
7
, c
10
u
51
− 3u
50
+ ··· − u + 7
c
11
u
51
− 23u
50
+ ··· + 85u − 49
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
51
+ 26y
50
+ ··· − 4y −1
c
2
y
51
+ 2y
50
+ ··· + 20y −1
c
3
, c
4
, c
8
c
9
y
51
− 61y
50
+ ··· + 208y −16
c
6
y
51
− 22y
50
+ ··· − 130628y −83521
c
7
, c
10
y
51
− 23y
50
+ ··· + 85y −49
c
11
y
51
+ 17y
50
+ ··· + 63869y −2401
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.653226 + 0.692698I
a = −0.148299 + 0.771802I
b = 0.548925 − 0.344769I
1.91333 + 3.68884I −0.17566 − 8.64084I
u = 0.653226 − 0.692698I
a = −0.148299 − 0.771802I
b = 0.548925 + 0.344769I
1.91333 − 3.68884I −0.17566 + 8.64084I
u = −0.373145 + 0.994821I
a = 1.14320 − 1.08432I
b = 1.269780 + 0.040551I
−4.95677 − 2.83280I −9.17472 + 5.31542I
u = −0.373145 − 0.994821I
a = 1.14320 + 1.08432I
b = 1.269780 − 0.040551I
−4.95677 + 2.83280I −9.17472 − 5.31542I
u = −0.761774 + 0.749195I
a = −0.278985 + 1.056910I
b = −1.57317 − 0.07465I
−5.34945 − 5.09088I −4.00636 + 5.74458I
u = −0.761774 − 0.749195I
a = −0.278985 − 1.056910I
b = −1.57317 + 0.07465I
−5.34945 + 5.09088I −4.00636 − 5.74458I
u = 0.873962 + 0.290660I
a = −0.558370 + 0.726636I
b = −1.61853 − 0.15433I
−8.11783 − 8.19112I −3.54072 + 4.45146I
u = 0.873962 − 0.290660I
a = −0.558370 − 0.726636I
b = −1.61853 + 0.15433I
−8.11783 + 8.19112I −3.54072 − 4.45146I
u = 0.606693 + 0.904521I
a = 0.425610 − 0.192324I
b = −0.478539 − 0.218508I
1.29833 + 1.21266I −3.42209 + 3.60169I
u = 0.606693 − 0.904521I
a = 0.425610 + 0.192324I
b = −0.478539 + 0.218508I
1.29833 − 1.21266I −3.42209 − 3.60169I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.477844 + 1.005770I
a = −1.81776 + 1.00351I
b = −0.550123 − 0.216418I
1.10277 − 2.92056I −4.16055 + 6.87287I
u = −0.477844 − 1.005770I
a = −1.81776 − 1.00351I
b = −0.550123 + 0.216418I
1.10277 + 2.92056I −4.16055 − 6.87287I
u = 0.848872 + 0.178353I
a = 0.815584 − 0.510581I
b = 1.63006 + 0.09121I
−10.01400 − 2.30364I −5.81940 + 0.26148I
u = 0.848872 − 0.178353I
a = 0.815584 + 0.510581I
b = 1.63006 − 0.09121I
−10.01400 + 2.30364I −5.81940 − 0.26148I
u = −0.715111 + 0.887420I
a = 0.440048 − 0.989396I
b = 1.56489 − 0.03455I
−5.76367 − 0.45170I −5.30593 + 0.I
u = −0.715111 − 0.887420I
a = 0.440048 + 0.989396I
b = 1.56489 + 0.03455I
−5.76367 + 0.45170I −5.30593 + 0.I
u = 0.385624 + 1.094960I
a = −0.487613 − 0.077571I
b = −0.003368 + 0.682499I
−1.93767 + 1.33394I −3.91651 + 0.I
u = 0.385624 − 1.094960I
a = −0.487613 + 0.077571I
b = −0.003368 − 0.682499I
−1.93767 − 1.33394I −3.91651 + 0.I
u = −0.777418 + 0.276187I
a = 0.106054 + 0.767256I
b = 0.725460 − 0.523141I
−0.15019 + 5.64266I −1.04154 − 6.14060I
u = −0.777418 − 0.276187I
a = 0.106054 − 0.767256I
b = 0.725460 + 0.523141I
−0.15019 − 5.64266I −1.04154 + 6.14060I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.393138 + 1.114690I
a = 1.037440 − 0.580996I
b = 1.049420 − 0.251699I
−5.15851 − 2.68412I −8.38581 + 3.33159I
u = −0.393138 − 1.114690I
a = 1.037440 + 0.580996I
b = 1.049420 + 0.251699I
−5.15851 + 2.68412I −8.38581 − 3.33159I
u = −0.282693 + 1.153160I
a = −0.980168 + 0.289348I
b = −0.854041 + 0.456398I
−4.54342 + 2.50022I −7.39422 − 3.48023I
u = −0.282693 − 1.153160I
a = −0.980168 − 0.289348I
b = −0.854041 − 0.456398I
−4.54342 − 2.50022I −7.39422 + 3.48023I
u = 0.452176 + 1.119860I
a = 3.26876 + 1.81417I
b = 1.58540 − 0.04944I
−6.32061 + 3.82021I 0
u = 0.452176 − 1.119860I
a = 3.26876 − 1.81417I
b = 1.58540 + 0.04944I
−6.32061 − 3.82021I 0
u = 0.503800 + 1.120900I
a = 0.470374 + 0.032521I
b = −0.202005 − 0.728941I
−1.07037 + 6.18731I 0
u = 0.503800 − 1.120900I
a = 0.470374 − 0.032521I
b = −0.202005 + 0.728941I
−1.07037 − 6.18731I 0
u = −0.484334 + 1.137730I
a = 1.38555 − 0.92980I
b = 0.839056 + 0.455492I
−4.51627 − 5.12379I 0
u = −0.484334 − 1.137730I
a = 1.38555 + 0.92980I
b = 0.839056 − 0.455492I
−4.51627 + 5.12379I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.269126 + 0.708216I
a = −0.449611 − 0.544666I
b = −0.265341 + 0.389045I
−0.326016 + 1.158490I −3.80255 − 5.96760I
u = 0.269126 − 0.708216I
a = −0.449611 + 0.544666I
b = −0.265341 − 0.389045I
−0.326016 − 1.158490I −3.80255 + 5.96760I
u = −0.468235 + 0.565840I
a = 0.731516 + 1.135060I
b = 0.363476 − 0.377017I
2.43662 − 1.03982I 2.70309 − 2.37854I
u = −0.468235 − 0.565840I
a = 0.731516 − 1.135060I
b = 0.363476 + 0.377017I
2.43662 + 1.03982I 2.70309 + 2.37854I
u = 0.241188 + 1.242520I
a = 2.55925 + 0.13213I
b = 1.65434 + 0.12357I
−13.17000 − 4.70678I 0
u = 0.241188 − 1.242520I
a = 2.55925 − 0.13213I
b = 1.65434 − 0.12357I
−13.17000 + 4.70678I 0
u = −0.551420 + 1.150110I
a = −1.29108 + 0.99248I
b = −0.754244 − 0.593767I
−2.72526 − 10.62070I 0
u = −0.551420 − 1.150110I
a = −1.29108 − 0.99248I
b = −0.754244 + 0.593767I
−2.72526 + 10.62070I 0
u = 0.330757 + 1.237090I
a = −2.64813 − 0.57334I
b = −1.67128 − 0.05432I
−14.4656 + 1.6283I 0
u = 0.330757 − 1.237090I
a = −2.64813 + 0.57334I
b = −1.67128 + 0.05432I
−14.4656 − 1.6283I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.533489 + 1.196450I
a = −2.19793 − 1.79578I
b = −1.64958 + 0.12738I
−13.0576 + 7.3517I 0
u = 0.533489 − 1.196450I
a = −2.19793 + 1.79578I
b = −1.64958 − 0.12738I
−13.0576 − 7.3517I 0
u = 0.585702 + 1.179630I
a = 1.87475 + 2.03032I
b = 1.62902 − 0.17990I
−10.7944 + 13.5574I 0
u = 0.585702 − 1.179630I
a = 1.87475 − 2.03032I
b = 1.62902 + 0.17990I
−10.7944 − 13.5574I 0
u = −0.658054 + 0.143633I
a = −0.156833 − 0.508796I
b = −0.772507 + 0.296101I
−1.73343 + 0.77952I −4.48847 − 1.15850I
u = −0.658054 − 0.143633I
a = −0.156833 + 0.508796I
b = −0.772507 − 0.296101I
−1.73343 − 0.77952I −4.48847 + 1.15850I
u = 0.624363 + 0.237680I
a = 0.082181 + 1.030970I
b = 0.193282 − 0.611091I
1.42567 − 1.76270I 2.33352 + 1.54024I
u = 0.624363 − 0.237680I
a = 0.082181 − 1.030970I
b = 0.193282 + 0.611091I
1.42567 + 1.76270I 2.33352 − 1.54024I
u = −0.207283 + 0.506525I
a = −0.41811 + 2.77427I
b = −1.406490 − 0.077528I
−3.26856 − 0.24799I −3.08378 − 1.55453I
u = −0.207283 − 0.506525I
a = −0.41811 − 2.77427I
b = −1.406490 + 0.077528I
−3.26856 + 0.24799I −3.08378 + 1.55453I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.482939
a = −2.81485
b = −1.50782
−3.54033 −1.57180
10
II. I
u
2
= h−au + b − a − 1, a
2
− 2au + u + 1, u
2
+ u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u + 1
a
9
=
a
au + a + 1
a
10
=
−au − 1
au + a + 1
a
1
=
−u
u + 1
a
3
=
−1
0
a
7
=
−u
u + 1
a
4
=
a + u + 1
−2
a
8
=
au + 1
−au − a − 1
a
11
=
−au − u − 1
au + a + u + 2
a
11
=
−au − u − 1
au + a + u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
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
, c
11
(u − 1)
4
c
10
(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 = 0.207107 − 0.358719I
b = 1.41421
−3.28987 − 2.02988I −2.00000 + 3.46410I
u = −0.500000 + 0.866025I
a = −1.20711 + 2.09077I
b = −1.41421
−3.28987 − 2.02988I −2.00000 + 3.46410I
u = −0.500000 − 0.866025I
a = 0.207107 + 0.358719I
b = 1.41421
−3.28987 + 2.02988I −2.00000 − 3.46410I
u = −0.500000 − 0.866025I
a = −1.20711 − 2.09077I
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
=
0
u − 1
a
11
=
0
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
51
− 2u
50
+ ··· + 2u − 1)
c
2
((u
2
+ u + 1)
3
)(u
51
+ 26u
50
+ ··· − 4u − 1)
c
3
, c
4
, c
8
c
9
u
2
(u
2
− 2)
2
(u
51
− u
50
+ ··· + 12u + 4)
c
5
(u
2
− u + 1)(u
2
+ u + 1)
2
(u
51
− 2u
50
+ ··· + 2u − 1)
c
6
((u
2
− u + 1)
2
)(u
2
+ u + 1)(u
51
+ 2u
50
+ ··· + 102u − 289)
c
7
((u − 1)
4
)(u + 1)
2
(u
51
− 3u
50
+ ··· − u + 7)
c
10
((u − 1)
2
)(u + 1)
4
(u
51
− 3u
50
+ ··· − u + 7)
c
11
((u − 1)
6
)(u
51
− 23u
50
+ ··· + 85u − 49)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
((y
2
+ y + 1)
3
)(y
51
+ 26y
50
+ ··· − 4y −1)
c
2
((y
2
+ y + 1)
3
)(y
51
+ 2y
50
+ ··· + 20y −1)
c
3
, c
4
, c
8
c
9
y
2
(y −2)
4
(y
51
− 61y
50
+ ··· + 208y −16)
c
6
((y
2
+ y + 1)
3
)(y
51
− 22y
50
+ ··· − 130628y −83521)
c
7
, c
10
((y −1)
6
)(y
51
− 23y
50
+ ··· + 85y −49)
c
11
((y −1)
6
)(y
51
+ 17y
50
+ ··· + 63869y −2401)
20
