11a
80
(K11a
80
)
A knot diagram
1
Linearized knot diagam
6 1 9 10 2 3 4 11 7 8 5
Solving Sequence
2,5
6 1 3
8,11
9 10 4 7
c
5
c
1
c
2
c
11
c
8
c
10
c
4
c
7
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.10807 × 10
23
u
69
+ 2.13624 × 10
23
u
68
+ ··· + 3.25909 × 10
22
b + 1.02987 × 10
23
,
7.69171 × 10
22
u
69
− 4.41119 × 10
22
u
68
+ ··· + 3.25909 × 10
22
a − 4.48719 × 10
22
, u
70
− 2u
69
+ ··· − 5u + 1i
I
u
2
= hb + 2u − 1, a − 2, u
2
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 72 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−1.11×10
23
u
69
+2.14×10
23
u
68
+· · ·+3.26×10
22
b+1.03×10
23
, 7.69×
10
22
u
69
−4.41×10
22
u
68
+· · ·+3.26×10
22
a−4.49×10
22
, u
70
−2u
69
+· · ·−5u+1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
8
=
−2.36008u
69
+ 1.35350u
68
+ ··· + 2.96444u + 1.37682
3.39992u
69
− 6.55471u
68
+ ··· + 15.8232u − 3.16000
a
11
=
u
3
u
3
+ u
a
9
=
−2.36035u
69
+ 1.58814u
68
+ ··· + 2.07836u + 1.59404
3.19965u
69
− 6.13729u
68
+ ··· + 14.0060u − 2.96000
a
10
=
2.55997u
69
− 1.82063u
68
+ ··· − 3.25615u − 1.70993
−3.20003u
69
+ 6.36373u
68
+ ··· − 14.8901u + 3.16000
a
4
=
6.40571u
69
− 13.1764u
68
+ ··· + 34.5221u − 3.44819
1.36498u
69
+ 3.63005u
68
+ ··· − 22.5376u + 5.79503
a
7
=
−u
6
− u
4
+ 1
u
8
+ 2u
6
+ 2u
4
a
7
=
−u
6
− u
4
+ 1
u
8
+ 2u
6
+ 2u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes =
80166540663254872590873
10863644501129272985843
u
69
−
390207808448510879557707
10863644501129272985843
u
68
+ ··· +
1547885087409440226722281
10863644501129272985843
u −
321339458068418410398408
10863644501129272985843
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
70
− 2u
69
+ ··· − 5u + 1
c
2
u
70
+ 38u
69
+ ··· − u + 1
c
3
u
70
+ 2u
69
+ ··· + 23u + 107
c
4
u
70
+ 31u
68
+ ··· − 13u + 1
c
6
, c
11
u
70
+ 2u
69
+ ··· − 169u + 17
c
7
u
70
− 2u
69
+ ··· − u + 1
c
8
, c
10
u
70
+ 3u
69
+ ··· − 4u + 1
c
9
u
70
− 11u
69
+ ··· + 4u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
70
+ 38y
69
+ ··· − y + 1
c
2
y
70
− 10y
69
+ ··· − 93y + 1
c
3
y
70
+ 70y
69
+ ··· + 344439y + 11449
c
4
y
70
+ 62y
69
+ ··· + 127y + 1
c
6
, c
11
y
70
− 58y
69
+ ··· − 16865y + 289
c
7
y
70
− 10y
69
+ ··· − y + 1
c
8
, c
10
y
70
− 41y
69
+ ··· + 16y + 1
c
9
y
70
− 15y
69
+ ··· − 200y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.629527 + 0.806981I
a = 1.41570 − 0.09923I
b = 0.33030 − 1.77174I
1.04825 + 2.45107I 0
u = 0.629527 − 0.806981I
a = 1.41570 + 0.09923I
b = 0.33030 + 1.77174I
1.04825 − 2.45107I 0
u = −0.067651 + 1.027570I
a = 0.485648 + 1.262690I
b = 0.577177 + 0.334792I
−3.59009 + 0.96831I 0
u = −0.067651 − 1.027570I
a = 0.485648 − 1.262690I
b = 0.577177 − 0.334792I
−3.59009 − 0.96831I 0
u = 0.384830 + 0.888904I
a = 0.644025 + 0.369584I
b = 0.586602 − 0.314795I
−0.32453 + 1.95228I 0. − 3.30692I
u = 0.384830 − 0.888904I
a = 0.644025 − 0.369584I
b = 0.586602 + 0.314795I
−0.32453 − 1.95228I 0. + 3.30692I
u = −0.479076 + 0.914334I
a = −0.835502 − 0.636450I
b = −0.0502703 − 0.0626528I
−0.79732 − 5.73779I 0
u = −0.479076 − 0.914334I
a = −0.835502 + 0.636450I
b = −0.0502703 + 0.0626528I
−0.79732 + 5.73779I 0
u = −0.463852 + 0.816066I
a = 1.03712 − 1.14502I
b = −0.065861 + 1.165360I
3.32585 − 3.64623I 8.36983 + 8.12955I
u = −0.463852 − 0.816066I
a = 1.03712 + 1.14502I
b = −0.065861 − 1.165360I
3.32585 + 3.64623I 8.36983 − 8.12955I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.584393 + 0.923619I
a = −2.09703 + 0.21211I
b = −0.57442 − 1.93822I
3.25750 − 10.82580I 0
u = −0.584393 − 0.923619I
a = −2.09703 − 0.21211I
b = −0.57442 + 1.93822I
3.25750 + 10.82580I 0
u = 0.377490 + 0.808869I
a = −4.46362 − 0.46805I
b = 0.09813 + 3.87415I
1.50422 + 1.66288I −31.1505 + 27.2219I
u = 0.377490 − 0.808869I
a = −4.46362 + 0.46805I
b = 0.09813 − 3.87415I
1.50422 − 1.66288I −31.1505 − 27.2219I
u = −0.653862 + 0.578775I
a = −0.775452 + 0.290765I
b = 0.31099 − 1.84334I
4.24693 + 6.03843I 5.38503 − 4.49312I
u = −0.653862 − 0.578775I
a = −0.775452 − 0.290765I
b = 0.31099 + 1.84334I
4.24693 − 6.03843I 5.38503 + 4.49312I
u = 0.851538 + 0.139959I
a = −1.044180 − 0.205566I
b = −1.12487 − 1.81917I
−0.99836 − 11.50700I 1.84093 + 6.73084I
u = 0.851538 − 0.139959I
a = −1.044180 + 0.205566I
b = −1.12487 + 1.81917I
−0.99836 + 11.50700I 1.84093 − 6.73084I
u = 0.060029 + 1.146880I
a = −0.18745 + 2.16143I
b = −0.299074 + 1.201650I
−1.44288 + 5.44607I 0
u = 0.060029 − 1.146880I
a = −0.18745 − 2.16143I
b = −0.299074 − 1.201650I
−1.44288 − 5.44607I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.830885 + 0.169788I
a = 0.885873 − 0.209106I
b = 1.24593 − 1.41968I
−2.35547 + 3.73849I −0.65968 − 5.52505I
u = −0.830885 − 0.169788I
a = 0.885873 + 0.209106I
b = 1.24593 + 1.41968I
−2.35547 − 3.73849I −0.65968 + 5.52505I
u = −0.844269 + 0.045265I
a = 0.529036 − 0.217259I
b = 0.438531 + 0.049854I
−3.62841 + 0.20387I −2.37460 + 1.94241I
u = −0.844269 − 0.045265I
a = 0.529036 + 0.217259I
b = 0.438531 − 0.049854I
−3.62841 − 0.20387I −2.37460 − 1.94241I
u = 0.696611 + 0.477869I
a = −0.242169 + 0.044656I
b = −0.23295 − 1.56391I
3.77878 + 3.85148I 5.41405 − 7.02923I
u = 0.696611 − 0.477869I
a = −0.242169 − 0.044656I
b = −0.23295 + 1.56391I
3.77878 − 3.85148I 5.41405 + 7.02923I
u = −0.441288 + 0.716327I
a = 1.55504 − 1.61375I
b = 0.220804 + 0.919376I
3.62277 − 0.21985I 9.90987 + 0.81181I
u = −0.441288 − 0.716327I
a = 1.55504 + 1.61375I
b = 0.220804 − 0.919376I
3.62277 + 0.21985I 9.90987 − 0.81181I
u = 0.589180 + 1.012730I
a = 2.20968 − 0.22515I
b = 0.60519 − 1.40546I
2.24373 + 1.06051I 0
u = 0.589180 − 1.012730I
a = 2.20968 + 0.22515I
b = 0.60519 + 1.40546I
2.24373 − 1.06051I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.816520 + 0.092061I
a = −0.246027 − 0.625616I
b = 0.227076 + 0.411053I
−4.47780 − 5.27299I −1.13386 + 5.09920I
u = 0.816520 − 0.092061I
a = −0.246027 + 0.625616I
b = 0.227076 − 0.411053I
−4.47780 + 5.27299I −1.13386 − 5.09920I
u = 0.155133 + 0.771122I
a = 1.09854 − 0.97547I
b = −0.000848 − 1.218090I
0.526876 + 1.304500I 2.10750 − 3.09155I
u = 0.155133 − 0.771122I
a = 1.09854 + 0.97547I
b = −0.000848 + 1.218090I
0.526876 − 1.304500I 2.10750 + 3.09155I
u = −0.751358 + 0.033892I
a = −1.004370 + 0.873364I
b = −0.74452 + 2.95488I
−0.708262 + 0.627776I 0.33072 + 10.74054I
u = −0.751358 − 0.033892I
a = −1.004370 − 0.873364I
b = −0.74452 − 2.95488I
−0.708262 − 0.627776I 0.33072 − 10.74054I
u = 0.741533 + 0.089293I
a = 0.873738 − 0.398690I
b = 0.309943 + 1.288770I
0.80687 − 3.39629I 5.02552 + 6.06179I
u = 0.741533 − 0.089293I
a = 0.873738 + 0.398690I
b = 0.309943 − 1.288770I
0.80687 + 3.39629I 5.02552 − 6.06179I
u = 0.457271 + 1.166860I
a = −2.33391 − 0.73724I
b = −0.832098 + 0.217701I
−0.90108 + 4.15644I 0
u = 0.457271 − 1.166860I
a = −2.33391 + 0.73724I
b = −0.832098 − 0.217701I
−0.90108 − 4.15644I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.420042 + 1.181250I
a = −0.283873 − 1.352310I
b = −0.459172 − 1.228100I
−2.80139 + 0.62222I 0
u = 0.420042 − 1.181250I
a = −0.283873 + 1.352310I
b = −0.459172 + 1.228100I
−2.80139 − 0.62222I 0
u = −0.441328 + 1.192850I
a = −0.53713 − 4.16968I
b = 1.05472 − 2.74195I
−4.22443 − 3.62054I 0
u = −0.441328 − 1.192850I
a = −0.53713 + 4.16968I
b = 1.05472 + 2.74195I
−4.22443 + 3.62054I 0
u = −0.359060 + 1.223280I
a = −1.37931 + 2.37042I
b = −1.29014 + 1.14965I
−6.61992 − 0.21045I 0
u = −0.359060 − 1.223280I
a = −1.37931 − 2.37042I
b = −1.29014 − 1.14965I
−6.61992 + 0.21045I 0
u = 0.482887 + 1.183360I
a = −2.25253 + 0.52090I
b = −0.35025 + 1.40847I
−2.35077 + 7.93022I 0
u = 0.482887 − 1.183360I
a = −2.25253 − 0.52090I
b = −0.35025 − 1.40847I
−2.35077 − 7.93022I 0
u = −0.466698 + 1.191900I
a = 4.54250 + 2.63619I
b = 0.94499 + 3.21611I
−4.04232 − 5.06949I 0
u = −0.466698 − 1.191900I
a = 4.54250 − 2.63619I
b = 0.94499 − 3.21611I
−4.04232 + 5.06949I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.407480 + 1.222900I
a = 0.1138890 − 0.0689488I
b = −0.380064 − 0.448611I
−8.41392 − 1.04197I 0
u = 0.407480 − 1.222900I
a = 0.1138890 + 0.0689488I
b = −0.380064 + 0.448611I
−8.41392 + 1.04197I 0
u = 0.373837 + 1.243620I
a = 1.02834 + 2.75293I
b = 1.16246 + 1.65065I
−5.26246 − 7.34394I 0
u = 0.373837 − 1.243620I
a = 1.02834 − 2.75293I
b = 1.16246 − 1.65065I
−5.26246 + 7.34394I 0
u = 0.496707 + 1.207980I
a = −0.337756 − 0.265720I
b = −0.173373 + 0.523060I
−7.77710 + 10.05510I 0
u = 0.496707 − 1.207980I
a = −0.337756 + 0.265720I
b = −0.173373 − 0.523060I
−7.77710 − 10.05510I 0
u = −0.529273 + 1.198990I
a = −3.19515 − 0.09398I
b = −1.41652 − 1.47211I
−5.41659 − 8.73511I 0
u = −0.529273 − 1.198990I
a = −3.19515 + 0.09398I
b = −1.41652 + 1.47211I
−5.41659 + 8.73511I 0
u = −0.429294 + 1.241130I
a = −0.746467 + 0.490350I
b = −0.261834 − 0.041559I
−7.52357 − 4.28857I 0
u = −0.429294 − 1.241130I
a = −0.746467 − 0.490350I
b = −0.261834 + 0.041559I
−7.52357 + 4.28857I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.482173 + 1.223350I
a = −0.689773 + 0.346822I
b = −0.471666 + 0.181421I
−7.14118 − 4.96161I 0
u = −0.482173 − 1.223350I
a = −0.689773 − 0.346822I
b = −0.471666 − 0.181421I
−7.14118 + 4.96161I 0
u = 0.522937 + 1.211780I
a = 3.48715 − 0.59028I
b = 1.23167 − 1.87815I
−4.1996 + 16.5161I 0
u = 0.522937 − 1.211780I
a = 3.48715 + 0.59028I
b = 1.23167 + 1.87815I
−4.1996 − 16.5161I 0
u = −0.442791 + 0.496185I
a = 0.799445 − 0.541455I
b = −0.011200 − 0.386745I
0.30075 + 1.79611I 2.68640 − 3.79960I
u = −0.442791 − 0.496185I
a = 0.799445 + 0.541455I
b = −0.011200 + 0.386745I
0.30075 − 1.79611I 2.68640 + 3.79960I
u = 0.316117 + 0.579912I
a = 0.878662 − 0.498135I
b = −0.214555 − 0.695078I
0.42343 + 1.35672I 2.64097 − 4.74847I
u = 0.316117 − 0.579912I
a = 0.878662 + 0.498135I
b = −0.214555 + 0.695078I
0.42343 − 1.35672I 2.64097 + 4.74847I
u = 0.643531
a = 1.80099
b = 0.494211
2.26336 7.42670
u = 0.331630
a = 3.33367
b = −0.275880
2.41420 4.13220
11
II. I
u
2
= hb + 2u − 1, a − 2, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
−u + 1
a
1
=
−u
u − 1
a
3
=
1
0
a
8
=
2
−2u + 1
a
11
=
−1
u − 1
a
9
=
1
−u
a
10
=
1
−u
a
4
=
u + 1
−u + 1
a
7
=
u
−u + 1
a
7
=
u
−u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u + 5
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
, c
7
u
2
+ u + 1
c
5
, c
11
u
2
− u + 1
c
8
(u + 1)
2
c
9
u
2
c
10
(u − 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
11
y
2
+ y + 1
c
8
, c
10
(y −1)
2
c
9
y
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 2.00000
b = − 1.73205I
1.64493 + 2.02988I 3.00000 − 3.46410I
u = 0.500000 − 0.866025I
a = 2.00000
b = 1.73205I
1.64493 − 2.02988I 3.00000 + 3.46410I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)(u
70
− 2u
69
+ ··· − 5u + 1)
c
2
(u
2
+ u + 1)(u
70
+ 38u
69
+ ··· − u + 1)
c
3
(u
2
+ u + 1)(u
70
+ 2u
69
+ ··· + 23u + 107)
c
4
(u
2
+ u + 1)(u
70
+ 31u
68
+ ··· − 13u + 1)
c
5
(u
2
− u + 1)(u
70
− 2u
69
+ ··· − 5u + 1)
c
6
(u
2
+ u + 1)(u
70
+ 2u
69
+ ··· − 169u + 17)
c
7
(u
2
+ u + 1)(u
70
− 2u
69
+ ··· − u + 1)
c
8
((u + 1)
2
)(u
70
+ 3u
69
+ ··· − 4u + 1)
c
9
u
2
(u
70
− 11u
69
+ ··· + 4u + 4)
c
10
((u − 1)
2
)(u
70
+ 3u
69
+ ··· − 4u + 1)
c
11
(u
2
− u + 1)(u
70
+ 2u
69
+ ··· − 169u + 17)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
2
+ y + 1)(y
70
+ 38y
69
+ ··· − y + 1)
c
2
(y
2
+ y + 1)(y
70
− 10y
69
+ ··· − 93y + 1)
c
3
(y
2
+ y + 1)(y
70
+ 70y
69
+ ··· + 344439y + 11449)
c
4
(y
2
+ y + 1)(y
70
+ 62y
69
+ ··· + 127y + 1)
c
6
, c
11
(y
2
+ y + 1)(y
70
− 58y
69
+ ··· − 16865y + 289)
c
7
(y
2
+ y + 1)(y
70
− 10y
69
+ ··· − y + 1)
c
8
, c
10
((y −1)
2
)(y
70
− 41y
69
+ ··· + 16y + 1)
c
9
y
2
(y
70
− 15y
69
+ ··· − 200y + 16)
17
