11a
78
(K11a
78
)
A knot diagram
1
Linearized knot diagam
6 1 8 10 2 3 4 7 11 5 9
Solving Sequence
4,8 1,3
2 7 9 6 5 11 10
c
3
c
2
c
7
c
8
c
6
c
5
c
11
c
9
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
24
− u
23
+ ··· + 4b + 1, −u
24
+ u
23
+ ··· + 4a − 5, u
25
+ 6u
23
+ ··· + u − 1i
I
u
2
= h−4476694012u
39
− 10696306396u
38
+ ··· + 7868062579b + 9351862960,
− 1184460310u
39
− 263051448u
38
+ ··· + 605235583a − 1972197779, u
40
+ u
39
+ ··· + 2u + 1i
I
u
3
= hb + a + 1, a
2
− au + 2a − u, u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 69 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
= hu
24
−u
23
+· · ·+4b+1, −u
24
+u
23
+· · ·+4a−5, u
25
+6u
23
+· · ·+u−1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
1
=
1
4
u
24
−
1
4
u
23
+ ··· −
1
2
u +
5
4
−
1
4
u
24
+
1
4
u
23
+ ··· +
1
2
u −
1
4
a
3
=
1
u
2
a
2
=
1
4
u
24
−
1
4
u
23
+ ··· −
1
2
u +
5
4
−
1
4
u
24
+
1
4
u
23
+ ··· +
1
2
u −
1
4
a
7
=
−u
u
a
9
=
−u
3
u
3
+ u
a
6
=
u
3
u
5
+ u
3
+ u
a
5
=
1
4
u
24
+
1
4
u
23
+ ··· − u −
1
4
−
1
4
u
24
−
1
4
u
23
+ ··· + u +
1
4
a
11
=
1
2
u
24
−
1
2
u
23
+ ··· − u +
3
2
−
1
4
u
24
+
1
4
u
23
+ ··· +
1
2
u −
1
4
a
10
=
5
4
u
24
+
5
4
u
23
+ ··· − u −
9
4
−
1
2
u
24
−
1
2
u
23
+ ··· + u + 1
a
10
=
5
4
u
24
+
5
4
u
23
+ ··· − u −
9
4
−
1
2
u
24
−
1
2
u
23
+ ··· + u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3u
24
+ u
23
− 18u
22
+ 11u
21
− 60u
20
+ 44u
19
− 127u
18
+
110u
17
− 194u
16
+ 179u
15
− 221u
14
+ 213u
13
− 204u
12
+ 178u
11
− 159u
10
+ 120u
9
−
111u
8
+ 65u
7
− 70u
6
+ 53u
5
− 34u
4
+ 32u
3
− 17u
2
+ 10u − 8
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
7
u
25
+ 6u
23
+ ··· + u + 1
c
2
, c
8
u
25
+ 12u
24
+ ··· − 5u − 1
c
4
, c
10
u
25
− 3u
24
+ ··· − 5u + 2
c
6
u
25
+ 3u
24
+ ··· + 16u + 32
c
9
, c
11
u
25
+ 9u
24
+ ··· − 7u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
7
y
25
+ 12y
24
+ ··· − 5y −1
c
2
, c
8
y
25
+ 8y
24
+ ··· + 3y −1
c
4
, c
10
y
25
− 9y
24
+ ··· − 7y −4
c
6
y
25
− 11y
24
+ ··· − 13568y −1024
c
9
, c
11
y
25
+ 15y
24
+ ··· + 273y −16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.668066 + 0.826958I
a = −0.391410 + 0.121275I
b = −0.010569 − 0.701256I
4.42357 − 2.28876I 0.90025 + 3.22916I
u = −0.668066 − 0.826958I
a = −0.391410 − 0.121275I
b = −0.010569 + 0.701256I
4.42357 + 2.28876I 0.90025 − 3.22916I
u = 0.387315 + 0.828510I
a = −0.057213 − 1.406030I
b = 0.39665 + 1.35928I
−2.29786 + 4.38512I −6.23003 − 9.05656I
u = 0.387315 − 0.828510I
a = −0.057213 + 1.406030I
b = 0.39665 − 1.35928I
−2.29786 − 4.38512I −6.23003 + 9.05656I
u = 0.663122 + 0.885711I
a = −0.620402 − 0.123885I
b = 0.014657 + 0.488612I
4.05826 + 8.02736I −0.26249 − 8.69949I
u = 0.663122 − 0.885711I
a = −0.620402 + 0.123885I
b = 0.014657 − 0.488612I
4.05826 − 8.02736I −0.26249 + 8.69949I
u = 0.781060 + 0.295309I
a = 0.725790 + 0.096907I
b = 0.857621 + 0.846789I
2.49934 − 5.05647I 0.76088 + 3.39553I
u = 0.781060 − 0.295309I
a = 0.725790 − 0.096907I
b = 0.857621 − 0.846789I
2.49934 + 5.05647I 0.76088 − 3.39553I
u = −0.732724 + 0.365786I
a = 0.646963 − 0.060825I
b = 0.631263 − 0.907356I
3.32057 − 0.44324I 2.54503 + 2.33373I
u = −0.732724 − 0.365786I
a = 0.646963 + 0.060825I
b = 0.631263 + 0.907356I
3.32057 + 0.44324I 2.54503 − 2.33373I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.440401 + 1.120690I
a = −2.18870 + 1.03108I
b = 2.28016 + 0.07839I
−4.91803 − 1.59228I −7.91949 + 2.30620I
u = −0.440401 − 1.120690I
a = −2.18870 − 1.03108I
b = 2.28016 − 0.07839I
−4.91803 + 1.59228I −7.91949 − 2.30620I
u = 0.496157 + 1.112700I
a = −1.97870 − 0.70710I
b = 1.75155 − 0.37924I
−2.95653 + 6.50680I −4.30037 − 6.80019I
u = 0.496157 − 1.112700I
a = −1.97870 + 0.70710I
b = 1.75155 + 0.37924I
−2.95653 − 6.50680I −4.30037 + 6.80019I
u = −0.447856 + 0.612567I
a = 0.505867 + 0.568532I
b = 0.048924 − 0.925546I
0.53657 − 1.46473I 1.57744 + 4.49882I
u = −0.447856 − 0.612567I
a = 0.505867 − 0.568532I
b = 0.048924 + 0.925546I
0.53657 + 1.46473I 1.57744 − 4.49882I
u = −0.502100 + 1.180640I
a = −2.34071 + 0.47753I
b = 2.09699 + 1.04430I
−8.02282 − 8.65791I −10.60850 + 6.91846I
u = −0.502100 − 1.180640I
a = −2.34071 − 0.47753I
b = 2.09699 − 1.04430I
−8.02282 + 8.65791I −10.60850 − 6.91846I
u = 0.562594 + 1.178700I
a = −2.15539 − 0.17720I
b = 1.47455 − 1.34225I
−1.63771 + 9.61928I −3.84139 − 5.85883I
u = 0.562594 − 1.178700I
a = −2.15539 + 0.17720I
b = 1.47455 + 1.34225I
−1.63771 − 9.61928I −3.84139 + 5.85883I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.147311 + 0.674791I
a = 1.71030 − 0.90481I
b = −0.995418 + 0.931192I
−1.78656 − 1.53483I −3.61707 + 0.13208I
u = 0.147311 − 0.674791I
a = 1.71030 + 0.90481I
b = −0.995418 − 0.931192I
−1.78656 + 1.53483I −3.61707 − 0.13208I
u = −0.562275 + 1.202520I
a = −2.27068 + 0.11315I
b = 1.58876 + 1.59048I
−2.9757 − 15.3316I −5.87847 + 10.26197I
u = −0.562275 − 1.202520I
a = −2.27068 − 0.11315I
b = 1.58876 − 1.59048I
−2.9757 + 15.3316I −5.87847 − 10.26197I
u = 0.631724
a = 0.828591
b = 0.729746
−1.87036 −4.25160
7
II.
I
u
2
= h−4.48 × 10
9
u
39
− 1.07 × 10
10
u
38
+ · · · + 7.87× 10
9
b + 9.35 ×10
9
, −1.18 ×
10
9
u
39
− 2.63× 10
8
u
38
+ · · · + 6.05 × 10
8
a −1.97 × 10
9
, u
40
+ u
39
+ · · · + 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
1
=
1.95702u
39
+ 0.434627u
38
+ ··· − 0.306306u + 3.25856
0.568970u
39
+ 1.35946u
38
+ ··· + 0.868382u − 1.18859
a
3
=
1
u
2
a
2
=
2.52599u
39
+ 1.79409u
38
+ ··· + 0.562076u + 3.06998
−1.08110u
39
− 0.476540u
38
+ ··· − 0.632572u − 3.87864
a
7
=
−u
u
a
9
=
−u
3
u
3
+ u
a
6
=
u
3
u
5
+ u
3
+ u
a
5
=
−1.92049u
39
− 1.64843u
38
+ ··· − 4.76213u − 5.77155
−2.08550u
39
− 1.17361u
38
+ ··· − 1.60565u − 2.79806
a
11
=
2.26791u
39
− 0.119746u
38
+ ··· − 1.61688u + 3.05922
−0.653801u
39
+ 0.802602u
38
+ ··· + 0.806017u − 3.07474
a
10
=
−2.49055u
39
− 0.832197u
38
+ ··· − 2.76553u − 7.09778
−1.67912u
39
− 1.52806u
38
+ ··· − 2.35663u − 1.41907
a
10
=
−2.49055u
39
− 0.832197u
38
+ ··· − 2.76553u − 7.09778
−1.67912u
39
− 1.52806u
38
+ ··· − 2.35663u − 1.41907
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
51184596416
7868062579
u
39
−
71297250008
7868062579
u
38
+ ··· −
117349868140
7868062579
u −
113505824050
7868062579
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
7
u
40
− u
39
+ ··· − 2u + 1
c
2
, c
8
u
40
+ 23u
39
+ ··· − 16u
2
+ 1
c
4
, c
10
(u
20
+ u
19
+ ··· + 3u
2
− 1)
2
c
6
(u
20
− u
19
+ ··· + 4u − 1)
2
c
9
, c
11
(u
20
+ 7u
19
+ ··· + 6u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
7
y
40
+ 23y
39
+ ··· − 16y
2
+ 1
c
2
, c
8
y
40
− 13y
39
+ ··· − 32y + 1
c
4
, c
10
(y
20
− 7y
19
+ ··· − 6y + 1)
2
c
6
(y
20
− 11y
19
+ ··· − 6y + 1)
2
c
9
, c
11
(y
20
+ 13y
19
+ ··· − 6y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.680660 + 0.735978I
a = 1.061240 − 0.028188I
b = −0.0630213 − 0.1220620I
4.68486 − 2.84648I 1.60998 + 2.97861I
u = −0.680660 − 0.735978I
a = 1.061240 + 0.028188I
b = −0.0630213 + 0.1220620I
4.68486 + 2.84648I 1.60998 − 2.97861I
u = 0.703070 + 0.667774I
a = 0.935371 + 0.031857I
b = −0.0630213 − 0.1220620I
4.68486 − 2.84648I 1.60998 + 2.97861I
u = 0.703070 − 0.667774I
a = 0.935371 − 0.031857I
b = −0.0630213 + 0.1220620I
4.68486 + 2.84648I 1.60998 − 2.97861I
u = 0.179409 + 1.047170I
a = −1.007340 − 0.708627I
b = 0.274077
−3.97005 −10.76209 + 0.I
u = 0.179409 − 1.047170I
a = −1.007340 + 0.708627I
b = 0.274077
−3.97005 −10.76209 + 0.I
u = −0.406752 + 0.984604I
a = 1.305660 − 0.307787I
b = −0.994955 − 0.489591I
−0.52569 − 2.16136I −0.73748 + 3.31855I
u = −0.406752 − 0.984604I
a = 1.305660 + 0.307787I
b = −0.994955 + 0.489591I
−0.52569 + 2.16136I −0.73748 − 3.31855I
u = −0.883398 + 0.214209I
a = −0.296276 − 0.096762I
b = −1.25336 + 1.31067I
−0.00745 + 10.05770I −2.70834 − 7.26612I
u = −0.883398 − 0.214209I
a = −0.296276 + 0.096762I
b = −1.25336 − 1.31067I
−0.00745 − 10.05770I −2.70834 + 7.26612I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.847173 + 0.247485I
a = −0.164766 + 0.157989I
b = −1.09019 − 1.18394I
1.14075 − 4.43308I −0.68370 + 2.52728I
u = 0.847173 − 0.247485I
a = −0.164766 − 0.157989I
b = −1.09019 + 1.18394I
1.14075 + 4.43308I −0.68370 − 2.52728I
u = 0.240047 + 1.118770I
a = 1.126200 + 0.481500I
b = −1.340740 + 0.080597I
−2.02098 − 2.13456I −4.50898 + 2.16962I
u = 0.240047 − 1.118770I
a = 1.126200 − 0.481500I
b = −1.340740 − 0.080597I
−2.02098 + 2.13456I −4.50898 − 2.16962I
u = 0.416062 + 1.082120I
a = −1.36848 − 1.28995I
b = 1.070070 − 0.629261I
−3.61438 + 0.81573I −5.67172 − 1.07888I
u = 0.416062 − 1.082120I
a = −1.36848 + 1.28995I
b = 1.070070 + 0.629261I
−3.61438 − 0.81573I −5.67172 + 1.07888I
u = −0.017851 + 1.176950I
a = 0.345233 − 0.405044I
b = −0.710796 + 0.321114I
−1.62333 − 2.35832I −2.35225 + 4.49783I
u = −0.017851 − 1.176950I
a = 0.345233 + 0.405044I
b = −0.710796 − 0.321114I
−1.62333 + 2.35832I −2.35225 − 4.49783I
u = −0.460657 + 1.121820I
a = −1.40263 + 1.43442I
b = 1.42212 + 0.74562I
−4.77271 − 6.07240I −7.45285 + 5.87540I
u = −0.460657 − 1.121820I
a = −1.40263 − 1.43442I
b = 1.42212 − 0.74562I
−4.77271 + 6.07240I −7.45285 − 5.87540I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.771680 + 0.120837I
a = −0.436638 − 0.516967I
b = −1.45055 + 0.79305I
−4.94645 + 3.96853I −7.89349 − 3.79787I
u = −0.771680 − 0.120837I
a = −0.436638 + 0.516967I
b = −1.45055 − 0.79305I
−4.94645 − 3.96853I −7.89349 + 3.79787I
u = 0.444139 + 1.139190I
a = 1.44372 + 0.43742I
b = −1.45055 + 0.79305I
−4.94645 + 3.96853I −7.89349 − 3.79787I
u = 0.444139 − 1.139190I
a = 1.44372 − 0.43742I
b = −1.45055 − 0.79305I
−4.94645 − 3.96853I −7.89349 + 3.79787I
u = −0.551606 + 1.104560I
a = 1.52922 − 0.28411I
b = −1.09019 − 1.18394I
1.14075 − 4.43308I −0.68370 + 2.52728I
u = −0.551606 − 1.104560I
a = 1.52922 + 0.28411I
b = −1.09019 + 1.18394I
1.14075 + 4.43308I −0.68370 − 2.52728I
u = −0.386163 + 1.203070I
a = −1.11143 + 1.51116I
b = 1.54877
−8.84775 −12.44026 + 0.I
u = −0.386163 − 1.203070I
a = −1.11143 − 1.51116I
b = 1.54877
−8.84775 −12.44026 + 0.I
u = 0.276270 + 1.238300I
a = −0.75891 − 1.40625I
b = 1.070070 + 0.629261I
−3.61438 − 0.81573I −5.67172 + 1.07888I
u = 0.276270 − 1.238300I
a = −0.75891 + 1.40625I
b = 1.070070 − 0.629261I
−3.61438 + 0.81573I −5.67172 − 1.07888I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.555192 + 1.143400I
a = 1.58253 + 0.32035I
b = −1.25336 + 1.31067I
−0.00745 + 10.05770I −3.00000 − 7.26612I
u = 0.555192 − 1.143400I
a = 1.58253 − 0.32035I
b = −1.25336 − 1.31067I
−0.00745 − 10.05770I −3.00000 + 7.26612I
u = −0.312447 + 1.274980I
a = −0.79278 + 1.57779I
b = 1.42212 − 0.74562I
−4.77271 + 6.07240I −7.45285 − 5.87540I
u = −0.312447 − 1.274980I
a = −0.79278 − 1.57779I
b = 1.42212 + 0.74562I
−4.77271 − 6.07240I −7.45285 + 5.87540I
u = 0.605286 + 0.255049I
a = 0.207408 + 0.820889I
b = −0.994955 − 0.489591I
−0.52569 − 2.16136I −0.73748 + 3.31855I
u = 0.605286 − 0.255049I
a = 0.207408 − 0.820889I
b = −0.994955 + 0.489591I
−0.52569 + 2.16136I −0.73748 − 3.31855I
u = 0.219360 + 0.513597I
a = −2.33551 − 0.75634I
b = −0.710796 − 0.321114I
−1.62333 + 2.35832I −2.35225 − 4.49783I
u = 0.219360 − 0.513597I
a = −2.33551 + 0.75634I
b = −0.710796 + 0.321114I
−1.62333 − 2.35832I −2.35225 + 4.49783I
u = −0.514794 + 0.049169I
a = −0.86181 + 1.57235I
b = −1.340740 − 0.080597I
−2.02098 + 2.13456I −4.50898 − 2.16962I
u = −0.514794 − 0.049169I
a = −0.86181 − 1.57235I
b = −1.340740 + 0.080597I
−2.02098 − 2.13456I −4.50898 + 2.16962I
14
III. I
u
3
= hb + a + 1, a
2
− au + 2a − u, u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
1
=
a
−a − 1
a
3
=
1
−1
a
2
=
a + 1
−a − 2
a
7
=
−u
u
a
9
=
u
0
a
6
=
−u
u
a
5
=
au
−au − u
a
11
=
2a + 1
−a − 1
a
10
=
au + 2a + 2
−a + u − 1
a
10
=
au + 2a + 2
−a + u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4au − 4u − 12
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
7
(u
2
+ 1)
2
c
2
, c
8
(u + 1)
4
c
4
, c
10
u
4
− u
2
+ 1
c
6
u
4
c
9
(u
2
− u + 1)
2
c
11
(u
2
+ u + 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
7
(y + 1)
4
c
2
, c
8
(y −1)
4
c
4
, c
10
(y
2
− y + 1)
2
c
6
y
4
c
9
, c
11
(y
2
+ y + 1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = −0.133975 + 0.500000I
b = −0.866025 − 0.500000I
−3.28987 + 2.02988I −10.00000 − 3.46410I
u = 1.000000I
a = −1.86603 + 0.50000I
b = 0.866025 − 0.500000I
−3.28987 − 2.02988I −10.00000 + 3.46410I
u = − 1.000000I
a = −0.133975 − 0.500000I
b = −0.866025 + 0.500000I
−3.28987 − 2.02988I −10.00000 + 3.46410I
u = − 1.000000I
a = −1.86603 − 0.50000I
b = 0.866025 + 0.500000I
−3.28987 + 2.02988I −10.00000 − 3.46410I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
7
((u
2
+ 1)
2
)(u
25
+ 6u
23
+ ··· + u + 1)(u
40
− u
39
+ ··· − 2u + 1)
c
2
, c
8
((u + 1)
4
)(u
25
+ 12u
24
+ ··· − 5u − 1)(u
40
+ 23u
39
+ ··· − 16u
2
+ 1)
c
4
, c
10
(u
4
− u
2
+ 1)(u
20
+ u
19
+ ··· + 3u
2
− 1)
2
(u
25
− 3u
24
+ ··· − 5u + 2)
c
6
u
4
(u
20
− u
19
+ ··· + 4u − 1)
2
(u
25
+ 3u
24
+ ··· + 16u + 32)
c
9
((u
2
− u + 1)
2
)(u
20
+ 7u
19
+ ··· + 6u + 1)
2
(u
25
+ 9u
24
+ ··· − 7u + 4)
c
11
((u
2
+ u + 1)
2
)(u
20
+ 7u
19
+ ··· + 6u + 1)
2
(u
25
+ 9u
24
+ ··· − 7u + 4)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
7
((y + 1)
4
)(y
25
+ 12y
24
+ ··· − 5y −1)(y
40
+ 23y
39
+ ··· − 16y
2
+ 1)
c
2
, c
8
((y −1)
4
)(y
25
+ 8y
24
+ ··· + 3y −1)(y
40
− 13y
39
+ ··· − 32y + 1)
c
4
, c
10
((y
2
− y + 1)
2
)(y
20
− 7y
19
+ ··· − 6y + 1)
2
(y
25
− 9y
24
+ ··· − 7y −4)
c
6
y
4
(y
20
− 11y
19
+ ··· − 6y + 1)
2
(y
25
− 11y
24
+ ··· − 13568y −1024)
c
9
, c
11
((y
2
+ y + 1)
2
)(y
20
+ 13y
19
+ ··· − 6y + 1)
2
· (y
25
+ 15y
24
+ ··· + 273y −16)
20
