11a
42
(K11a
42
)
A knot diagram
1
Linearized knot diagam
4 1 7 2 10 8 3 6 11 5 9
Solving Sequence
5,10
6
2,11
4 1 9 8 7 3
c
5
c
10
c
4
c
1
c
9
c
8
c
6
c
3
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
53
+ u
52
+ ··· + b + 1, −u
54
− u
53
+ ··· + a − 1, u
55
+ 2u
54
+ ··· + 2u + 1i
I
u
2
= hb + 1, a − u + 1, u
2
+ u + 1i
* 2 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
= hu
53
+u
52
+· · · +b + 1, −u
54
−u
53
+· · · +a − 1, u
55
+2u
54
+· · · +2u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
−u
2
a
2
=
u
54
+ u
53
+ ··· − 3u + 1
−u
53
− u
52
+ ··· + u − 1
a
11
=
u
u
a
4
=
u
54
+ 9u
52
+ ··· − 4u + 1
−u
53
− u
52
+ ··· + u
2
− 1
a
1
=
u
5
+ u
u
5
+ u
3
+ u
a
9
=
u
3
u
3
+ u
a
8
=
−u
5
− u
u
7
+ u
5
+ 2u
3
+ u
a
7
=
u
10
+ u
8
+ 2u
6
+ u
4
+ u
2
+ 1
−u
12
− 2u
10
− 4u
8
− 4u
6
− 3u
4
− 2u
2
a
3
=
u
54
+ 2u
53
+ ··· − 2u + 2
−u
53
− u
52
+ ··· + u − 1
a
3
=
u
54
+ 2u
53
+ ··· − 2u + 2
−u
53
− u
52
+ ··· + u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
54
− 7u
53
+ ··· − u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
55
− 3u
54
+ ··· − 5u + 1
c
2
u
55
+ 31u
54
+ ··· − 7u + 1
c
3
, c
7
u
55
+ u
54
+ ··· + 8u + 4
c
5
, c
10
u
55
+ 2u
54
+ ··· + 2u + 1
c
6
, c
8
u
55
− 15u
54
+ ··· − 168u + 16
c
9
, c
11
u
55
+ 20u
54
+ ··· + 14u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
55
− 31y
54
+ ··· − 7y −1
c
2
y
55
− 11y
54
+ ··· + 101y −1
c
3
, c
7
y
55
+ 15y
54
+ ··· − 168y −16
c
5
, c
10
y
55
+ 20y
54
+ ··· + 14y −1
c
6
, c
8
y
55
+ 47y
54
+ ··· + 3616y −256
c
9
, c
11
y
55
+ 32y
54
+ ··· + 490y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.816179 + 0.574717I
a = 1.027890 + 0.674902I
b = 1.204850 − 0.521092I
−2.90431 + 8.91686I −3.42760 − 5.44869I
u = −0.816179 − 0.574717I
a = 1.027890 − 0.674902I
b = 1.204850 + 0.521092I
−2.90431 − 8.91686I −3.42760 + 5.44869I
u = 0.239129 + 0.986379I
a = 2.23250 + 0.41423I
b = 0.941364 − 0.397946I
−1.92448 + 4.39584I −6.07569 − 8.49319I
u = 0.239129 − 0.986379I
a = 2.23250 − 0.41423I
b = 0.941364 + 0.397946I
−1.92448 − 4.39584I −6.07569 + 8.49319I
u = −0.779335 + 0.590843I
a = 0.007618 − 0.199836I
b = 0.147161 + 0.837390I
0.24633 + 3.95028I −0.20932 − 2.43300I
u = −0.779335 − 0.590843I
a = 0.007618 + 0.199836I
b = 0.147161 − 0.837390I
0.24633 − 3.95028I −0.20932 + 2.43300I
u = 0.658398 + 0.801536I
a = 0.867357 + 0.882946I
b = −0.733611 − 0.391605I
0.872499 + 0.772147I −1.84032 + 0.30762I
u = 0.658398 − 0.801536I
a = 0.867357 − 0.882946I
b = −0.733611 + 0.391605I
0.872499 − 0.772147I −1.84032 − 0.30762I
u = 0.759593 + 0.559351I
a = −1.09162 + 0.93530I
b = −1.176880 − 0.449966I
−3.79702 − 2.69601I −4.74745 + 1.11286I
u = 0.759593 − 0.559351I
a = −1.09162 − 0.93530I
b = −1.176880 + 0.449966I
−3.79702 + 2.69601I −4.74745 − 1.11286I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.628216 + 0.858582I
a = −1.51296 + 0.91306I
b = −1.203820 + 0.035992I
−0.64263 − 2.45826I 0. + 4.47694I
u = −0.628216 − 0.858582I
a = −1.51296 − 0.91306I
b = −1.203820 − 0.035992I
−0.64263 + 2.45826I 0. − 4.47694I
u = 0.451120 + 0.966547I
a = 1.27088 + 0.78560I
b = 0.763301 + 0.197825I
−0.85220 + 1.53742I −0.475415 + 0.770388I
u = 0.451120 − 0.966547I
a = 1.27088 − 0.78560I
b = 0.763301 − 0.197825I
−0.85220 − 1.53742I −0.475415 − 0.770388I
u = −0.761308 + 0.748686I
a = 0.068239 + 0.640254I
b = 0.916664 − 0.588628I
4.30983 + 3.18273I 1.66711 − 3.75336I
u = −0.761308 − 0.748686I
a = 0.068239 − 0.640254I
b = 0.916664 + 0.588628I
4.30983 − 3.18273I 1.66711 + 3.75336I
u = −0.735974 + 0.536493I
a = −1.28675 + 0.70502I
b = −1.228780 − 0.367943I
−3.97885 − 0.10775I −4.88979 + 0.08750I
u = −0.735974 − 0.536493I
a = −1.28675 − 0.70502I
b = −1.228780 + 0.367943I
−3.97885 + 0.10775I −4.88979 − 0.08750I
u = −0.740147 + 0.806502I
a = 0.213975 − 0.919578I
b = 0.579824 + 0.662419I
5.27340 − 1.63575I 3.78529 + 2.66903I
u = −0.740147 − 0.806502I
a = 0.213975 + 0.919578I
b = 0.579824 − 0.662419I
5.27340 + 1.63575I 3.78529 − 2.66903I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.034329 + 1.104990I
a = 0.080168 + 1.136900I
b = 0.053635 + 0.828871I
−5.60698 + 2.95534I −7.15421 − 2.80412I
u = 0.034329 − 1.104990I
a = 0.080168 − 1.136900I
b = 0.053635 − 0.828871I
−5.60698 − 2.95534I −7.15421 + 2.80412I
u = −0.009089 + 1.113840I
a = −3.11350 + 0.11167I
b = −1.231540 − 0.429492I
−9.45702 − 1.46557I −10.98966 + 0.I
u = −0.009089 − 1.113840I
a = −3.11350 − 0.11167I
b = −1.231540 + 0.429492I
−9.45702 + 1.46557I −10.98966 + 0.I
u = 0.660868 + 0.897456I
a = −0.21776 − 2.20899I
b = −0.826919 + 0.421607I
0.57728 + 4.35301I −2.97848 − 6.56505I
u = 0.660868 − 0.897456I
a = −0.21776 + 2.20899I
b = −0.826919 − 0.421607I
0.57728 − 4.35301I −2.97848 + 6.56505I
u = 0.757497 + 0.440100I
a = 1.156460 + 0.615207I
b = 1.177720 − 0.463008I
−3.70073 + 5.77207I −4.07257 − 5.94241I
u = 0.757497 − 0.440100I
a = 1.156460 − 0.615207I
b = 1.177720 + 0.463008I
−3.70073 − 5.77207I −4.07257 + 5.94241I
u = 0.047537 + 1.140170I
a = 2.98663 + 0.01514I
b = 1.219040 − 0.483533I
−9.06604 + 7.69131I −10.03059 − 5.89654I
u = 0.047537 − 1.140170I
a = 2.98663 − 0.01514I
b = 1.219040 + 0.483533I
−9.06604 − 7.69131I −10.03059 + 5.89654I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.718549 + 0.906381I
a = −0.652105 + 0.027561I
b = 0.517863 − 0.687312I
4.96946 − 3.90710I 0
u = −0.718549 − 0.906381I
a = −0.652105 − 0.027561I
b = 0.517863 + 0.687312I
4.96946 + 3.90710I 0
u = 0.669924 + 0.499239I
a = 0.164189 − 0.143161I
b = 0.025988 + 0.692151I
−0.47649 + 1.47491I −0.96799 − 2.91910I
u = 0.669924 − 0.499239I
a = 0.164189 + 0.143161I
b = 0.025988 − 0.692151I
−0.47649 − 1.47491I −0.96799 + 2.91910I
u = −0.717366 + 0.952779I
a = 1.15907 − 1.72863I
b = 0.963009 + 0.589107I
3.69457 − 8.78385I 0
u = −0.717366 − 0.952779I
a = 1.15907 + 1.72863I
b = 0.963009 − 0.589107I
3.69457 + 8.78385I 0
u = 0.629765 + 1.027960I
a = 1.069910 − 0.306602I
b = −0.051867 − 0.757851I
−1.91291 + 3.57990I 0
u = 0.629765 − 1.027960I
a = 1.069910 + 0.306602I
b = −0.051867 + 0.757851I
−1.91291 − 3.57990I 0
u = 0.362022 + 0.691095I
a = 0.432775 + 0.109549I
b = 0.059148 + 0.370271I
−0.194248 + 1.398020I −2.04153 − 4.84692I
u = 0.362022 − 0.691095I
a = 0.432775 − 0.109549I
b = 0.059148 − 0.370271I
−0.194248 − 1.398020I −2.04153 + 4.84692I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.647113 + 1.040820I
a = −1.50753 + 1.09395I
b = −1.261440 + 0.376282I
−5.43130 − 5.17320I 0
u = −0.647113 − 1.040820I
a = −1.50753 − 1.09395I
b = −1.261440 − 0.376282I
−5.43130 + 5.17320I 0
u = 0.612711 + 1.063030I
a = 1.45098 + 1.12168I
b = 1.194960 + 0.434256I
−5.49641 − 0.62899I 0
u = 0.612711 − 1.063030I
a = 1.45098 − 1.12168I
b = 1.194960 − 0.434256I
−5.49641 + 0.62899I 0
u = 0.659279 + 1.042970I
a = −2.25573 − 2.04389I
b = −1.193240 + 0.473729I
−5.21292 + 8.08647I 0
u = 0.659279 − 1.042970I
a = −2.25573 + 2.04389I
b = −1.193240 − 0.473729I
−5.21292 − 8.08647I 0
u = −0.674581 + 1.040260I
a = −0.956881 − 0.394384I
b = 0.134773 − 0.873581I
−1.08802 − 9.45303I 0
u = −0.674581 − 1.040260I
a = −0.956881 + 0.394384I
b = 0.134773 + 0.873581I
−1.08802 + 9.45303I 0
u = −0.088965 + 0.747457I
a = −2.45827 + 1.39779I
b = −1.051280 − 0.242889I
−3.08639 − 0.93841I −10.69919 − 0.06174I
u = −0.088965 − 0.747457I
a = −2.45827 − 1.39779I
b = −1.051280 + 0.242889I
−3.08639 + 0.93841I −10.69919 + 0.06174I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.681167 + 1.057900I
a = 2.24142 − 1.78647I
b = 1.221340 + 0.526305I
−4.3508 − 14.5336I 0
u = −0.681167 − 1.057900I
a = 2.24142 + 1.78647I
b = 1.221340 − 0.526305I
−4.3508 + 14.5336I 0
u = 0.561929 + 0.106681I
a = 0.365566 + 0.579622I
b = 0.769448 − 0.437822I
1.33757 + 1.88655I 2.60483 − 4.69845I
u = 0.561929 − 0.106681I
a = 0.365566 − 0.579622I
b = 0.769448 + 0.437822I
1.33757 − 1.88655I 2.60483 + 4.69845I
u = −0.212225
a = 2.51493
b = −0.861415
−1.25349 −8.32260
10
II. I
u
2
= hb + 1, a − u + 1, u
2
+ u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u + 1
a
2
=
u − 1
−1
a
11
=
u
u
a
4
=
u
−1
a
1
=
−1
0
a
9
=
1
u + 1
a
8
=
1
u + 1
a
7
=
1
u + 1
a
3
=
u
−1
a
3
=
u
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u − 7
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
c
2
, c
4
(u + 1)
2
c
3
, c
6
, c
7
c
8
u
2
c
5
, c
11
u
2
+ u + 1
c
9
, c
10
u
2
− u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
2
c
3
, c
6
, c
7
c
8
y
2
c
5
, c
9
, c
10
c
11
y
2
+ y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.50000 + 0.86603I
b = −1.00000
−1.64493 − 2.02988I −9.00000 + 3.46410I
u = −0.500000 − 0.866025I
a = −1.50000 − 0.86603I
b = −1.00000
−1.64493 + 2.02988I −9.00000 − 3.46410I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
2
)(u
55
− 3u
54
+ ··· − 5u + 1)
c
2
((u + 1)
2
)(u
55
+ 31u
54
+ ··· − 7u + 1)
c
3
, c
7
u
2
(u
55
+ u
54
+ ··· + 8u + 4)
c
4
((u + 1)
2
)(u
55
− 3u
54
+ ··· − 5u + 1)
c
5
(u
2
+ u + 1)(u
55
+ 2u
54
+ ··· + 2u + 1)
c
6
, c
8
u
2
(u
55
− 15u
54
+ ··· − 168u + 16)
c
9
(u
2
− u + 1)(u
55
+ 20u
54
+ ··· + 14u − 1)
c
10
(u
2
− u + 1)(u
55
+ 2u
54
+ ··· + 2u + 1)
c
11
(u
2
+ u + 1)(u
55
+ 20u
54
+ ··· + 14u − 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
2
)(y
55
− 31y
54
+ ··· − 7y −1)
c
2
((y −1)
2
)(y
55
− 11y
54
+ ··· + 101y −1)
c
3
, c
7
y
2
(y
55
+ 15y
54
+ ··· − 168y −16)
c
5
, c
10
(y
2
+ y + 1)(y
55
+ 20y
54
+ ··· + 14y −1)
c
6
, c
8
y
2
(y
55
+ 47y
54
+ ··· + 3616y −256)
c
9
, c
11
(y
2
+ y + 1)(y
55
+ 32y
54
+ ··· + 490y −1)
16
