11a
41
(K11a
41
)
A knot diagram
1
Linearized knot diagam
4 1 8 2 11 10 3 7 5 6 9
Solving Sequence
5,11 2,6
4 10 7 9 1 8 3
c
5
c
4
c
10
c
6
c
9
c
11
c
8
c
3
c
1
, c
2
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
57
− u
56
+ ··· + b + 1, u
59
− 2u
58
+ ··· + a + 3, u
60
− 2u
59
+ ··· + 3u − 1i
I
u
2
= hb + 1, u
2
+ a − u + 3, u
3
− u
2
+ 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 63 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
57
− u
56
+ · · · + b + 1, u
59
− 2u
58
+ · · · + a + 3, u
60
− 2u
59
+ · · · + 3u − 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
2
=
−u
59
+ 2u
58
+ ··· + u − 3
−u
57
+ u
56
+ ··· + u − 1
a
6
=
1
u
2
a
4
=
−u
59
+ 2u
58
+ ··· + 2u − 3
−u
57
+ u
56
+ ··· − 3u
3
− 1
a
10
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
u
3
+ 2u
u
3
+ u
a
1
=
−u
7
− 4u
5
− 4u
3
−u
7
− 3u
5
− 2u
3
+ u
a
8
=
u
9
+ 4u
7
+ 5u
5
+ 2u
3
+ u
u
11
+ 5u
9
+ 8u
7
+ 3u
5
− u
3
+ u
a
3
=
−u
59
+ 2u
58
+ ··· − u
2
− 2
−u
57
+ u
56
+ ··· + u − 1
a
3
=
−u
59
+ 2u
58
+ ··· − u
2
− 2
−u
57
+ u
56
+ ··· + u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
59
− 2u
58
+ ··· + 8u − 3
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
60
− 4u
59
+ ··· + 4u − 1
c
2
u
60
+ 32u
59
+ ··· + 4u + 1
c
3
, c
7
u
60
+ u
59
+ ··· + 4u + 8
c
5
, c
6
, c
10
u
60
− 2u
59
+ ··· + 3u − 1
c
8
u
60
− 21u
59
+ ··· − 1040u + 64
c
9
u
60
+ 2u
59
+ ··· + 3u − 1
c
11
u
60
− 14u
59
+ ··· − 1087u + 131
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
60
− 32y
59
+ ··· − 4y + 1
c
2
y
60
− 4y
59
+ ··· − 32y + 1
c
3
, c
7
y
60
− 21y
59
+ ··· − 1040y + 64
c
5
, c
6
, c
10
y
60
+ 54y
59
+ ··· − 7y + 1
c
8
y
60
+ 31y
59
+ ··· − 118016y + 4096
c
9
y
60
− 2y
59
+ ··· − 7y + 1
c
11
y
60
+ 10y
59
+ ··· + 159609y + 17161
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.272258 + 1.012540I
a = 1.93515 + 0.62774I
b = 1.147190 − 0.478763I
−2.04150 + 6.75419I −6.05975 − 7.03761I
u = −0.272258 − 1.012540I
a = 1.93515 − 0.62774I
b = 1.147190 + 0.478763I
−2.04150 − 6.75419I −6.05975 + 7.03761I
u = −0.156290 + 1.052030I
a = 0.095451 + 0.296346I
b = 0.098316 + 0.688037I
0.89236 + 2.41054I −2.85789 − 3.50583I
u = −0.156290 − 1.052030I
a = 0.095451 − 0.296346I
b = 0.098316 − 0.688037I
0.89236 − 2.41054I −2.85789 + 3.50583I
u = 0.102597 + 0.926022I
a = −1.92726 + 0.84189I
b = −1.169680 − 0.370214I
−2.71127 − 1.29749I −7.32877 + 0.87949I
u = 0.102597 − 0.926022I
a = −1.92726 − 0.84189I
b = −1.169680 + 0.370214I
−2.71127 + 1.29749I −7.32877 − 0.87949I
u = 0.362204 + 0.739680I
a = 1.398890 + 0.042352I
b = 1.157070 − 0.528981I
−1.51448 + 6.91671I −4.99151 − 4.33152I
u = 0.362204 − 0.739680I
a = 1.398890 − 0.042352I
b = 1.157070 + 0.528981I
−1.51448 − 6.91671I −4.99151 + 4.33152I
u = 0.739190 + 0.273449I
a = 2.83377 − 1.12471I
b = 1.183660 + 0.548618I
−3.14550 − 10.93560I −7.60991 + 8.98761I
u = 0.739190 − 0.273449I
a = 2.83377 + 1.12471I
b = 1.183660 − 0.548618I
−3.14550 + 10.93560I −7.60991 − 8.98761I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.705650 + 0.274949I
a = −0.556763 − 0.943620I
b = 0.216325 − 0.833418I
−0.27172 − 5.84779I −4.34743 + 6.06110I
u = 0.705650 − 0.274949I
a = −0.556763 + 0.943620I
b = 0.216325 + 0.833418I
−0.27172 + 5.84779I −4.34743 − 6.06110I
u = −0.739469 + 0.157117I
a = 2.42529 + 0.98016I
b = 1.123680 + 0.435823I
−4.64706 − 2.94332I −9.69548 + 3.11009I
u = −0.739469 − 0.157117I
a = 2.42529 − 0.98016I
b = 1.123680 − 0.435823I
−4.64706 + 2.94332I −9.69548 − 3.11009I
u = −0.701322 + 0.243359I
a = −2.80040 − 1.59166I
b = −1.129360 + 0.462569I
−4.44900 + 4.80272I −9.53100 − 5.34375I
u = −0.701322 − 0.243359I
a = −2.80040 + 1.59166I
b = −1.129360 − 0.462569I
−4.44900 − 4.80272I −9.53100 + 5.34375I
u = 0.691544 + 0.218830I
a = −2.61676 + 0.96703I
b = −1.228960 + 0.314277I
−4.78959 − 2.10958I −9.89618 + 4.41005I
u = 0.691544 − 0.218830I
a = −2.61676 − 0.96703I
b = −1.228960 − 0.314277I
−4.78959 + 2.10958I −9.89618 − 4.41005I
u = −0.150600 + 0.704962I
a = −1.51108 + 0.72061I
b = −1.130100 − 0.383816I
−2.66735 − 1.26395I −6.69853 + 0.15559I
u = −0.150600 − 0.704962I
a = −1.51108 − 0.72061I
b = −1.130100 + 0.383816I
−2.66735 + 1.26395I −6.69853 − 0.15559I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.245563 + 1.262290I
a = 1.207160 + 0.477268I
b = 0.712663 − 0.173753I
2.15190 + 3.30985I 0
u = −0.245563 − 1.262290I
a = 1.207160 − 0.477268I
b = 0.712663 + 0.173753I
2.15190 − 3.30985I 0
u = 0.313312 + 0.634127I
a = 0.406095 + 0.033528I
b = 0.231815 + 0.743223I
1.19086 + 2.11650I −1.10142 − 0.94504I
u = 0.313312 − 0.634127I
a = 0.406095 − 0.033528I
b = 0.231815 − 0.743223I
1.19086 − 2.11650I −1.10142 + 0.94504I
u = 0.593362 + 0.375996I
a = 1.44574 − 0.93956I
b = 0.826187 + 0.623051I
3.02257 − 4.24450I −1.33904 + 7.25011I
u = 0.593362 − 0.375996I
a = 1.44574 + 0.93956I
b = 0.826187 − 0.623051I
3.02257 + 4.24450I −1.33904 − 7.25011I
u = −0.651026 + 0.178717I
a = 0.833384 − 0.653334I
b = −0.075209 − 0.564522I
−1.64038 + 0.76431I −6.82050 − 1.17334I
u = −0.651026 − 0.178717I
a = 0.833384 + 0.653334I
b = −0.075209 + 0.564522I
−1.64038 − 0.76431I −6.82050 + 1.17334I
u = 0.514134 + 0.433646I
a = 0.120502 − 0.319390I
b = 0.725195 − 0.626130I
3.31167 + 0.60747I 0.058994 + 0.358835I
u = 0.514134 − 0.433646I
a = 0.120502 + 0.319390I
b = 0.725195 + 0.626130I
3.31167 − 0.60747I 0.058994 − 0.358835I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.667151
a = 1.87106
b = 0.617384
−1.74355 −3.65290
u = 0.146423 + 1.356920I
a = −1.11641 + 0.87341I
b = −1.211750 − 0.122488I
2.27680 − 1.86506I 0
u = 0.146423 − 1.356920I
a = −1.11641 − 0.87341I
b = −1.211750 + 0.122488I
2.27680 + 1.86506I 0
u = −0.298418 + 1.347350I
a = 0.950662 + 0.883761I
b = 1.102840 + 0.401160I
0.089664 + 0.805813I 0
u = −0.298418 − 1.347350I
a = 0.950662 − 0.883761I
b = 1.102840 − 0.401160I
0.089664 − 0.805813I 0
u = −0.112811 + 1.380760I
a = 0.088761 + 1.367980I
b = −0.973157 − 0.442087I
3.11222 − 0.32948I 0
u = −0.112811 − 1.380760I
a = 0.088761 − 1.367980I
b = −0.973157 + 0.442087I
3.11222 + 0.32948I 0
u = −0.181790 + 1.380090I
a = 0.51009 − 1.34681I
b = −0.578631 + 0.449363I
4.27304 + 3.48079I 0
u = −0.181790 − 1.380090I
a = 0.51009 + 1.34681I
b = −0.578631 − 0.449363I
4.27304 − 3.48079I 0
u = −0.252426 + 1.375440I
a = 1.054820 + 0.112572I
b = −0.213723 − 0.598525I
3.31453 + 4.03685I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.252426 − 1.375440I
a = 1.054820 − 0.112572I
b = −0.213723 + 0.598525I
3.31453 − 4.03685I 0
u = 0.272964 + 1.386080I
a = −1.045560 + 0.896556I
b = −1.260740 + 0.293725I
0.31494 − 5.61200I 0
u = 0.272964 − 1.386080I
a = −1.045560 − 0.896556I
b = −1.260740 − 0.293725I
0.31494 + 5.61200I 0
u = −0.27784 + 1.39711I
a = −1.46445 − 2.26687I
b = −1.121330 + 0.494109I
0.77544 + 8.36220I 0
u = −0.27784 − 1.39711I
a = −1.46445 + 2.26687I
b = −1.121330 − 0.494109I
0.77544 − 8.36220I 0
u = 0.11177 + 1.42352I
a = 0.003244 − 0.724114I
b = 0.361594 + 0.782628I
7.44712 + 0.69473I 0
u = 0.11177 − 1.42352I
a = 0.003244 + 0.724114I
b = 0.361594 − 0.782628I
7.44712 − 0.69473I 0
u = 0.27859 + 1.41128I
a = −0.929433 − 0.027526I
b = 0.233048 − 0.870544I
5.10898 − 9.43023I 0
u = 0.27859 − 1.41128I
a = −0.929433 + 0.027526I
b = 0.233048 + 0.870544I
5.10898 + 9.43023I 0
u = 0.07750 + 1.43810I
a = 0.274235 + 0.847102I
b = 1.113070 − 0.571356I
5.22134 + 5.76496I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.07750 − 1.43810I
a = 0.274235 − 0.847102I
b = 1.113070 + 0.571356I
5.22134 − 5.76496I 0
u = 0.29362 + 1.41349I
a = 1.61836 − 1.90667I
b = 1.192200 + 0.565015I
2.2343 − 14.6854I 0
u = 0.29362 − 1.41349I
a = 1.61836 + 1.90667I
b = 1.192200 − 0.565015I
2.2343 + 14.6854I 0
u = 0.19005 + 1.43268I
a = −0.563532 + 0.432636I
b = 0.708476 − 0.712296I
9.23623 − 1.96231I 0
u = 0.19005 − 1.43268I
a = −0.563532 − 0.432636I
b = 0.708476 + 0.712296I
9.23623 + 1.96231I 0
u = 0.22072 + 1.43184I
a = 0.55993 − 1.54260I
b = 0.857884 + 0.678909I
8.80345 − 7.21631I 0
u = 0.22072 − 1.43184I
a = 0.55993 + 1.54260I
b = 0.857884 − 0.678909I
8.80345 + 7.21631I 0
u = −0.434286 + 0.236524I
a = 0.227567 − 1.379360I
b = −0.654919 + 0.246891I
−0.85637 + 1.13107I −6.00125 − 6.01444I
u = −0.434286 − 0.236524I
a = 0.227567 + 1.379360I
b = −0.654919 − 0.246891I
−0.85637 − 1.13107I −6.00125 + 6.01444I
u = 0.388108
a = −3.78596
b = −1.10470
−2.19031 0.722320
10
II. I
u
2
= hb + 1, u
2
+ a − u + 3, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
2
=
−u
2
+ u − 3
−1
a
6
=
1
u
2
a
4
=
−u
2
+ u − 2
−1
a
10
=
u
u
2
− u + 1
a
7
=
u
2
+ 1
u
2
− u + 1
a
9
=
u
2
+ 1
u
2
− u + 1
a
1
=
−1
0
a
8
=
u
2
+ 1
u
2
− u + 1
a
3
=
−u
2
+ u − 2
−1
a
3
=
−u
2
+ u − 2
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
2
+ 4u − 16
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
3
c
2
, c
4
(u + 1)
3
c
3
, c
7
, c
8
u
3
c
5
, c
6
u
3
− u
2
+ 2u − 1
c
9
, c
11
u
3
− u
2
+ 1
c
10
u
3
+ u
2
+ 2u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
3
c
3
, c
7
, c
8
y
3
c
5
, c
6
, c
10
y
3
+ 3y
2
+ 2y −1
c
9
, c
11
y
3
− y
2
+ 2y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −1.122560 + 0.744862I
b = −1.00000
1.37919 − 2.82812I −6.82789 + 2.41717I
u = 0.215080 − 1.307140I
a = −1.122560 − 0.744862I
b = −1.00000
1.37919 + 2.82812I −6.82789 − 2.41717I
u = 0.569840
a = −2.75488
b = −1.00000
−2.75839 −15.3440
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
60
− 4u
59
+ ··· + 4u − 1)
c
2
((u + 1)
3
)(u
60
+ 32u
59
+ ··· + 4u + 1)
c
3
, c
7
u
3
(u
60
+ u
59
+ ··· + 4u + 8)
c
4
((u + 1)
3
)(u
60
− 4u
59
+ ··· + 4u − 1)
c
5
, c
6
(u
3
− u
2
+ 2u − 1)(u
60
− 2u
59
+ ··· + 3u − 1)
c
8
u
3
(u
60
− 21u
59
+ ··· − 1040u + 64)
c
9
(u
3
− u
2
+ 1)(u
60
+ 2u
59
+ ··· + 3u − 1)
c
10
(u
3
+ u
2
+ 2u + 1)(u
60
− 2u
59
+ ··· + 3u − 1)
c
11
(u
3
− u
2
+ 1)(u
60
− 14u
59
+ ··· − 1087u + 131)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
3
)(y
60
− 32y
59
+ ··· − 4y + 1)
c
2
((y −1)
3
)(y
60
− 4y
59
+ ··· − 32y + 1)
c
3
, c
7
y
3
(y
60
− 21y
59
+ ··· − 1040y + 64)
c
5
, c
6
, c
10
(y
3
+ 3y
2
+ 2y −1)(y
60
+ 54y
59
+ ··· − 7y + 1)
c
8
y
3
(y
60
+ 31y
59
+ ··· − 118016y + 4096)
c
9
(y
3
− y
2
+ 2y −1)(y
60
− 2y
59
+ ··· − 7y + 1)
c
11
(y
3
− y
2
+ 2y −1)(y
60
+ 10y
59
+ ··· + 159609y + 17161)
16
