11n
108
(K11n
108
)
A knot diagram
1
Linearized knot diagam
7 1 8 9 11 2 10 4 6 8 9
Solving Sequence
4,8
9
5,11
6 1 3 2 10 7
c
8
c
4
c
5
c
11
c
3
c
2
c
10
c
7
c
1
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.49684 × 10
62
u
47
+ 2.31669 × 10
62
u
46
+ ··· + 7.77951 × 10
62
b − 8.70495 × 10
63
,
8.71448 × 10
63
u
47
− 2.39101 × 10
63
u
46
+ ··· + 8.55746 × 10
63
a + 4.29322 × 10
64
, u
48
− u
47
+ ··· + 16u − 11i
I
u
2
= hu
10
− 4u
8
− u
7
+ 7u
6
+ 3u
5
− 9u
4
− 2u
3
+ 6u
2
+ b,
2u
10
− 10u
8
− 2u
7
+ 21u
6
+ 8u
5
− 29u
4
− 9u
3
+ 26u
2
+ a + 2u − 7,
u
12
− 5u
10
− u
9
+ 11u
8
+ 4u
7
− 16u
6
− 5u
5
+ 15u
4
+ 2u
3
− 6u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 60 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−4.50 × 10
62
u
47
+ 2.32 × 10
62
u
46
+ · · · + 7.78 × 10
62
b − 8.70 ×
10
63
, 8.71 × 10
63
u
47
− 2.39 × 10
63
u
46
+ · · · + 8.56 × 10
63
a + 4.29 ×
10
64
, u
48
− u
47
+ · · · + 16u − 11i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
5
=
u
−u
3
+ u
a
11
=
−1.01835u
47
+ 0.279406u
46
+ ··· + 6.57363u − 5.01693
0.578037u
47
− 0.297794u
46
+ ··· + 2.06984u + 11.1896
a
6
=
−1.01567u
47
+ 0.683761u
46
+ ··· − 1.11353u − 14.1587
−0.0891298u
47
− 0.145158u
46
+ ··· + 6.89698u + 1.47011
a
1
=
−0.866912u
47
+ 0.322213u
46
+ ··· + 3.88254u − 8.07815
0.221406u
47
− 0.178838u
46
+ ··· + 3.51193u + 9.05291
a
3
=
−u
u
a
2
=
−1.06034u
47
+ 0.621352u
46
+ ··· + 3.40978u − 11.7196
0.128714u
47
− 0.148448u
46
+ ··· − 0.760314u + 0.405016
a
10
=
−1.59639u
47
+ 0.577200u
46
+ ··· + 4.50378u − 16.2065
0.578037u
47
− 0.297794u
46
+ ··· + 2.06984u + 11.1896
a
7
=
−0.0768387u
47
− 0.280256u
46
+ ··· − 3.25826u + 6.11664
−0.0786313u
47
+ 0.170391u
46
+ ··· + 3.31403u − 5.72912
a
7
=
−0.0768387u
47
− 0.280256u
46
+ ··· − 3.25826u + 6.11664
−0.0786313u
47
+ 0.170391u
46
+ ··· + 3.31403u − 5.72912
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.320053u
47
− 0.920029u
46
+ ··· + 14.1517u + 26.9488
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
48
+ 12u
46
+ ··· − u + 1
c
2
u
48
+ 24u
47
+ ··· + 13u + 1
c
3
, c
4
, c
8
u
48
+ u
47
+ ··· − 16u − 11
c
5
u
48
+ 3u
47
+ ··· − 14u + 1
c
7
, c
10
u
48
− u
47
+ ··· + 268u − 119
c
9
u
48
− u
47
+ ··· + 10u − 27
c
11
u
48
− 5u
47
+ ··· − 22u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
48
+ 24y
47
+ ··· + 13y + 1
c
2
y
48
+ 8y
47
+ ··· − 71y + 1
c
3
, c
4
, c
8
y
48
− 17y
47
+ ··· − 2302y + 121
c
5
y
48
+ 35y
47
+ ··· − 126y + 1
c
7
, c
10
y
48
− 25y
47
+ ··· − 291260y + 14161
c
9
y
48
− 19y
47
+ ··· − 6904y + 729
c
11
y
48
− 37y
47
+ ··· + 18y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.541870 + 0.901222I
a = 0.024980 + 0.703983I
b = 0.816951 + 0.697564I
−5.53120 + 0.07674I 3.78825 − 1.36866I
u = −0.541870 − 0.901222I
a = 0.024980 − 0.703983I
b = 0.816951 − 0.697564I
−5.53120 − 0.07674I 3.78825 + 1.36866I
u = −0.869571 + 0.293240I
a = 0.127295 + 0.324289I
b = −1.41833 − 0.31833I
3.26073 + 2.43030I 10.07781 − 2.10293I
u = −0.869571 − 0.293240I
a = 0.127295 − 0.324289I
b = −1.41833 + 0.31833I
3.26073 − 2.43030I 10.07781 + 2.10293I
u = 0.883071 + 0.696886I
a = 0.586523 − 1.138810I
b = −0.304793 − 0.919600I
−2.06429 + 2.66223I 9.42585 − 6.21325I
u = 0.883071 − 0.696886I
a = 0.586523 + 1.138810I
b = −0.304793 + 0.919600I
−2.06429 − 2.66223I 9.42585 + 6.21325I
u = 0.843476 + 0.745354I
a = 0.486746 − 1.003540I
b = 0.111927 − 0.997408I
−2.19332 + 2.77840I 8.82502 − 3.26643I
u = 0.843476 − 0.745354I
a = 0.486746 + 1.003540I
b = 0.111927 + 0.997408I
−2.19332 − 2.77840I 8.82502 + 3.26643I
u = −0.702040 + 0.493195I
a = 0.76028 − 2.18802I
b = 0.951952 + 0.007910I
3.52678 − 2.80965I 12.72101 + 4.52739I
u = −0.702040 − 0.493195I
a = 0.76028 + 2.18802I
b = 0.951952 − 0.007910I
3.52678 + 2.80965I 12.72101 − 4.52739I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.741649 + 0.369863I
a = −0.35152 − 1.72739I
b = −1.046450 − 0.878314I
2.97315 + 6.07189I 11.5551 − 10.8395I
u = 0.741649 − 0.369863I
a = −0.35152 + 1.72739I
b = −1.046450 + 0.878314I
2.97315 − 6.07189I 11.5551 + 10.8395I
u = −0.684846 + 0.951602I
a = −0.519439 − 0.379915I
b = −1.025990 − 0.559251I
−0.10143 + 2.03024I 9.27605 − 1.57972I
u = −0.684846 − 0.951602I
a = −0.519439 + 0.379915I
b = −1.025990 + 0.559251I
−0.10143 − 2.03024I 9.27605 + 1.57972I
u = 1.048110 + 0.559665I
a = 0.76825 − 1.24356I
b = −0.594486 − 0.287588I
−1.85237 + 2.17126I 11.26403 + 0.I
u = 1.048110 − 0.559665I
a = 0.76825 + 1.24356I
b = −0.594486 + 0.287588I
−1.85237 − 2.17126I 11.26403 + 0.I
u = −0.690139 + 0.360388I
a = −0.72752 + 1.24362I
b = −1.089830 + 0.609642I
3.63018 − 0.51155I 11.50496 + 4.41570I
u = −0.690139 − 0.360388I
a = −0.72752 − 1.24362I
b = −1.089830 − 0.609642I
3.63018 + 0.51155I 11.50496 − 4.41570I
u = 0.748525
a = −2.51365
b = 1.31936
5.55263 20.1450
u = −0.587154 + 0.447682I
a = −1.33591 − 2.09829I
b = 1.297980 − 0.296087I
2.15454 − 5.46033I 6.95643 + 10.69062I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.587154 − 0.447682I
a = −1.33591 + 2.09829I
b = 1.297980 + 0.296087I
2.15454 + 5.46033I 6.95643 − 10.69062I
u = 0.377726 + 0.619690I
a = 0.599599 − 1.043790I
b = −0.047506 − 0.807730I
−2.18331 + 1.63548I 3.97796 − 4.36559I
u = 0.377726 − 0.619690I
a = 0.599599 + 1.043790I
b = −0.047506 + 0.807730I
−2.18331 − 1.63548I 3.97796 + 4.36559I
u = −0.902068 + 0.916115I
a = 0.512066 + 0.717598I
b = 0.44776 + 1.37089I
−4.30258 − 7.07120I 7.00000 + 6.78102I
u = −0.902068 − 0.916115I
a = 0.512066 − 0.717598I
b = 0.44776 − 1.37089I
−4.30258 + 7.07120I 7.00000 − 6.78102I
u = 0.659900 + 0.253316I
a = 0.97673 + 2.73037I
b = 0.801186 − 0.190096I
2.78226 − 3.51974I 11.16150 + 1.38253I
u = 0.659900 − 0.253316I
a = 0.97673 − 2.73037I
b = 0.801186 + 0.190096I
2.78226 + 3.51974I 11.16150 − 1.38253I
u = 0.640560 + 1.139710I
a = −0.470605 + 0.463131I
b = −1.104340 + 0.854023I
−3.03425 − 7.47849I 0
u = 0.640560 − 1.139710I
a = −0.470605 − 0.463131I
b = −1.104340 − 0.854023I
−3.03425 + 7.47849I 0
u = 0.904630 + 0.964964I
a = 0.086405 + 1.139180I
b = 0.865094 + 0.549237I
−5.42165 + 4.76380I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.904630 − 0.964964I
a = 0.086405 − 1.139180I
b = 0.865094 − 0.549237I
−5.42165 − 4.76380I 0
u = −0.981632 + 0.915325I
a = 0.605329 + 1.050400I
b = −0.831231 + 1.115400I
−4.08127 + 0.33982I 0
u = −0.981632 − 0.915325I
a = 0.605329 − 1.050400I
b = −0.831231 − 1.115400I
−4.08127 − 0.33982I 0
u = −1.089380 + 0.813811I
a = −0.29168 − 1.41143I
b = 1.258230 − 0.611794I
1.11909 − 8.52957I 0
u = −1.089380 − 0.813811I
a = −0.29168 + 1.41143I
b = 1.258230 + 0.611794I
1.11909 + 8.52957I 0
u = 0.994777 + 0.952249I
a = −0.355078 + 0.290456I
b = −0.602542 + 0.470290I
−5.15741 + 2.22291I 0
u = 0.994777 − 0.952249I
a = −0.355078 − 0.290456I
b = −0.602542 − 0.470290I
−5.15741 − 2.22291I 0
u = 0.504319 + 0.352823I
a = 0.390749 − 0.726369I
b = −1.63711 + 0.11804I
3.91125 + 1.34687I 8.42551 − 6.39280I
u = 0.504319 − 0.352823I
a = 0.390749 + 0.726369I
b = −1.63711 − 0.11804I
3.91125 − 1.34687I 8.42551 + 6.39280I
u = −1.208410 + 0.710850I
a = 0.774025 + 1.048360I
b = −1.106840 + 0.481324I
−3.44366 − 6.15745I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.208410 − 0.710850I
a = 0.774025 − 1.048360I
b = −1.106840 − 0.481324I
−3.44366 + 6.15745I 0
u = 1.40818 + 0.13200I
a = −0.772395 + 0.203916I
b = 1.185140 − 0.228161I
7.19540 + 0.40564I 0
u = 1.40818 − 0.13200I
a = −0.772395 − 0.203916I
b = 1.185140 + 0.228161I
7.19540 − 0.40564I 0
u = 1.18080 + 0.85198I
a = −0.443194 + 1.290850I
b = 1.34618 + 0.78553I
−1.3361 + 14.6102I 0
u = 1.18080 − 0.85198I
a = −0.443194 − 1.290850I
b = 1.34618 − 0.78553I
−1.3361 − 14.6102I 0
u = −0.475453
a = 0.423852
b = −0.331940
0.656820 15.2640
u = −1.56662 + 0.07941I
a = −0.523086 − 0.170729I
b = 0.733336 + 0.437414I
5.39976 + 3.46453I 0
u = −1.56662 − 0.07941I
a = −0.523086 + 0.170729I
b = 0.733336 − 0.437414I
5.39976 − 3.46453I 0
9
II.
I
u
2
= hu
10
−4u
8
+· · ·+6u
2
+b, 2u
10
−10u
8
+· · ·+a−7, u
12
−5u
10
+· · ·−6u
2
+1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
5
=
u
−u
3
+ u
a
11
=
−2u
10
+ 10u
8
+ 2u
7
− 21u
6
− 8u
5
+ 29u
4
+ 9u
3
− 26u
2
− 2u + 7
−u
10
+ 4u
8
+ u
7
− 7u
6
− 3u
5
+ 9u
4
+ 2u
3
− 6u
2
a
6
=
−5u
11
+ 23u
9
+ ··· + 10u − 2
u
11
− 5u
9
− u
8
+ 11u
7
+ 4u
6
− 16u
5
− 5u
4
+ 14u
3
+ 2u
2
− 5u
a
1
=
−u
10
+ 5u
8
+ u
7
− 11u
6
− 4u
5
+ 16u
4
+ 5u
3
− 15u
2
− 2u + 5
−u
10
+ 5u
8
+ u
7
− 10u
6
− 4u
5
+ 13u
4
+ 4u
3
− 10u
2
+ 1
a
3
=
−u
u
a
2
=
−4u
11
+ 18u
9
+ ··· + 4u − 2
3u
11
− u
10
+ ··· − 9u + 2
a
10
=
−u
10
+ 6u
8
+ u
7
− 14u
6
− 5u
5
+ 20u
4
+ 7u
3
− 20u
2
− 2u + 7
−u
10
+ 4u
8
+ u
7
− 7u
6
− 3u
5
+ 9u
4
+ 2u
3
− 6u
2
a
7
=
−u
11
+ 2u
10
+ ··· + 3u − 8
u
10
− 5u
8
− u
7
+ 10u
6
+ 4u
5
− 13u
4
− 4u
3
+ 11u
2
− 1
a
7
=
−u
11
+ 2u
10
+ ··· + 3u − 8
u
10
− 5u
8
− u
7
+ 10u
6
+ 4u
5
− 13u
4
− 4u
3
+ 11u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −2u
10
+ 3u
9
+ 7u
8
− 8u
7
− 17u
6
+ 12u
5
+ 31u
4
− 14u
3
− 24u
2
+ 2u + 19
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
+ u
11
+ ··· + u + 1
c
2
u
12
+ 7u
11
+ ··· + 7u + 1
c
3
, c
4
u
12
− 5u
10
+ u
9
+ 11u
8
− 4u
7
− 16u
6
+ 5u
5
+ 15u
4
− 2u
3
− 6u
2
+ 1
c
5
u
12
+ u
10
− 3u
9
− 2u
7
+ 4u
6
− u
5
+ 3u
4
+ u
3
− 4u
2
+ 1
c
6
u
12
− u
11
+ ··· − u + 1
c
7
u
12
+ 2u
11
+ ··· + 2u + 1
c
8
u
12
− 5u
10
− u
9
+ 11u
8
+ 4u
7
− 16u
6
− 5u
5
+ 15u
4
+ 2u
3
− 6u
2
+ 1
c
9
u
12
− 4u
10
+ u
9
+ 3u
8
− u
7
+ 4u
6
− 2u
5
− 3u
3
+ u
2
+ 1
c
10
u
12
− 2u
11
+ ··· − 2u + 1
c
11
u
12
+ 2u
11
− u
10
− 2u
9
+ 3u
8
+ u
7
+ u
6
+ 7u
5
+ 2u
4
+ 2u
2
+ 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
12
+ 7y
11
+ ··· + 7y + 1
c
2
y
12
+ 3y
11
+ ··· − y + 1
c
3
, c
4
, c
8
y
12
− 10y
11
+ ··· − 12y + 1
c
5
y
12
+ 2y
11
+ ··· − 8y + 1
c
7
, c
10
y
12
− 10y
11
+ ··· + 2y + 1
c
9
y
12
− 8y
11
+ ··· + 2y + 1
c
11
y
12
− 6y
11
+ ··· + 4y + 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.944121 + 0.586418I
a = 0.85764 − 1.21516I
b = −0.316252 − 0.773855I
−2.69108 + 2.27732I −0.79309 − 1.51304I
u = 0.944121 − 0.586418I
a = 0.85764 + 1.21516I
b = −0.316252 + 0.773855I
−2.69108 − 2.27732I −0.79309 + 1.51304I
u = −0.971824 + 0.903078I
a = 0.199108 + 0.774068I
b = −0.226863 + 0.457126I
−5.04286 − 3.33069I 6.48064 + 3.71539I
u = −0.971824 − 0.903078I
a = 0.199108 − 0.774068I
b = −0.226863 − 0.457126I
−5.04286 + 3.33069I 6.48064 − 3.71539I
u = −1.339700 + 0.047045I
a = −0.920911 − 0.442643I
b = 1.230580 + 0.195712I
7.43656 − 1.12784I 13.7843 + 5.8074I
u = −1.339700 − 0.047045I
a = −0.920911 + 0.442643I
b = 1.230580 − 0.195712I
7.43656 + 1.12784I 13.7843 − 5.8074I
u = 0.555310 + 0.250101I
a = 0.60842 − 3.02308I
b = −1.167560 − 0.430017I
2.81163 + 4.85898I 13.04273 − 4.67018I
u = 0.555310 − 0.250101I
a = 0.60842 + 3.02308I
b = −1.167560 + 0.430017I
2.81163 − 4.85898I 13.04273 + 4.67018I
u = 1.399120 + 0.104604I
a = −0.338465 + 0.499440I
b = 0.964221 − 0.298157I
6.28022 − 3.33267I 14.8487 + 3.1328I
u = 1.399120 − 0.104604I
a = −0.338465 − 0.499440I
b = 0.964221 + 0.298157I
6.28022 + 3.33267I 14.8487 − 3.1328I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.587029 + 0.077244I
a = 0.59421 + 1.34198I
b = −1.48412 + 0.20351I
4.36500 + 0.58143I 14.6367 + 0.1461I
u = −0.587029 − 0.077244I
a = 0.59421 − 1.34198I
b = −1.48412 − 0.20351I
4.36500 − 0.58143I 14.6367 − 0.1461I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
12
+ u
11
+ ··· + u + 1)(u
48
+ 12u
46
+ ··· − u + 1)
c
2
(u
12
+ 7u
11
+ ··· + 7u + 1)(u
48
+ 24u
47
+ ··· + 13u + 1)
c
3
, c
4
(u
12
− 5u
10
+ u
9
+ 11u
8
− 4u
7
− 16u
6
+ 5u
5
+ 15u
4
− 2u
3
− 6u
2
+ 1)
· (u
48
+ u
47
+ ··· − 16u − 11)
c
5
(u
12
+ u
10
− 3u
9
− 2u
7
+ 4u
6
− u
5
+ 3u
4
+ u
3
− 4u
2
+ 1)
· (u
48
+ 3u
47
+ ··· − 14u + 1)
c
6
(u
12
− u
11
+ ··· − u + 1)(u
48
+ 12u
46
+ ··· − u + 1)
c
7
(u
12
+ 2u
11
+ ··· + 2u + 1)(u
48
− u
47
+ ··· + 268u − 119)
c
8
(u
12
− 5u
10
− u
9
+ 11u
8
+ 4u
7
− 16u
6
− 5u
5
+ 15u
4
+ 2u
3
− 6u
2
+ 1)
· (u
48
+ u
47
+ ··· − 16u − 11)
c
9
(u
12
− 4u
10
+ u
9
+ 3u
8
− u
7
+ 4u
6
− 2u
5
− 3u
3
+ u
2
+ 1)
· (u
48
− u
47
+ ··· + 10u − 27)
c
10
(u
12
− 2u
11
+ ··· − 2u + 1)(u
48
− u
47
+ ··· + 268u − 119)
c
11
(u
12
+ 2u
11
− u
10
− 2u
9
+ 3u
8
+ u
7
+ u
6
+ 7u
5
+ 2u
4
+ 2u
2
+ 1)
· (u
48
− 5u
47
+ ··· − 22u + 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
12
+ 7y
11
+ ··· + 7y + 1)(y
48
+ 24y
47
+ ··· + 13y + 1)
c
2
(y
12
+ 3y
11
+ ··· − y + 1)(y
48
+ 8y
47
+ ··· − 71y + 1)
c
3
, c
4
, c
8
(y
12
− 10y
11
+ ··· − 12y + 1)(y
48
− 17y
47
+ ··· − 2302y + 121)
c
5
(y
12
+ 2y
11
+ ··· − 8y + 1)(y
48
+ 35y
47
+ ··· − 126y + 1)
c
7
, c
10
(y
12
− 10y
11
+ ··· + 2y + 1)(y
48
− 25y
47
+ ··· − 291260y + 14161)
c
9
(y
12
− 8y
11
+ ··· + 2y + 1)(y
48
− 19y
47
+ ··· − 6904y + 729)
c
11
(y
12
− 6y
11
+ ··· + 4y + 1)(y
48
− 37y
47
+ ··· + 18y + 1)
16
