11a
54
(K11a
54
)
A knot diagram
1
Linearized knot diagam
5 1 11 2 10 9 3 4 6 7 8
Solving Sequence
5,10 2,6
1 3 4 9 7 11 8
c
5
c
1
c
2
c
4
c
9
c
6
c
10
c
8
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.90257 × 10
44
u
68
+ 2.07176 × 10
44
u
67
+ ··· + 1.04013 × 10
45
b − 2.13904 × 10
44
,
− 5.37164 × 10
44
u
68
+ 1.14801 × 10
45
u
67
+ ··· + 1.04013 × 10
45
a − 2.55357 × 10
45
, u
69
− u
68
+ ··· + 5u + 1i
* 1 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
= h−2.90×10
44
u
68
+2.07×10
44
u
67
+· · ·+1.04×10
45
b−2.14×10
44
, −5.37×
10
44
u
68
+1.15×10
45
u
67
+· · ·+1.04×10
45
a−2.55×10
45
, u
69
−u
68
+· · ·+5u+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
2
=
0.516440u
68
− 1.10372u
67
+ ··· − 0.812598u + 2.45506
0.279059u
68
− 0.199183u
67
+ ··· − 2.53271u + 0.205651
a
6
=
1
−u
2
a
1
=
0.237382u
68
− 0.904533u
67
+ ··· + 1.72012u + 2.24940
0.279059u
68
− 0.199183u
67
+ ··· − 2.53271u + 0.205651
a
3
=
0.842780u
68
− 2.31989u
67
+ ··· + 2.72044u + 1.93889
0.303058u
68
− 0.207469u
67
+ ··· − 1.50616u − 0.583069
a
4
=
0.747601u
68
− 2.15154u
67
+ ··· + 1.25494u + 1.59403
0.253468u
68
− 0.180079u
67
+ ··· − 2.44759u − 0.761967
a
9
=
−u
u
3
+ u
a
7
=
u
2
+ 1
−u
4
− 2u
2
a
11
=
u
5
+ 2u
3
+ u
−u
7
− 3u
5
− 2u
3
+ u
a
8
=
0.932153u
68
− 1.40919u
67
+ ··· + 9.77228u + 1.12782
0.109511u
68
− 0.0467228u
67
+ ··· + 3.97590u + 0.0969479
a
8
=
0.932153u
68
− 1.40919u
67
+ ··· + 9.77228u + 1.12782
0.109511u
68
− 0.0467228u
67
+ ··· + 3.97590u + 0.0969479
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5.57648u
68
+ 4.72032u
67
+ ··· + 8.97518u + 3.36143
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
69
+ u
68
+ ··· + 7u − 1
c
2
u
69
+ 27u
68
+ ··· + 7u − 1
c
3
u
69
+ 7u
68
+ ··· + u + 1
c
5
, c
6
, c
9
u
69
+ u
68
+ ··· + 5u − 1
c
7
u
69
− u
68
+ ··· − 375u − 103
c
8
u
69
+ u
68
+ ··· + 137u − 119
c
10
u
69
− u
68
+ ··· + 12027u − 1217
c
11
u
69
+ 5u
68
+ ··· − u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
69
+ 27y
68
+ ··· + 7y −1
c
2
y
69
+ 31y
68
+ ··· + 611y −1
c
3
y
69
− 5y
68
+ ··· + 7y −1
c
5
, c
6
, c
9
y
69
+ 59y
68
+ ··· − 5y −1
c
7
y
69
+ 83y
68
+ ··· − 603653y −10609
c
8
y
69
+ 59y
68
+ ··· − 207093y −14161
c
10
y
69
− 25y
68
+ ··· − 20237733y −1481089
c
11
y
69
+ 7y
68
+ ··· − 5y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.474255 + 0.934497I
a = 0.022719 + 0.709370I
b = −0.674946 + 1.055980I
1.05725 − 7.83679I 0
u = 0.474255 − 0.934497I
a = 0.022719 − 0.709370I
b = −0.674946 − 1.055980I
1.05725 + 7.83679I 0
u = −0.544160 + 0.765066I
a = 0.116423 − 0.432919I
b = −0.607578 − 0.720494I
1.57123 − 1.30415I 10.11030 + 4.92987I
u = −0.544160 − 0.765066I
a = 0.116423 + 0.432919I
b = −0.607578 + 0.720494I
1.57123 + 1.30415I 10.11030 − 4.92987I
u = −0.878362 + 0.307679I
a = 1.22977 + 0.73621I
b = −0.604946 + 0.875247I
3.10224 − 3.65612I 14.6967 + 8.0899I
u = −0.878362 − 0.307679I
a = 1.22977 − 0.73621I
b = −0.604946 − 0.875247I
3.10224 + 3.65612I 14.6967 − 8.0899I
u = 0.398272 + 0.993300I
a = 0.482088 − 0.750712I
b = −0.821583 − 0.588202I
2.48274 − 2.22918I 0
u = 0.398272 − 0.993300I
a = 0.482088 + 0.750712I
b = −0.821583 + 0.588202I
2.48274 + 2.22918I 0
u = −0.905812 + 0.191744I
a = 0.496640 + 0.086483I
b = −0.597458 − 0.808717I
3.31253 + 1.10291I 16.0867 + 0.I
u = −0.905812 − 0.191744I
a = 0.496640 − 0.086483I
b = −0.597458 + 0.808717I
3.31253 − 1.10291I 16.0867 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.541206 + 0.947022I
a = 0.800012 + 1.062110I
b = −0.618942 + 0.924861I
0.96001 − 6.16584I 0
u = −0.541206 − 0.947022I
a = 0.800012 − 1.062110I
b = −0.618942 − 0.924861I
0.96001 + 6.16584I 0
u = 0.829619 + 0.237108I
a = 1.54992 − 0.77867I
b = −0.692620 − 1.100100I
3.23009 + 12.46900I 6.85262 − 8.75626I
u = 0.829619 − 0.237108I
a = 1.54992 + 0.77867I
b = −0.692620 + 1.100100I
3.23009 − 12.46900I 6.85262 + 8.75626I
u = 0.807997 + 0.195414I
a = 0.482484 − 0.581590I
b = −0.899108 + 0.540063I
4.94303 + 6.60072I 9.45233 − 4.66175I
u = 0.807997 − 0.195414I
a = 0.482484 + 0.581590I
b = −0.899108 − 0.540063I
4.94303 − 6.60072I 9.45233 + 4.66175I
u = 0.213572 + 1.224400I
a = 0.477570 − 0.495136I
b = 0.821651 − 1.021950I
−0.91382 − 1.30908I 0
u = 0.213572 − 1.224400I
a = 0.477570 + 0.495136I
b = 0.821651 + 1.021950I
−0.91382 + 1.30908I 0
u = 0.098130 + 1.263710I
a = 0.91347 − 2.06956I
b = 0.389681 − 1.187680I
−4.28780 − 2.43362I 0
u = 0.098130 − 1.263710I
a = 0.91347 + 2.06956I
b = 0.389681 + 1.187680I
−4.28780 + 2.43362I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.261774 + 1.251380I
a = 0.711660 + 0.599885I
b = 1.010780 − 0.331574I
0.61350 + 1.71624I 0
u = 0.261774 − 1.251380I
a = 0.711660 − 0.599885I
b = 1.010780 + 0.331574I
0.61350 − 1.71624I 0
u = −0.228426 + 1.276370I
a = −0.60596 − 1.62424I
b = 0.551106 + 0.795185I
−2.50160 − 0.87317I 0
u = −0.228426 − 1.276370I
a = −0.60596 + 1.62424I
b = 0.551106 − 0.795185I
−2.50160 + 0.87317I 0
u = 0.667506 + 0.220812I
a = −0.614338 + 0.663614I
b = 0.083389 + 1.231880I
−1.87888 + 4.75178I 3.16509 − 7.67915I
u = 0.667506 − 0.220812I
a = −0.614338 − 0.663614I
b = 0.083389 − 1.231880I
−1.87888 − 4.75178I 3.16509 + 7.67915I
u = −0.259393 + 1.276300I
a = 0.507456 − 0.058898I
b = 0.254514 − 0.249135I
−2.37890 − 3.34092I 0
u = −0.259393 − 1.276300I
a = 0.507456 + 0.058898I
b = 0.254514 + 0.249135I
−2.37890 + 3.34092I 0
u = 0.696765 + 0.023683I
a = −0.911462 − 0.318031I
b = 0.985003 + 0.485819I
4.38283 + 1.75150I 16.4419 − 3.6342I
u = 0.696765 − 0.023683I
a = −0.911462 + 0.318031I
b = 0.985003 − 0.485819I
4.38283 − 1.75150I 16.4419 + 3.6342I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.274685 + 1.282870I
a = −0.160254 + 1.132300I
b = 1.013220 + 0.613592I
0.32305 + 5.26485I 0
u = 0.274685 − 1.282870I
a = −0.160254 − 1.132300I
b = 1.013220 − 0.613592I
0.32305 − 5.26485I 0
u = 0.675565 + 0.090170I
a = −1.56040 + 0.21247I
b = 0.741295 + 1.123290I
2.46511 + 4.51237I 11.3986 − 8.8654I
u = 0.675565 − 0.090170I
a = −1.56040 − 0.21247I
b = 0.741295 − 1.123290I
2.46511 − 4.51237I 11.3986 + 8.8654I
u = −0.167578 + 1.317380I
a = 0.89036 + 3.40700I
b = 0.380257 + 0.909412I
−3.74691 − 0.61271I 0
u = −0.167578 − 1.317380I
a = 0.89036 − 3.40700I
b = 0.380257 − 0.909412I
−3.74691 + 0.61271I 0
u = −0.241087 + 1.312890I
a = −3.38443 − 2.06516I
b = 0.546073 − 0.910104I
−2.86842 − 5.27183I 0
u = −0.241087 − 1.312890I
a = −3.38443 + 2.06516I
b = 0.546073 + 0.910104I
−2.86842 + 5.27183I 0
u = −0.663268
a = 0.468971
b = 0.189635
1.60413 5.38980
u = 0.323648 + 0.563013I
a = 1.39577 − 1.31325I
b = −0.017291 − 1.055820I
−3.31539 − 1.42653I −1.46022 + 0.90595I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.323648 − 0.563013I
a = 1.39577 + 1.31325I
b = −0.017291 + 1.055820I
−3.31539 + 1.42653I −1.46022 − 0.90595I
u = 0.275545 + 1.322890I
a = −1.11206 + 2.21999I
b = 0.716579 + 1.203070I
−1.97766 + 7.97069I 0
u = 0.275545 − 1.322890I
a = −1.11206 − 2.21999I
b = 0.716579 − 1.203070I
−1.97766 − 7.97069I 0
u = −0.616761 + 0.031191I
a = −4.35476 + 1.75506I
b = 0.540656 − 0.860419I
1.37720 − 2.17002I −20.8441 − 10.9028I
u = −0.616761 − 0.031191I
a = −4.35476 − 1.75506I
b = 0.540656 + 0.860419I
1.37720 + 2.17002I −20.8441 + 10.9028I
u = −0.380195 + 1.353450I
a = −0.173256 − 0.145320I
b = −0.568825 − 0.669802I
−1.50104 − 3.50534I 0
u = −0.380195 − 1.353450I
a = −0.173256 + 0.145320I
b = −0.568825 + 0.669802I
−1.50104 + 3.50534I 0
u = 0.276062 + 1.378580I
a = −0.90488 + 2.16282I
b = 0.036581 + 1.312140I
−6.94265 + 8.21032I 0
u = 0.276062 − 1.378580I
a = −0.90488 − 2.16282I
b = 0.036581 − 1.312140I
−6.94265 − 8.21032I 0
u = −0.04736 + 1.41955I
a = −0.293334 − 0.561445I
b = −0.634036 − 0.280540I
−5.27570 − 2.79528I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.04736 − 1.41955I
a = −0.293334 + 0.561445I
b = −0.634036 + 0.280540I
−5.27570 + 2.79528I 0
u = 0.33764 + 1.38231I
a = −0.663824 − 0.414973I
b = −0.939775 + 0.500176I
−0.04985 + 10.73450I 0
u = 0.33764 − 1.38231I
a = −0.663824 + 0.414973I
b = −0.939775 − 0.500176I
−0.04985 − 10.73450I 0
u = 0.07786 + 1.42827I
a = 0.66709 − 2.40876I
b = −0.194887 − 1.153270I
−9.60907 − 0.11401I 0
u = 0.07786 − 1.42827I
a = 0.66709 + 2.40876I
b = −0.194887 + 1.153270I
−9.60907 + 0.11401I 0
u = −0.21019 + 1.41955I
a = 0.01506 − 1.66109I
b = −0.155367 − 0.798808I
−4.90709 − 3.41016I 0
u = −0.21019 − 1.41955I
a = 0.01506 + 1.66109I
b = −0.155367 + 0.798808I
−4.90709 + 3.41016I 0
u = 0.34352 + 1.40634I
a = 1.21013 − 2.12096I
b = −0.691729 − 1.130530I
−1.9859 + 16.7029I 0
u = 0.34352 − 1.40634I
a = 1.21013 + 2.12096I
b = −0.691729 + 1.130530I
−1.9859 − 16.7029I 0
u = −0.37055 + 1.42903I
a = 1.04218 + 1.70770I
b = −0.591164 + 0.961287I
−2.38282 − 8.18392I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.37055 − 1.42903I
a = 1.04218 − 1.70770I
b = −0.591164 − 0.961287I
−2.38282 + 8.18392I 0
u = −0.03392 + 1.50679I
a = −0.00525 + 2.05953I
b = −0.557159 + 1.062340I
−7.30954 − 7.36946I 0
u = −0.03392 − 1.50679I
a = −0.00525 − 2.05953I
b = −0.557159 − 1.062340I
−7.30954 + 7.36946I 0
u = −0.370929 + 0.272771I
a = 1.030350 − 0.760360I
b = 0.180375 − 0.359379I
0.572882 − 1.093980I 6.17226 + 6.06480I
u = −0.370929 − 0.272771I
a = 1.030350 + 0.760360I
b = 0.180375 + 0.359379I
0.572882 + 1.093980I 6.17226 − 6.06480I
u = −0.342089 + 0.112981I
a = 2.59464 + 1.55121I
b = 0.476152 + 0.761801I
0.64094 + 1.45108I 5.67805 − 6.58266I
u = −0.342089 − 0.112981I
a = 2.59464 − 1.55121I
b = 0.476152 − 0.761801I
0.64094 − 1.45108I 5.67805 + 6.58266I
u = −0.062768 + 0.268464I
a = 1.87391 − 1.74824I
b = 0.545287 − 0.961436I
−0.07982 − 2.77352I 2.01744 + 1.22489I
u = −0.062768 − 0.268464I
a = 1.87391 + 1.74824I
b = 0.545287 + 0.961436I
−0.07982 + 2.77352I 2.01744 − 1.22489I
11
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
u
69
+ u
68
+ ··· + 7u − 1
c
2
u
69
+ 27u
68
+ ··· + 7u − 1
c
3
u
69
+ 7u
68
+ ··· + u + 1
c
5
, c
6
, c
9
u
69
+ u
68
+ ··· + 5u − 1
c
7
u
69
− u
68
+ ··· − 375u − 103
c
8
u
69
+ u
68
+ ··· + 137u − 119
c
10
u
69
− u
68
+ ··· + 12027u − 1217
c
11
u
69
+ 5u
68
+ ··· − u − 1
12
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
69
+ 27y
68
+ ··· + 7y −1
c
2
y
69
+ 31y
68
+ ··· + 611y −1
c
3
y
69
− 5y
68
+ ··· + 7y −1
c
5
, c
6
, c
9
y
69
+ 59y
68
+ ··· − 5y −1
c
7
y
69
+ 83y
68
+ ··· − 603653y −10609
c
8
y
69
+ 59y
68
+ ··· − 207093y −14161
c
10
y
69
− 25y
68
+ ··· − 20237733y −1481089
c
11
y
69
+ 7y
68
+ ··· − 5y −1
13
