11a
8
(K11a
8
)
A knot diagram
1
Linearized knot diagam
5 1 8 2 3 11 10 4 6 7 9
Solving Sequence
7,11 3,6
5 10 8 4 9 1 2
c
6
c
5
c
10
c
7
c
3
c
9
c
11
c
2
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h4u
63
− 11u
62
+ ··· + 2b − 2, −5u
63
+ 14u
62
+ ··· + 2a + 12, u
64
− 3u
63
+ ··· − 3u + 1i
I
u
2
= h−u
2
a − au + b, −u
2
a + a
2
− au + 2u
2
− 2a + u + 3, u
3
+ u
2
+ 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 70 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
=
h4u
63
−11u
62
+· · ·+2b−2, −5u
63
+14u
62
+· · ·+2a+12, u
64
−3u
63
+· · ·−3u+1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
5
2
u
63
− 7u
62
+ ··· + 7u − 6
−2u
63
+
11
2
u
62
+ ··· −
1
2
u + 1
a
6
=
1
u
2
a
5
=
1
2
u
63
− u
62
+ ··· + 4u + 1
−
1
2
u
62
+ u
61
+ ··· −
5
2
u
2
−
1
2
u
a
10
=
−u
u
a
8
=
u
2
+ 1
−u
2
a
4
=
9
2
u
63
− 10u
62
+ ··· + 8u − 7
−4u
63
+
17
2
u
62
+ ··· −
1
2
u + 1
a
9
=
−u
3
− 2u
−u
5
− u
3
+ u
a
1
=
u
7
+ 4u
5
+ 4u
3
u
9
+ 3u
7
+ u
5
− 2u
3
+ u
a
2
=
4u
63
− 9u
62
+ ··· +
17
2
u −
13
2
−3u
63
+ 6u
62
+ ··· +
3
2
u +
1
2
a
2
=
4u
63
− 9u
62
+ ··· +
17
2
u −
13
2
−3u
63
+ 6u
62
+ ··· +
3
2
u +
1
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
63
−
3
2
u
62
+ ··· + 7u +
1
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
64
+ 4u
63
+ ··· + 4u + 1
c
2
u
64
+ 32u
63
+ ··· + 4u + 1
c
3
, c
8
u
64
− u
63
+ ··· + 32u + 64
c
5
u
64
− 4u
63
+ ··· + 393u + 306
c
6
, c
7
, c
10
u
64
+ 3u
63
+ ··· + 3u + 1
c
9
u
64
− 3u
63
+ ··· + 139u + 34
c
11
u
64
+ 13u
63
+ ··· + 9803u + 563
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
64
+ 32y
63
+ ··· + 4y + 1
c
2
y
64
+ 4y
63
+ ··· + 32y + 1
c
3
, c
8
y
64
− 35y
63
+ ··· − 62464y + 4096
c
5
y
64
− 24y
63
+ ··· − 628749y + 93636
c
6
, c
7
, c
10
y
64
+ 59y
63
+ ··· + 9y + 1
c
9
y
64
+ 7y
63
+ ··· + 48679y + 1156
c
11
y
64
+ 27y
63
+ ··· − 7846307y + 316969
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.015524 + 1.136780I
a = −0.552080 − 1.014190I
b = 0.36725 + 2.32487I
−0.80196 − 1.43696I 0
u = −0.015524 − 1.136780I
a = −0.552080 + 1.014190I
b = 0.36725 − 2.32487I
−0.80196 + 1.43696I 0
u = −0.214167 + 1.143170I
a = −0.357469 − 0.874324I
b = 0.61975 + 1.95833I
−1.39099 − 2.85342I 0
u = −0.214167 − 1.143170I
a = −0.357469 + 0.874324I
b = 0.61975 − 1.95833I
−1.39099 + 2.85342I 0
u = −0.298079 + 1.147240I
a = 0.375987 + 1.027900I
b = −0.93034 − 2.15707I
−3.53941 − 7.25346I 0
u = −0.298079 − 1.147240I
a = 0.375987 − 1.027900I
b = −0.93034 + 2.15707I
−3.53941 + 7.25346I 0
u = 0.476512 + 0.657222I
a = 0.793347 − 0.123841I
b = −1.54179 − 0.10637I
−4.93845 − 6.98785I −1.90680 + 3.70412I
u = 0.476512 − 0.657222I
a = 0.793347 + 0.123841I
b = −1.54179 + 0.10637I
−4.93845 + 6.98785I −1.90680 − 3.70412I
u = 0.735326 + 0.331337I
a = 0.68785 − 2.32153I
b = −0.1013060 + 0.0578601I
−3.76417 + 11.20390I 0.56898 − 8.94453I
u = 0.735326 − 0.331337I
a = 0.68785 + 2.32153I
b = −0.1013060 − 0.0578601I
−3.76417 − 11.20390I 0.56898 + 8.94453I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.064188 + 1.195330I
a = 0.61441 + 1.33088I
b = −0.13482 − 2.80368I
−2.10866 + 3.26818I 0
u = 0.064188 − 1.195330I
a = 0.61441 − 1.33088I
b = −0.13482 + 2.80368I
−2.10866 − 3.26818I 0
u = 0.685998 + 0.378244I
a = 0.37879 − 1.68792I
b = 0.181491 − 0.102139I
−5.86520 + 2.84323I −2.57675 − 3.28324I
u = 0.685998 − 0.378244I
a = 0.37879 + 1.68792I
b = 0.181491 + 0.102139I
−5.86520 − 2.84323I −2.57675 + 3.28324I
u = 0.705613 + 0.324529I
a = −0.36569 + 2.26750I
b = −0.0346428 − 0.1104610I
−1.18297 + 6.07475I 3.41678 − 5.69062I
u = 0.705613 − 0.324529I
a = −0.36569 − 2.26750I
b = −0.0346428 + 0.1104610I
−1.18297 − 6.07475I 3.41678 + 5.69062I
u = 0.536487 + 0.551979I
a = 0.443112 + 0.230612I
b = −1.088190 + 0.137761I
−6.52829 + 1.28000I −4.07342 − 3.16356I
u = 0.536487 − 0.551979I
a = 0.443112 − 0.230612I
b = −1.088190 − 0.137761I
−6.52829 − 1.28000I −4.07342 + 3.16356I
u = −0.749948 + 0.055820I
a = 1.85877 − 0.48714I
b = −0.0293520 + 0.1192290I
−0.20927 + 3.41413I 1.14237 − 4.37134I
u = −0.749948 − 0.055820I
a = 1.85877 + 0.48714I
b = −0.0293520 − 0.1192290I
−0.20927 − 3.41413I 1.14237 + 4.37134I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.439249 + 0.595498I
a = −0.832885 − 0.094483I
b = 1.269290 + 0.214528I
−2.26669 − 2.10675I 0.859060 + 0.119964I
u = 0.439249 − 0.595498I
a = −0.832885 + 0.094483I
b = 1.269290 − 0.214528I
−2.26669 + 2.10675I 0.859060 − 0.119964I
u = −0.299362 + 1.265870I
a = 0.850164 + 0.773878I
b = −1.58589 − 1.35845I
−4.30101 − 0.38221I 0
u = −0.299362 − 1.265870I
a = 0.850164 − 0.773878I
b = −1.58589 + 1.35845I
−4.30101 + 0.38221I 0
u = −0.619945 + 0.317199I
a = 0.53019 − 1.60674I
b = 0.658299 − 0.081366I
−0.84283 − 5.16860I 1.77998 + 6.94898I
u = −0.619945 − 0.317199I
a = 0.53019 + 1.60674I
b = 0.658299 + 0.081366I
−0.84283 + 5.16860I 1.77998 − 6.94898I
u = −0.664883 + 0.102386I
a = −1.170250 + 0.773392I
b = −0.144321 − 0.070324I
1.72799 − 0.42864I 6.50290 − 0.62963I
u = −0.664883 − 0.102386I
a = −1.170250 − 0.773392I
b = −0.144321 + 0.070324I
1.72799 + 0.42864I 6.50290 + 0.62963I
u = −0.082869 + 1.329720I
a = 0.019279 + 1.184640I
b = 0.42102 − 1.92368I
−4.92247 − 2.18904I 0
u = −0.082869 − 1.329720I
a = 0.019279 − 1.184640I
b = 0.42102 + 1.92368I
−4.92247 + 2.18904I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.600593 + 0.259671I
a = 0.91292 + 2.31668I
b = −0.406450 − 0.377479I
1.11308 + 3.77623I 3.53850 − 8.28052I
u = 0.600593 − 0.259671I
a = 0.91292 − 2.31668I
b = −0.406450 + 0.377479I
1.11308 − 3.77623I 3.53850 + 8.28052I
u = −0.259122 + 1.329370I
a = −0.933554 − 0.063987I
b = 1.58037 + 0.14438I
−2.78162 − 3.76575I 0
u = −0.259122 − 1.329370I
a = −0.933554 + 0.063987I
b = 1.58037 − 0.14438I
−2.78162 + 3.76575I 0
u = −0.592120 + 0.224814I
a = −0.69623 + 1.29343I
b = −0.391449 + 0.069510I
1.38695 − 0.99326I 6.93338 + 2.70050I
u = −0.592120 − 0.224814I
a = −0.69623 − 1.29343I
b = −0.391449 − 0.069510I
1.38695 + 0.99326I 6.93338 − 2.70050I
u = −0.449959 + 0.389908I
a = 0.250099 − 1.181500I
b = 0.500682 − 0.586321I
−1.42932 + 1.81815I −0.185423 + 0.070708I
u = −0.449959 − 0.389908I
a = 0.250099 + 1.181500I
b = 0.500682 + 0.586321I
−1.42932 − 1.81815I −0.185423 − 0.070708I
u = −0.226982 + 1.394010I
a = −1.153900 + 0.797633I
b = 1.89226 − 1.16346I
−3.79975 − 3.98351I 0
u = −0.226982 − 1.394010I
a = −1.153900 − 0.797633I
b = 1.89226 + 1.16346I
−3.79975 + 3.98351I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.20854 + 1.39910I
a = −1.022540 − 0.095130I
b = 2.59444 + 1.05724I
−4.62918 + 1.44235I 0
u = 0.20854 − 1.39910I
a = −1.022540 + 0.095130I
b = 2.59444 − 1.05724I
−4.62918 − 1.44235I 0
u = 0.23406 + 1.40484I
a = 1.162710 + 0.633487I
b = −2.56792 − 1.98653I
−4.22111 + 6.84171I 0
u = 0.23406 − 1.40484I
a = 1.162710 − 0.633487I
b = −2.56792 + 1.98653I
−4.22111 − 6.84171I 0
u = −0.18905 + 1.42427I
a = 0.98672 − 1.33216I
b = −1.67530 + 1.89832I
−7.17316 − 0.63151I 0
u = −0.18905 − 1.42427I
a = 0.98672 + 1.33216I
b = −1.67530 − 1.89832I
−7.17316 + 0.63151I 0
u = 0.511462 + 0.222716I
a = −1.82560 − 1.87884I
b = 0.636732 + 0.407279I
0.617090 − 1.254920I 0.39440 − 2.97018I
u = 0.511462 − 0.222716I
a = −1.82560 + 1.87884I
b = 0.636732 − 0.407279I
0.617090 + 1.254920I 0.39440 + 2.97018I
u = −0.24055 + 1.42343I
a = 1.51122 − 0.99157I
b = −2.38619 + 1.44111I
−6.41876 − 8.33142I 0
u = −0.24055 − 1.42343I
a = 1.51122 + 0.99157I
b = −2.38619 − 1.44111I
−6.41876 + 8.33142I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.27335 + 1.43352I
a = 0.93968 + 1.54462I
b = −1.82680 − 3.22208I
−6.81464 + 9.64252I 0
u = 0.27335 − 1.43352I
a = 0.93968 − 1.54462I
b = −1.82680 + 3.22208I
−6.81464 − 9.64252I 0
u = 0.13955 + 1.45581I
a = 0.374359 + 0.392616I
b = 0.375841 − 0.169773I
−8.74276 − 0.11604I 0
u = 0.13955 − 1.45581I
a = 0.374359 − 0.392616I
b = 0.375841 + 0.169773I
−8.74276 + 0.11604I 0
u = 0.28510 + 1.43978I
a = −0.92380 − 1.78639I
b = 1.70565 + 3.54725I
−9.4393 + 14.9162I 0
u = 0.28510 − 1.43978I
a = −0.92380 + 1.78639I
b = 1.70565 − 3.54725I
−9.4393 − 14.9162I 0
u = 0.25765 + 1.45108I
a = −0.52150 − 1.40966I
b = 1.29040 + 2.86879I
−11.74310 + 6.28318I 0
u = 0.25765 − 1.45108I
a = −0.52150 + 1.40966I
b = 1.29040 − 2.86879I
−11.74310 − 6.28318I 0
u = 0.12283 + 1.47595I
a = −0.686055 − 0.523479I
b = 0.129256 + 0.402174I
−11.78020 − 5.04358I 0
u = 0.12283 − 1.47595I
a = −0.686055 + 0.523479I
b = 0.129256 − 0.402174I
−11.78020 + 5.04358I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.16758 + 1.47356I
a = −0.473637 + 0.079429I
b = −0.152957 − 0.582701I
−13.05130 + 3.75910I 0
u = 0.16758 − 1.47356I
a = −0.473637 − 0.079429I
b = −0.152957 + 0.582701I
−13.05130 − 3.75910I 0
u = −0.041522 + 0.342357I
a = −1.174420 + 0.757126I
b = 0.274979 + 0.620859I
−0.108314 − 1.390220I −0.08539 + 5.01290I
u = −0.041522 − 0.342357I
a = −1.174420 − 0.757126I
b = 0.274979 − 0.620859I
−0.108314 + 1.390220I −0.08539 − 5.01290I
11
II.
I
u
2
= h−u
2
a − au + b, −u
2
a + a
2
− au + 2u
2
− 2a + u + 3, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
3
=
a
u
2
a + au
a
6
=
1
u
2
a
5
=
−u
2
+ a − u − 1
u
2
a + au + u
2
+ u + 1
a
10
=
−u
u
a
8
=
u
2
+ 1
−u
2
a
4
=
a
u
2
a + au
a
9
=
u
2
+ 1
−u
2
a
1
=
−1
−u
2
a
2
=
au + a
−au − a
a
2
=
au + a
−au − a
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
2
a − 4au + 3u
2
+ a + 3u + 4
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
(u
2
+ u + 1)
3
c
3
, c
8
u
6
c
4
(u
2
− u + 1)
3
c
6
, c
7
(u
3
+ u
2
+ 2u + 1)
2
c
9
, c
11
(u
3
+ u
2
− 1)
2
c
10
(u
3
− u
2
+ 2u − 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
3
c
3
, c
8
y
6
c
6
, c
7
, c
10
(y
3
+ 3y
2
+ 2y −1)
2
c
9
, c
11
(y
3
− y
2
+ 2y −1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0.706350 + 0.266290I
b = −1.52448 + 0.02619I
−3.02413 − 4.85801I −1.45566 + 6.64456I
u = −0.215080 + 1.307140I
a = −0.583789 + 0.478572I
b = 0.73956 − 1.33333I
−3.02413 − 0.79824I 2.09851 − 0.12339I
u = −0.215080 − 1.307140I
a = 0.706350 − 0.266290I
b = −1.52448 − 0.02619I
−3.02413 + 4.85801I −1.45566 − 6.64456I
u = −0.215080 − 1.307140I
a = −0.583789 − 0.478572I
b = 0.73956 + 1.33333I
−3.02413 + 0.79824I 2.09851 + 0.12339I
u = −0.569840
a = 0.87744 + 1.51977I
b = −0.215080 − 0.372529I
1.11345 − 2.02988I 5.85715 + 4.49037I
u = −0.569840
a = 0.87744 − 1.51977I
b = −0.215080 + 0.372529I
1.11345 + 2.02988I 5.85715 − 4.49037I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
3
)(u
64
+ 4u
63
+ ··· + 4u + 1)
c
2
((u
2
+ u + 1)
3
)(u
64
+ 32u
63
+ ··· + 4u + 1)
c
3
, c
8
u
6
(u
64
− u
63
+ ··· + 32u + 64)
c
4
((u
2
− u + 1)
3
)(u
64
+ 4u
63
+ ··· + 4u + 1)
c
5
((u
2
+ u + 1)
3
)(u
64
− 4u
63
+ ··· + 393u + 306)
c
6
, c
7
((u
3
+ u
2
+ 2u + 1)
2
)(u
64
+ 3u
63
+ ··· + 3u + 1)
c
9
((u
3
+ u
2
− 1)
2
)(u
64
− 3u
63
+ ··· + 139u + 34)
c
10
((u
3
− u
2
+ 2u − 1)
2
)(u
64
+ 3u
63
+ ··· + 3u + 1)
c
11
((u
3
+ u
2
− 1)
2
)(u
64
+ 13u
63
+ ··· + 9803u + 563)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
3
)(y
64
+ 32y
63
+ ··· + 4y + 1)
c
2
((y
2
+ y + 1)
3
)(y
64
+ 4y
63
+ ··· + 32y + 1)
c
3
, c
8
y
6
(y
64
− 35y
63
+ ··· − 62464y + 4096)
c
5
((y
2
+ y + 1)
3
)(y
64
− 24y
63
+ ··· − 628749y + 93636)
c
6
, c
7
, c
10
((y
3
+ 3y
2
+ 2y −1)
2
)(y
64
+ 59y
63
+ ··· + 9y + 1)
c
9
((y
3
− y
2
+ 2y −1)
2
)(y
64
+ 7y
63
+ ··· + 48679y + 1156)
c
11
((y
3
− y
2
+ 2y −1)
2
)(y
64
+ 27y
63
+ ··· − 7846307y + 316969)
17
