11a
48
(K11a
48
)
A knot diagram
1
Linearized knot diagam
5 1 8 2 4 10 3 6 11 7 9
Solving Sequence
1,5
2 3 4
6,9
8 7 11 10
c
1
c
2
c
4
c
5
c
8
c
7
c
11
c
9
c
3
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−14u
61
+ 23u
60
+ ··· + 4b − 7, −9u
61
+ 37u
60
+ ··· + 4a + 12, u
62
− 4u
61
+ ··· + u + 1i
I
u
2
= h−au + b − a, a
3
+ a
2
u − 2au − 2a + 1, u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 68 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−14u
61
+ 23u
60
+ · · · + 4b − 7, −9u
61
+ 37u
60
+ · · · + 4a + 12, u
62
−
4u
61
+ · · · + u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
4
=
−u
u
3
+ u
a
6
=
−u
3
u
5
+ u
3
+ u
a
9
=
9
4
u
61
−
37
4
u
60
+ ··· −
3
4
u − 3
7
2
u
61
−
23
4
u
60
+ ··· +
13
2
u +
7
4
a
8
=
11
4
u
61
−
35
2
u
60
+ ··· −
49
4
u −
35
4
13
2
u
61
−
47
4
u
60
+ ··· +
23
2
u +
11
4
a
7
=
13
4
u
61
−
23
2
u
60
+ ··· −
7
4
u −
13
4
3
2
u
61
−
1
4
u
60
+ ··· +
13
2
u +
9
4
a
11
=
−
1
4
u
60
+
3
4
u
59
+ ··· +
5
2
u +
7
4
1
4
u
61
− u
60
+ ··· −
5
4
u −
1
4
a
10
=
−
11
4
u
61
+
47
4
u
60
+ ··· +
7
4
u + 1
−
3
4
u
61
−
1
4
u
60
+ ··· −
17
4
u −
5
2
a
10
=
−
11
4
u
61
+
47
4
u
60
+ ··· +
7
4
u + 1
−
3
4
u
61
−
1
4
u
60
+ ··· −
17
4
u −
5
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3u
61
+
1
2
u
60
+ ··· + u + 16
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
62
+ 4u
61
+ ··· − u + 1
c
2
, c
5
u
62
+ 20u
61
+ ··· − 17u + 1
c
3
, c
7
u
62
− u
61
+ ··· + 224u − 64
c
6
, c
10
u
62
− 3u
61
+ ··· + 2u − 1
c
8
u
62
+ 3u
61
+ ··· − 4452u − 1201
c
9
, c
11
u
62
− 21u
61
+ ··· − 16u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
62
+ 20y
61
+ ··· − 17y + 1
c
2
, c
5
y
62
+ 48y
61
+ ··· − 369y + 1
c
3
, c
7
y
62
− 35y
61
+ ··· − 37888y + 4096
c
6
, c
10
y
62
− 21y
61
+ ··· − 16y + 1
c
8
y
62
− 17y
61
+ ··· − 41957136y + 1442401
c
9
, c
11
y
62
+ 43y
61
+ ··· − 16y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.580047 + 0.850451I
a = −0.615466 − 0.047953I
b = −0.105015 + 0.107324I
0.46590 − 2.28716I 1.57514 + 4.44404I
u = −0.580047 − 0.850451I
a = −0.615466 + 0.047953I
b = −0.105015 − 0.107324I
0.46590 + 2.28716I 1.57514 − 4.44404I
u = −0.708480 + 0.748571I
a = −0.625956 − 0.954656I
b = −0.035473 + 0.874104I
−0.06793 − 2.21961I 7.00000 + 3.72035I
u = −0.708480 − 0.748571I
a = −0.625956 + 0.954656I
b = −0.035473 − 0.874104I
−0.06793 + 2.21961I 7.00000 − 3.72035I
u = −0.176329 + 0.912969I
a = −0.631715 + 0.212995I
b = 0.204630 + 0.113298I
−1.47231 − 1.88154I 1.17198 + 4.94319I
u = −0.176329 − 0.912969I
a = −0.631715 − 0.212995I
b = 0.204630 − 0.113298I
−1.47231 + 1.88154I 1.17198 − 4.94319I
u = 0.067320 + 0.925637I
a = −1.65632 + 1.56093I
b = −0.021019 + 1.209610I
−5.17463 − 1.43170I −0.06499 + 2.83805I
u = 0.067320 − 0.925637I
a = −1.65632 − 1.56093I
b = −0.021019 − 1.209610I
−5.17463 + 1.43170I −0.06499 − 2.83805I
u = −0.762893 + 0.779001I
a = 0.88438 + 1.40384I
b = −0.547272 − 1.284430I
0.86999 + 2.89738I 0
u = −0.762893 − 0.779001I
a = 0.88438 − 1.40384I
b = −0.547272 + 1.284430I
0.86999 − 2.89738I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.672440 + 0.859246I
a = −1.094710 + 0.307283I
b = −0.15697 + 1.45420I
−1.87828 − 0.43024I 0
u = 0.672440 − 0.859246I
a = −1.094710 − 0.307283I
b = −0.15697 − 1.45420I
−1.87828 + 0.43024I 0
u = 0.113095 + 0.896419I
a = 1.43284 − 1.95950I
b = −0.35266 − 1.38822I
−4.68648 + 4.26236I 0.88079 − 2.61775I
u = 0.113095 − 0.896419I
a = 1.43284 + 1.95950I
b = −0.35266 + 1.38822I
−4.68648 − 4.26236I 0.88079 + 2.61775I
u = 0.848922 + 0.694333I
a = −0.858355 + 0.429131I
b = 0.287596 − 1.039470I
3.14061 − 3.35098I 0
u = 0.848922 − 0.694333I
a = −0.858355 − 0.429131I
b = 0.287596 + 1.039470I
3.14061 + 3.35098I 0
u = −0.288556 + 1.063810I
a = −0.278572 + 0.779132I
b = −0.996600 + 0.151978I
1.97217 − 3.44390I 0
u = −0.288556 − 1.063810I
a = −0.278572 − 0.779132I
b = −0.996600 − 0.151978I
1.97217 + 3.44390I 0
u = −0.172015 + 1.093990I
a = −1.05796 − 1.37125I
b = 0.117190 − 1.069160I
−3.80732 − 3.28559I 0
u = −0.172015 − 1.093990I
a = −1.05796 + 1.37125I
b = 0.117190 + 1.069160I
−3.80732 + 3.28559I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.872766 + 0.690242I
a = 0.873901 − 0.662198I
b = −0.58873 + 1.46893I
4.38951 − 9.08805I 0
u = 0.872766 − 0.690242I
a = 0.873901 + 0.662198I
b = −0.58873 − 1.46893I
4.38951 + 9.08805I 0
u = 0.673310 + 0.886698I
a = 0.848443 − 0.513970I
b = −0.08966 − 1.42530I
−1.96729 + 5.63314I 0
u = 0.673310 − 0.886698I
a = 0.848443 + 0.513970I
b = −0.08966 + 1.42530I
−1.96729 − 5.63314I 0
u = 0.811900 + 0.775479I
a = −1.206090 − 0.072648I
b = 0.416947 + 0.445355I
4.85281 − 0.38708I 0
u = 0.811900 − 0.775479I
a = −1.206090 + 0.072648I
b = 0.416947 − 0.445355I
4.85281 + 0.38708I 0
u = −0.193615 + 1.121270I
a = 0.76073 + 1.80584I
b = −0.50338 + 1.40284I
−2.88060 − 8.87825I 0
u = −0.193615 − 1.121270I
a = 0.76073 − 1.80584I
b = −0.50338 − 1.40284I
−2.88060 + 8.87825I 0
u = −0.491392 + 1.033550I
a = 0.487519 + 1.001310I
b = −0.126717 + 1.022770I
−1.94981 − 3.50251I 0
u = −0.491392 − 1.033550I
a = 0.487519 − 1.001310I
b = −0.126717 − 1.022770I
−1.94981 + 3.50251I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.740943 + 0.874063I
a = 1.87255 + 0.82263I
b = −1.074740 + 0.047853I
4.66247 − 2.81474I 0
u = −0.740943 − 0.874063I
a = 1.87255 − 0.82263I
b = −1.074740 − 0.047853I
4.66247 + 2.81474I 0
u = 0.866327 + 0.751351I
a = 1.39239 − 0.33135I
b = −1.227950 + 0.228420I
9.59400 − 2.64881I 0
u = 0.866327 − 0.751351I
a = 1.39239 + 0.33135I
b = −1.227950 − 0.228420I
9.59400 + 2.64881I 0
u = −0.446047 + 1.065130I
a = −0.990242 − 0.647003I
b = −0.466356 − 1.245930I
−1.36538 + 1.65817I 0
u = −0.446047 − 1.065130I
a = −0.990242 + 0.647003I
b = −0.466356 + 1.245930I
−1.36538 − 1.65817I 0
u = 0.838512 + 0.820293I
a = 1.45343 + 0.32563I
b = −0.784520 − 1.117280I
6.92919 + 4.19000I 0
u = 0.838512 − 0.820293I
a = 1.45343 − 0.32563I
b = −0.784520 + 1.117280I
6.92919 − 4.19000I 0
u = −0.696514 + 0.949067I
a = −2.10523 + 0.43360I
b = 0.084369 − 0.956151I
−0.66167 − 3.18112I 0
u = −0.696514 − 0.949067I
a = −2.10523 − 0.43360I
b = 0.084369 + 0.956151I
−0.66167 + 3.18112I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.728645 + 0.950887I
a = 2.59637 − 0.18053I
b = −0.54347 + 1.35036I
0.34590 − 8.55449I 0
u = −0.728645 − 0.950887I
a = 2.59637 + 0.18053I
b = −0.54347 − 1.35036I
0.34590 + 8.55449I 0
u = −0.760261 + 0.159745I
a = 0.938749 − 0.389340I
b = −0.56323 + 1.31677I
1.40736 − 5.86221I 11.56645 + 5.83230I
u = −0.760261 − 0.159745I
a = 0.938749 + 0.389340I
b = −0.56323 − 1.31677I
1.40736 + 5.86221I 11.56645 − 5.83230I
u = 0.752971 + 0.970116I
a = −0.630063 + 0.503155I
b = 0.456679 − 0.367835I
4.25170 + 6.26267I 0
u = 0.752971 − 0.970116I
a = −0.630063 − 0.503155I
b = 0.456679 + 0.367835I
4.25170 − 6.26267I 0
u = 0.789356 + 0.948317I
a = 0.026334 − 1.083390I
b = −0.815193 + 1.043280I
6.52873 + 1.87763I 0
u = 0.789356 − 0.948317I
a = 0.026334 + 1.083390I
b = −0.815193 − 1.043280I
6.52873 − 1.87763I 0
u = −0.744263
a = 1.16786
b = −1.09986
5.44766 16.7720
u = 0.741510 + 1.026060I
a = −2.01086 + 0.29598I
b = 0.288482 + 1.092220I
2.12433 + 9.28782I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.741510 − 1.026060I
a = −2.01086 − 0.29598I
b = 0.288482 − 1.092220I
2.12433 − 9.28782I 0
u = 0.774379 + 1.004960I
a = 1.35473 − 1.13843I
b = −1.218840 − 0.287269I
8.80808 + 8.74834I 0
u = 0.774379 − 1.004960I
a = 1.35473 + 1.13843I
b = −1.218840 + 0.287269I
8.80808 − 8.74834I 0
u = 0.749728 + 1.037360I
a = 2.34145 − 0.53630I
b = −0.56778 − 1.49568I
3.3199 + 15.1181I 0
u = 0.749728 − 1.037360I
a = 2.34145 + 0.53630I
b = −0.56778 + 1.49568I
3.3199 − 15.1181I 0
u = −0.675568 + 0.188318I
a = −0.786334 + 0.175025I
b = 0.053146 − 0.874363I
0.358267 − 0.639742I 9.73626 + 0.89260I
u = −0.675568 − 0.188318I
a = −0.786334 − 0.175025I
b = 0.053146 + 0.874363I
0.358267 + 0.639742I 9.73626 − 0.89260I
u = −0.017068 + 0.625651I
a = 0.059805 − 1.358870I
b = −0.665979 − 0.287190I
0.589690 + 0.350421I 8.57728 − 0.80469I
u = −0.017068 − 0.625651I
a = 0.059805 + 1.358870I
b = −0.665979 + 0.287190I
0.589690 − 0.350421I 8.57728 + 0.80469I
u = 0.361194 + 0.064869I
a = −0.06161 − 2.33790I
b = −0.267132 + 1.196310I
−2.33982 − 2.66219I 4.81398 + 3.49490I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.361194 − 0.064869I
a = −0.06161 + 2.33790I
b = −0.267132 − 1.196310I
−2.33982 + 2.66219I 4.81398 − 3.49490I
u = −0.246452
a = −1.59617
b = −0.280872
0.790964 12.7580
11
II. I
u
2
= h−au + b − a, a
3
+ a
2
u − 2au − 2a + 1, u
2
+ u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u + 1
a
3
=
−u
u + 1
a
4
=
−u
u + 1
a
6
=
−1
0
a
9
=
a
au + a
a
8
=
−au
au + a
a
7
=
−au
au + a
a
11
=
a
2
u + a
2
+ 1
a
2
u
a
10
=
a
2
u + a
2
+ au − u
a
2
u − au − a + 1
a
10
=
a
2
u + a
2
+ au − u
a
2
u − au − a + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6a
2
u + a
2
− 4au − 5a + u + 14
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
7
u
6
c
4
(u
2
− u + 1)
3
c
6
(u
3
− u
2
+ 1)
2
c
8
, c
11
(u
3
− u
2
+ 2u − 1)
2
c
9
(u
3
+ u
2
+ 2u + 1)
2
c
10
(u
3
+ u
2
− 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
7
y
6
c
6
, c
10
(y
3
− y
2
+ 2y −1)
2
c
8
, c
9
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.024480 − 0.839835I
b = 0.215080 − 1.307140I
−3.02413 − 4.85801I 4.03424 + 5.28153I
u = −0.500000 + 0.866025I
a = 1.239560 + 0.467306I
b = 0.215080 + 1.307140I
−3.02413 + 0.79824I 2.74410 − 0.29766I
u = −0.500000 + 0.866025I
a = 0.284920 − 0.493496I
b = 0.569840
1.11345 − 2.02988I 12.72167 + 1.07831I
u = −0.500000 − 0.866025I
a = −1.024480 + 0.839835I
b = 0.215080 + 1.307140I
−3.02413 + 4.85801I 4.03424 − 5.28153I
u = −0.500000 − 0.866025I
a = 1.239560 − 0.467306I
b = 0.215080 − 1.307140I
−3.02413 − 0.79824I 2.74410 + 0.29766I
u = −0.500000 − 0.866025I
a = 0.284920 + 0.493496I
b = 0.569840
1.11345 + 2.02988I 12.72167 − 1.07831I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
3
)(u
62
+ 4u
61
+ ··· − u + 1)
c
2
, c
5
((u
2
+ u + 1)
3
)(u
62
+ 20u
61
+ ··· − 17u + 1)
c
3
, c
7
u
6
(u
62
− u
61
+ ··· + 224u − 64)
c
4
((u
2
− u + 1)
3
)(u
62
+ 4u
61
+ ··· − u + 1)
c
6
((u
3
− u
2
+ 1)
2
)(u
62
− 3u
61
+ ··· + 2u − 1)
c
8
((u
3
− u
2
+ 2u − 1)
2
)(u
62
+ 3u
61
+ ··· − 4452u − 1201)
c
9
((u
3
+ u
2
+ 2u + 1)
2
)(u
62
− 21u
61
+ ··· − 16u + 1)
c
10
((u
3
+ u
2
− 1)
2
)(u
62
− 3u
61
+ ··· + 2u − 1)
c
11
((u
3
− u
2
+ 2u − 1)
2
)(u
62
− 21u
61
+ ··· − 16u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
3
)(y
62
+ 20y
61
+ ··· − 17y + 1)
c
2
, c
5
((y
2
+ y + 1)
3
)(y
62
+ 48y
61
+ ··· − 369y + 1)
c
3
, c
7
y
6
(y
62
− 35y
61
+ ··· − 37888y + 4096)
c
6
, c
10
((y
3
− y
2
+ 2y −1)
2
)(y
62
− 21y
61
+ ··· − 16y + 1)
c
8
((y
3
+ 3y
2
+ 2y −1)
2
)(y
62
− 17y
61
+ ··· − 4.19571 × 10
7
y + 1442401)
c
9
, c
11
((y
3
+ 3y
2
+ 2y −1)
2
)(y
62
+ 43y
61
+ ··· − 16y + 1)
17
