11a
23
(K11a
23
)
A knot diagram
1
Linearized knot diagam
4 1 7 2 10 3 6 11 5 9 8
Solving Sequence
5,9
10 6
2,11
4 1 8 7 3
c
9
c
5
c
10
c
4
c
1
c
8
c
7
c
3
c
2
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
53
− 2u
52
+ ··· + b + 1, u
52
− u
51
+ ··· + a − u, u
54
− 2u
53
+ ··· + 2u
2
− 1i
I
u
2
= h−u
2
+ b + u, u
2
+ a − u, u
3
− u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 57 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
53
−2u
52
+· · ·+b + 1, u
52
−u
51
+· · ·+a − u, u
54
−2u
53
+· · ·+2u
2
−1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
6
=
−u
−u
3
+ u
a
2
=
−u
52
+ u
51
+ ··· + 7u
3
+ u
−u
53
+ 2u
52
+ ··· − 2u − 1
a
11
=
−u
2
+ 1
u
2
a
4
=
−u
52
+ u
51
+ ··· + u − 1
u
52
− u
51
+ ··· − u
2
− u
a
1
=
−u
6
+ u
4
− 2u
2
+ 1
u
6
+ u
2
a
8
=
u
4
− u
2
+ 1
−u
4
a
7
=
u
8
− u
6
+ 3u
4
− 2u
2
+ 1
u
10
− 2u
8
+ 3u
6
− 4u
4
+ u
2
a
3
=
−u
52
+ u
51
+ ··· + 3u
3
+ 2u
−2u
53
+ 3u
52
+ ··· − 2u − 2
a
3
=
−u
52
+ u
51
+ ··· + 3u
3
+ 2u
−2u
53
+ 3u
52
+ ··· − 2u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
53
+ 2u
52
+ ··· − 13u − 5
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
54
− 4u
53
+ ··· + 5u − 1
c
2
u
54
+ 28u
53
+ ··· + 5u + 1
c
3
, c
6
u
54
− u
53
+ ··· + 28u + 8
c
5
, c
9
u
54
+ 2u
53
+ ··· + 2u
2
− 1
c
7
u
54
− 21u
53
+ ··· − 912u + 64
c
8
, c
10
, c
11
u
54
+ 14u
53
+ ··· + 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
54
− 28y
53
+ ··· − 5y + 1
c
2
y
54
+ 44y
52
+ ··· − 29y + 1
c
3
, c
6
y
54
− 21y
53
+ ··· − 912y + 64
c
5
, c
9
y
54
− 14y
53
+ ··· − 4y + 1
c
7
y
54
+ 19y
53
+ ··· − 85248y + 4096
c
8
, c
10
, c
11
y
54
+ 54y
53
+ ··· − 28y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.948112 + 0.298354I
a = 1.205050 + 0.065806I
b = −2.47632 + 1.36880I
−4.67558 − 3.96496I −10.65253 + 5.36076I
u = 0.948112 − 0.298354I
a = 1.205050 − 0.065806I
b = −2.47632 − 1.36880I
−4.67558 + 3.96496I −10.65253 − 5.36076I
u = −0.718756 + 0.708822I
a = 0.989080 + 0.349916I
b = −0.893237 − 0.687723I
1.72344 + 4.24877I −1.89208 − 7.05777I
u = −0.718756 − 0.708822I
a = 0.989080 − 0.349916I
b = −0.893237 + 0.687723I
1.72344 − 4.24877I −1.89208 + 7.05777I
u = −0.953732 + 0.349837I
a = −0.061370 + 0.782367I
b = 0.558618 − 0.498636I
−0.69346 + 4.89748I −4.90328 − 6.49260I
u = −0.953732 − 0.349837I
a = −0.061370 − 0.782367I
b = 0.558618 + 0.498636I
−0.69346 − 4.89748I −4.90328 + 6.49260I
u = −0.829612 + 0.586776I
a = 0.900184 + 0.101382I
b = −1.216120 − 0.670600I
1.80763 + 4.19776I −1.27767 − 7.87465I
u = −0.829612 − 0.586776I
a = 0.900184 − 0.101382I
b = −1.216120 + 0.670600I
1.80763 − 4.19776I −1.27767 + 7.87465I
u = 1.006640 + 0.186947I
a = −0.985399 + 0.649993I
b = 1.58875 − 0.30591I
−4.34560 + 3.65314I −10.05122 − 3.06776I
u = 1.006640 − 0.186947I
a = −0.985399 − 0.649993I
b = 1.58875 + 0.30591I
−4.34560 − 3.65314I −10.05122 + 3.06776I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.936944 + 0.259765I
a = −1.088760 − 0.644557I
b = 1.68766 + 0.11648I
−4.90867 + 1.39018I −11.17255 − 4.35263I
u = −0.936944 − 0.259765I
a = −1.088760 + 0.644557I
b = 1.68766 − 0.11648I
−4.90867 − 1.39018I −11.17255 + 4.35263I
u = −1.007510 + 0.341711I
a = 1.191860 − 0.125655I
b = −2.43976 − 0.96569I
−3.43639 + 9.75051I −8.30305 − 9.36472I
u = −1.007510 − 0.341711I
a = 1.191860 + 0.125655I
b = −2.43976 + 0.96569I
−3.43639 − 9.75051I −8.30305 + 9.36472I
u = 0.892491 + 0.183773I
a = −0.171964 − 0.552035I
b = 0.779603 + 0.338273I
−1.67290 − 0.31402I −7.28536 + 0.85083I
u = 0.892491 − 0.183773I
a = −0.171964 + 0.552035I
b = 0.779603 − 0.338273I
−1.67290 + 0.31402I −7.28536 − 0.85083I
u = 0.880753
a = −0.535851
b = 1.06380
−1.51820 −5.33260
u = 0.831263 + 0.825334I
a = 0.897031 − 0.632195I
b = −0.774607 + 0.728358I
1.86207 − 0.72710I −3.27217 + 0.I
u = 0.831263 − 0.825334I
a = 0.897031 + 0.632195I
b = −0.774607 − 0.728358I
1.86207 + 0.72710I −3.27217 + 0.I
u = −0.823137 + 0.844727I
a = −0.312862 − 0.944385I
b = −1.73844 − 0.80253I
2.56847 − 1.88759I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.823137 − 0.844727I
a = −0.312862 + 0.944385I
b = −1.73844 + 0.80253I
2.56847 + 1.88759I 0
u = −0.862381 + 0.818968I
a = −0.583547 + 0.090309I
b = 0.49799 + 1.75744I
4.38756 + 2.45269I 0
u = −0.862381 − 0.818968I
a = −0.583547 − 0.090309I
b = 0.49799 − 1.75744I
4.38756 − 2.45269I 0
u = 0.804605 + 0.877981I
a = −0.294081 + 1.060590I
b = −1.35489 + 0.61945I
4.52521 + 8.09679I 0
u = 0.804605 − 0.877981I
a = −0.294081 − 1.060590I
b = −1.35489 − 0.61945I
4.52521 − 8.09679I 0
u = −0.956300 + 0.721294I
a = 0.490288 + 0.770861I
b = −0.371501 − 0.639488I
1.09373 + 1.25845I 0
u = −0.956300 − 0.721294I
a = 0.490288 − 0.770861I
b = −0.371501 + 0.639488I
1.09373 − 1.25845I 0
u = 0.826228 + 0.868166I
a = −0.706693 − 0.315162I
b = 0.91045 − 1.19576I
7.09944 + 2.70045I 0
u = 0.826228 − 0.868166I
a = −0.706693 + 0.315162I
b = 0.91045 + 1.19576I
7.09944 − 2.70045I 0
u = −0.926090 + 0.797649I
a = 0.083529 − 0.557091I
b = −1.82650 + 0.41695I
4.18784 + 3.59964I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.926090 − 0.797649I
a = 0.083529 + 0.557091I
b = −1.82650 − 0.41695I
4.18784 − 3.59964I 0
u = −0.516406 + 0.577695I
a = −0.036990 + 1.075540I
b = 0.657739 + 0.015042I
2.66225 + 0.01615I 2.03217 − 0.16196I
u = −0.516406 − 0.577695I
a = −0.036990 − 1.075540I
b = 0.657739 − 0.015042I
2.66225 − 0.01615I 2.03217 + 0.16196I
u = 0.950127 + 0.790670I
a = 0.667535 − 0.810906I
b = −0.527757 + 0.770419I
1.49449 − 5.32145I 0
u = 0.950127 − 0.790670I
a = 0.667535 + 0.810906I
b = −0.527757 − 0.770419I
1.49449 + 5.32145I 0
u = 0.896659 + 0.861407I
a = −0.040376 + 0.871785I
b = −1.82541 + 0.01530I
9.95886 − 0.40591I 0
u = 0.896659 − 0.861407I
a = −0.040376 − 0.871785I
b = −1.82541 − 0.01530I
9.95886 + 0.40591I 0
u = −0.962624 + 0.798447I
a = −0.928929 − 0.233282I
b = 2.53779 + 2.34211I
2.13549 + 8.01692I 0
u = −0.962624 − 0.798447I
a = −0.928929 + 0.233282I
b = 2.53779 − 2.34211I
2.13549 − 8.01692I 0
u = 0.923219 + 0.851100I
a = −0.876432 + 0.007481I
b = 1.57894 − 1.93563I
9.87556 − 5.94354I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.923219 − 0.851100I
a = −0.876432 − 0.007481I
b = 1.57894 + 1.93563I
9.87556 + 5.94354I 0
u = 0.972034 + 0.812571I
a = 0.275106 + 0.680780I
b = −1.73893 − 0.27634I
6.64241 − 8.94495I 0
u = 0.972034 − 0.812571I
a = 0.275106 − 0.680780I
b = −1.73893 + 0.27634I
6.64241 + 8.94495I 0
u = 0.988340 + 0.806697I
a = −1.009690 + 0.227138I
b = 2.56726 − 1.93517I
3.9497 − 14.3488I 0
u = 0.988340 − 0.806697I
a = −1.009690 − 0.227138I
b = 2.56726 + 1.93517I
3.9497 + 14.3488I 0
u = −0.137568 + 0.670291I
a = −0.44103 + 1.74491I
b = 0.799841 − 0.000276I
−0.68378 − 6.18510I −2.38929 + 5.41509I
u = −0.137568 − 0.670291I
a = −0.44103 − 1.74491I
b = 0.799841 + 0.000276I
−0.68378 + 6.18510I −2.38929 − 5.41509I
u = 0.571380 + 0.287951I
a = 1.207730 − 0.200032I
b = 0.06093 + 1.45702I
−1.12376 − 1.18488I −5.58028 + 5.43531I
u = 0.571380 − 0.287951I
a = 1.207730 + 0.200032I
b = 0.06093 − 1.45702I
−1.12376 + 1.18488I −5.58028 − 5.43531I
u = −0.211819 + 0.582109I
a = 1.207330 + 0.116243I
b = −0.531021 − 0.291086I
1.59069 − 1.49648I 1.55257 + 1.21320I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.211819 − 0.582109I
a = 1.207330 − 0.116243I
b = −0.531021 + 0.291086I
1.59069 + 1.49648I 1.55257 − 1.21320I
u = −0.567584
a = −1.94525
b = 1.23770
−2.29901 2.64120
u = 0.075195 + 0.497044I
a = −0.33607 − 2.18707I
b = 0.838168 − 0.011197I
−2.17031 + 1.07616I −4.84925 − 0.51569I
u = 0.075195 − 0.497044I
a = −0.33607 + 2.18707I
b = 0.838168 + 0.011197I
−2.17031 − 1.07616I −4.84925 + 0.51569I
10
II. I
u
2
= h−u
2
+ b + u, u
2
+ a − u, u
3
− u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
6
=
−u
−u
2
+ u + 1
a
2
=
−u
2
+ u
u
2
− u
a
11
=
−u
2
+ 1
u
2
a
4
=
−u
2
+ u
u
2
a
1
=
0
−u
a
8
=
−u
−u
2
+ u + 1
a
7
=
−u
−u
2
+ u + 1
a
3
=
−u
2
+ u
u
2
a
3
=
−u
2
+ u
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2u
2
+ 7u − 10
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
6
, c
7
u
3
c
5
u
3
+ u
2
− 1
c
8
u
3
− u
2
+ 2u − 1
c
9
u
3
− u
2
+ 1
c
10
, c
11
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
6
, c
7
y
3
c
5
, c
9
y
3
− y
2
+ 2y −1
c
8
, c
10
, c
11
y
3
+ 3y
2
+ 2y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = 0.662359 − 0.562280I
b = −0.662359 + 0.562280I
1.37919 − 2.82812I −4.28809 + 2.59975I
u = 0.877439 − 0.744862I
a = 0.662359 + 0.562280I
b = −0.662359 − 0.562280I
1.37919 + 2.82812I −4.28809 − 2.59975I
u = −0.754878
a = −1.32472
b = 1.32472
−2.75839 −16.4240
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
54
− 4u
53
+ ··· + 5u − 1)
c
2
((u + 1)
3
)(u
54
+ 28u
53
+ ··· + 5u + 1)
c
3
, c
6
u
3
(u
54
− u
53
+ ··· + 28u + 8)
c
4
((u + 1)
3
)(u
54
− 4u
53
+ ··· + 5u − 1)
c
5
(u
3
+ u
2
− 1)(u
54
+ 2u
53
+ ··· + 2u
2
− 1)
c
7
u
3
(u
54
− 21u
53
+ ··· − 912u + 64)
c
8
(u
3
− u
2
+ 2u − 1)(u
54
+ 14u
53
+ ··· + 4u + 1)
c
9
(u
3
− u
2
+ 1)(u
54
+ 2u
53
+ ··· + 2u
2
− 1)
c
10
, c
11
(u
3
+ u
2
+ 2u + 1)(u
54
+ 14u
53
+ ··· + 4u + 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
3
)(y
54
− 28y
53
+ ··· − 5y + 1)
c
2
((y −1)
3
)(y
54
+ 44y
52
+ ··· − 29y + 1)
c
3
, c
6
y
3
(y
54
− 21y
53
+ ··· − 912y + 64)
c
5
, c
9
(y
3
− y
2
+ 2y −1)(y
54
− 14y
53
+ ··· − 4y + 1)
c
7
y
3
(y
54
+ 19y
53
+ ··· − 85248y + 4096)
c
8
, c
10
, c
11
(y
3
+ 3y
2
+ 2y −1)(y
54
+ 54y
53
+ ··· − 28y + 1)
16
