11a
159
(K11a
159
)
A knot diagram
1
Linearized knot diagam
5 1 9 7 2 11 4 10 3 8 6
Solving Sequence
3,9
4 10 8 11 7 5 6 1 2
c
3
c
9
c
8
c
10
c
7
c
4
c
6
c
11
c
2
c
1
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
55
+ u
54
+ ··· + 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 55 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
55
+ u
54
+ · · · + 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
10
=
−u
u
a
8
=
−u
3
u
3
+ u
a
11
=
−u
5
− u
u
5
+ u
3
+ u
a
7
=
u
5
+ u
u
7
+ u
5
+ 2u
3
+ u
a
5
=
u
10
+ u
8
+ 2u
6
+ u
4
+ u
2
+ 1
u
12
+ 2u
10
+ 4u
8
+ 4u
6
+ 3u
4
+ 2u
2
a
6
=
−u
17
− 2u
15
− 5u
13
− 6u
11
− 7u
9
− 6u
7
− 2u
5
− 2u
3
+ u
u
17
+ 3u
15
+ 7u
13
+ 10u
11
+ 11u
9
+ 10u
7
+ 6u
5
+ 4u
3
+ u
a
1
=
−u
29
− 4u
27
+ ··· + 2u
3
− u
u
29
+ 5u
27
+ ··· + 3u
3
+ u
a
2
=
−u
51
− 8u
49
+ ··· − 5u
3
− 2u
−u
53
− 9u
51
+ ··· + u
3
+ u
a
2
=
−u
51
− 8u
49
+ ··· − 5u
3
− 2u
−u
53
− 9u
51
+ ··· + u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
54
− 36u
52
+ ··· − 4u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
55
+ u
54
+ ··· + 2u
3
+ 1
c
2
u
55
+ 29u
54
+ ··· − 6u
2
+ 1
c
3
, c
9
u
55
+ u
54
+ ··· + 2u + 1
c
4
, c
7
u
55
− 5u
54
+ ··· − 4u + 1
c
6
, c
11
u
55
+ 3u
54
+ ··· + 35u + 16
c
8
, c
10
u
55
− 19u
54
+ ··· − 18u
2
+ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
55
− 29y
54
+ ··· + 6y
2
− 1
c
2
y
55
− 5y
54
+ ··· + 12y −1
c
3
, c
9
y
55
+ 19y
54
+ ··· + 18y
2
− 1
c
4
, c
7
y
55
+ 31y
54
+ ··· − 92y −1
c
6
, c
11
y
55
+ 39y
54
+ ··· − 6167y −256
c
8
, c
10
y
55
+ 35y
54
+ ··· + 36y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.784082 + 0.635234I
−1.91993 + 3.95621I −4.32723 − 2.21514I
u = 0.784082 − 0.635234I
−1.91993 − 3.95621I −4.32723 + 2.21514I
u = −0.799722 + 0.633488I
−4.89200 − 8.77056I −7.47137 + 5.34591I
u = −0.799722 − 0.633488I
−4.89200 + 8.77056I −7.47137 − 5.34591I
u = 0.695449 + 0.747109I
−3.52521 + 0.06578I −10.04150 − 0.64430I
u = 0.695449 − 0.747109I
−3.52521 − 0.06578I −10.04150 + 0.64430I
u = −0.785485 + 0.659519I
−5.96663 − 0.17301I −9.26357 − 0.91884I
u = −0.785485 − 0.659519I
−5.96663 + 0.17301I −9.26357 + 0.91884I
u = 0.515960 + 0.907861I
−2.45106 − 5.66045I −4.09002 + 7.28827I
u = 0.515960 − 0.907861I
−2.45106 + 5.66045I −4.09002 − 7.28827I
u = 0.087591 + 1.044510I
0.0418156 + 0.0593950I −1.97321 + 0.28127I
u = 0.087591 − 1.044510I
0.0418156 − 0.0593950I −1.97321 − 0.28127I
u = 0.732924 + 0.589195I
1.02771 + 3.24584I −2.27897 − 4.07779I
u = 0.732924 − 0.589195I
1.02771 − 3.24584I −2.27897 + 4.07779I
u = −0.518072 + 0.766150I
−0.11478 + 1.78039I −0.55066 − 3.60054I
u = −0.518072 − 0.766150I
−0.11478 − 1.78039I −0.55066 + 3.60054I
u = −0.066273 + 1.075310I
4.04900 + 3.40061I 3.11315 − 3.08609I
u = −0.066273 − 1.075310I
4.04900 − 3.40061I 3.11315 + 3.08609I
u = −0.013325 + 1.085250I
6.52620 + 2.29211I 4.76004 − 3.60647I
u = −0.013325 − 1.085250I
6.52620 − 2.29211I 4.76004 + 3.60647I
u = 0.080625 + 1.087480I
1.25671 − 8.17694I 0. + 6.49947I
u = 0.080625 − 1.087480I
1.25671 + 8.17694I 0. − 6.49947I
u = −0.682148 + 0.562866I
1.33027 + 1.15553I −1.16546 − 3.23863I
u = −0.682148 − 0.562866I
1.33027 − 1.15553I −1.16546 + 3.23863I
u = 0.741553 + 0.863345I
−5.44101 − 2.81013I −7.05601 + 3.05455I
u = 0.741553 − 0.863345I
−5.44101 + 2.81013I −7.05601 − 3.05455I
u = −0.757396 + 0.852445I
−8.97089 − 1.53080I −10.56468 + 0.I
u = −0.757396 − 0.852445I
−8.97089 + 1.53080I −10.56468 + 0.I
u = 0.578305 + 0.998594I
−1.71452 + 1.81047I 0
u = 0.578305 − 0.998594I
−1.71452 − 1.81047I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.663907 + 0.946346I
−2.91576 − 5.31435I −7.80390 + 6.55381I
u = 0.663907 − 0.946346I
−2.91576 + 5.31435I −7.80390 − 6.55381I
u = −0.751586 + 0.878593I
−8.89140 + 7.22930I −10.25643 − 6.47034I
u = −0.751586 − 0.878593I
−8.89140 − 7.22930I −10.25643 + 6.47034I
u = −0.606564 + 0.990704I
0.84076 + 2.75512I 0
u = −0.606564 − 0.990704I
0.84076 − 2.75512I 0
u = −0.644080 + 1.018780I
2.61827 + 4.00138I 0
u = −0.644080 − 1.018780I
2.61827 − 4.00138I 0
u = 0.660956 + 1.025220I
2.29946 − 8.58321I 0
u = 0.660956 − 1.025220I
2.29946 + 8.58321I 0
u = −0.698488 + 1.015790I
−4.89384 + 5.78358I 0
u = −0.698488 − 1.015790I
−4.89384 − 5.78358I 0
u = 0.690811 + 1.025790I
−0.74984 − 9.53517I 0
u = 0.690811 − 1.025790I
−0.74984 + 9.53517I 0
u = −0.696320 + 1.031360I
−3.6961 + 14.4089I 0
u = −0.696320 − 1.031360I
−3.6961 − 14.4089I 0
u = −0.171816 + 0.720092I
0.95831 + 1.60933I 1.49417 − 5.74918I
u = −0.171816 − 0.720092I
0.95831 − 1.60933I 1.49417 + 5.74918I
u = 0.630067 + 0.344372I
−3.34533 − 6.30811I −7.15638 + 6.23846I
u = 0.630067 − 0.344372I
−3.34533 + 6.30811I −7.15638 − 6.23846I
u = −0.561648 + 0.367518I
−0.48181 + 1.78744I −3.72385 − 3.38377I
u = −0.561648 − 0.367518I
−0.48181 − 1.78744I −3.72385 + 3.38377I
u = 0.569392 + 0.257173I
−4.05721 + 1.86906I −9.08122 − 0.59288I
u = 0.569392 − 0.257173I
−4.05721 − 1.86906I −9.08122 + 0.59288I
u = −0.357397
−1.02390 −10.8300
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
55
+ u
54
+ ··· + 2u
3
+ 1
c
2
u
55
+ 29u
54
+ ··· − 6u
2
+ 1
c
3
, c
9
u
55
+ u
54
+ ··· + 2u + 1
c
4
, c
7
u
55
− 5u
54
+ ··· − 4u + 1
c
6
, c
11
u
55
+ 3u
54
+ ··· + 35u + 16
c
8
, c
10
u
55
− 19u
54
+ ··· − 18u
2
+ 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
55
− 29y
54
+ ··· + 6y
2
− 1
c
2
y
55
− 5y
54
+ ··· + 12y −1
c
3
, c
9
y
55
+ 19y
54
+ ··· + 18y
2
− 1
c
4
, c
7
y
55
+ 31y
54
+ ··· − 92y −1
c
6
, c
11
y
55
+ 39y
54
+ ··· − 6167y −256
c
8
, c
10
y
55
+ 35y
54
+ ··· + 36y −1
8
