11a
153
(K11a
153
)
A knot diagram
1
Linearized knot diagam
5 1 9 6 2 4 11 10 3 7 8
Solving Sequence
1,5
2 3
6,9
10 4 7 8 11
c
1
c
2
c
5
c
9
c
4
c
6
c
8
c
11
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
45
+ u
44
+ ··· + 5u
4
+ b, −u
43
+ 6u
41
+ ··· − 5u
3
+ a, u
47
− 2u
46
+ ··· + 2u
2
− 1i
I
u
2
= hb − 1, a − u, u
3
+ u
2
− 1i
* 2 irreducible components of dim
C
= 0, with total 50 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−u
45
+u
44
+· · ·+5u
4
+b, −u
43
+6u
41
+· · ·−5u
3
+a, u
47
−2u
46
+· · ·+2u
2
−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
6
=
−u
−u
3
+ u
a
9
=
u
43
− 6u
41
+ ··· − 4u
5
+ 5u
3
u
45
− u
44
+ ··· + 5u
5
− 5u
4
a
10
=
2u
46
− 2u
45
+ ··· − u + 1
−u
46
+ u
45
+ ··· + u
2
+ u
a
4
=
u
3
u
5
− u
3
+ u
a
7
=
−u
5
− u
−u
7
+ u
5
− 2u
3
+ u
a
8
=
−u
44
+ u
43
+ ··· + 5u
3
− u
2
−u
46
+ u
45
+ ··· − 9u
4
+ u
2
a
11
=
u
46
− u
45
+ ··· − u + 1
−u
46
+ u
45
+ ··· + u
2
+ u
a
11
=
u
46
− u
45
+ ··· − u + 1
−u
46
+ u
45
+ ··· + u
2
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −u
46
+ 2u
45
+ ··· − 11u − 3
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
47
+ 2u
46
+ ··· − 2u
2
+ 1
c
2
, c
4
, c
6
u
47
+ 12u
46
+ ··· + 4u + 1
c
3
, c
9
u
47
+ u
46
+ ··· + 28u + 8
c
7
, c
10
, c
11
u
47
+ 4u
46
+ ··· + 5u + 1
c
8
u
47
− 21u
46
+ ··· − 112u + 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
47
− 12y
46
+ ··· + 4y −1
c
2
, c
4
, c
6
y
47
+ 48y
46
+ ··· − 20y −1
c
3
, c
9
y
47
+ 21y
46
+ ··· − 112y −64
c
7
, c
10
, c
11
y
47
− 42y
46
+ ··· + 53y −1
c
8
y
47
+ 5y
46
+ ··· + 249088y −4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.951038 + 0.332468I
a = −0.548939 − 0.454811I
b = −1.39671 − 0.26399I
−2.29859 + 5.08605I −6.19055 − 7.78708I
u = −0.951038 − 0.332468I
a = −0.548939 + 0.454811I
b = −1.39671 + 0.26399I
−2.29859 − 5.08605I −6.19055 + 7.78708I
u = 1.011380 + 0.139586I
a = 0.187121 − 1.081320I
b = 0.152878 + 0.035343I
1.25225 + 2.83779I −2.68977 − 2.39473I
u = 1.011380 − 0.139586I
a = 0.187121 + 1.081320I
b = 0.152878 − 0.035343I
1.25225 − 2.83779I −2.68977 + 2.39473I
u = 0.896160 + 0.336643I
a = 0.608816 − 1.251080I
b = 0.208048 + 0.420593I
0.73808 − 3.39872I −3.20420 + 5.17325I
u = 0.896160 − 0.336643I
a = 0.608816 + 1.251080I
b = 0.208048 − 0.420593I
0.73808 + 3.39872I −3.20420 − 5.17325I
u = 0.929490 + 0.212978I
a = −0.382863 + 1.063800I
b = −0.152157 − 0.188016I
−2.99267 − 0.24824I −9.15885 + 0.73721I
u = 0.929490 − 0.212978I
a = −0.382863 − 1.063800I
b = −0.152157 + 0.188016I
−2.99267 + 0.24824I −9.15885 − 0.73721I
u = −1.006120 + 0.373819I
a = 0.507879 + 0.365560I
b = 1.365760 + 0.114872I
2.62432 + 8.92326I −1.23068 − 8.39839I
u = −1.006120 − 0.373819I
a = 0.507879 − 0.365560I
b = 1.365760 − 0.114872I
2.62432 − 8.92326I −1.23068 + 8.39839I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.586342 + 0.704775I
a = 0.286240 − 0.496512I
b = −0.636220 − 0.653509I
6.94014 + 2.76747I 5.54266 − 3.60808I
u = −0.586342 − 0.704775I
a = 0.286240 + 0.496512I
b = −0.636220 + 0.653509I
6.94014 − 2.76747I 5.54266 + 3.60808I
u = −0.844254 + 0.267575I
a = 0.624042 + 0.701381I
b = 1.43152 + 0.59292I
0.239586 + 1.107160I −2.87652 − 5.48870I
u = −0.844254 − 0.267575I
a = 0.624042 − 0.701381I
b = 1.43152 − 0.59292I
0.239586 − 1.107160I −2.87652 + 5.48870I
u = −0.946938 + 0.664626I
a = −0.210609 − 0.192004I
b = −0.664543 + 0.135905I
5.98354 + 2.31808I 4.28165 − 1.64217I
u = −0.946938 − 0.664626I
a = −0.210609 + 0.192004I
b = −0.664543 − 0.135905I
5.98354 − 2.31808I 4.28165 + 1.64217I
u = −0.842514 + 0.793044I
a = −0.169363 + 0.125945I
b = 0.111786 + 0.476934I
3.10025 + 1.81367I −3.66686 − 2.05384I
u = −0.842514 − 0.793044I
a = −0.169363 − 0.125945I
b = 0.111786 − 0.476934I
3.10025 − 1.81367I −3.66686 + 2.05384I
u = 0.827943 + 0.860184I
a = 2.70969 + 0.79407I
b = −2.83895 + 0.82810I
5.30471 + 2.88795I 0.68944 − 2.66752I
u = 0.827943 − 0.860184I
a = 2.70969 − 0.79407I
b = −2.83895 − 0.82810I
5.30471 − 2.88795I 0.68944 + 2.66752I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.847216 + 0.855752I
a = 0.256476 − 0.116248I
b = −0.054478 − 0.688171I
8.19027 − 0.67694I 2.91715 + 0.I
u = −0.847216 − 0.855752I
a = 0.256476 + 0.116248I
b = −0.054478 + 0.688171I
8.19027 + 0.67694I 2.91715 + 0.I
u = 0.863506 + 0.840738I
a = −2.93690 − 1.29712I
b = 3.21491 − 0.72537I
7.05051 − 2.00460I 3.77294 + 2.26192I
u = 0.863506 − 0.840738I
a = −2.93690 + 1.29712I
b = 3.21491 + 0.72537I
7.05051 + 2.00460I 3.77294 − 2.26192I
u = 0.815670 + 0.889580I
a = −2.42001 − 0.70946I
b = 2.67739 − 0.69105I
10.89330 + 7.08520I 3.93867 − 3.32748I
u = 0.815670 − 0.889580I
a = −2.42001 + 0.70946I
b = 2.67739 + 0.69105I
10.89330 − 7.08520I 3.93867 + 3.32748I
u = −0.930838 + 0.775441I
a = 0.203539 + 0.027785I
b = 0.305087 − 0.418436I
2.82936 + 4.09126I −3.95731 − 3.33683I
u = −0.930838 − 0.775441I
a = 0.203539 − 0.027785I
b = 0.305087 + 0.418436I
2.82936 − 4.09126I −3.95731 + 3.33683I
u = 0.935935 + 0.814528I
a = −2.21964 − 2.45540I
b = 3.34946 + 0.19998I
6.82306 − 4.16721I 3.15551 + 3.14334I
u = 0.935935 − 0.814528I
a = −2.21964 + 2.45540I
b = 3.34946 − 0.19998I
6.82306 + 4.16721I 3.15551 − 3.14334I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.953997 + 0.816453I
a = −0.258063 − 0.008399I
b = −0.328975 + 0.602645I
7.85574 + 6.89913I 0. − 4.81630I
u = −0.953997 − 0.816453I
a = −0.258063 + 0.008399I
b = −0.328975 − 0.602645I
7.85574 − 6.89913I 0. + 4.81630I
u = 0.967508 + 0.809416I
a = 1.72066 + 2.45725I
b = −3.04108 − 0.38491I
4.86878 − 9.09918I 0. + 7.51593I
u = 0.967508 − 0.809416I
a = 1.72066 − 2.45725I
b = −3.04108 + 0.38491I
4.86878 + 9.09918I 0. − 7.51593I
u = 0.917330 + 0.873542I
a = 2.18776 + 1.62070I
b = −3.01700 + 0.23550I
15.4002 − 3.2295I 6.21908 + 0.I
u = 0.917330 − 0.873542I
a = 2.18776 − 1.62070I
b = −3.01700 − 0.23550I
15.4002 + 3.2295I 6.21908 + 0.I
u = −0.194123 + 0.690391I
a = −0.768909 + 0.672272I
b = 0.832582 + 0.572354I
5.21653 − 5.13195I 4.47363 + 3.77222I
u = −0.194123 − 0.690391I
a = −0.768909 − 0.672272I
b = 0.832582 − 0.572354I
5.21653 + 5.13195I 4.47363 − 3.77222I
u = 0.989025 + 0.818280I
a = −1.52457 − 2.27011I
b = 2.85418 + 0.32452I
10.3470 − 13.4113I 0. + 8.12644I
u = 0.989025 − 0.818280I
a = −1.52457 + 2.27011I
b = 2.85418 − 0.32452I
10.3470 + 13.4113I 0. − 8.12644I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.682080
a = 0.611660
b = −0.132637
−0.926103 −11.4570
u = −0.525813 + 0.373412I
a = −0.094058 + 1.038330I
b = 0.733120 + 0.760322I
1.13890 + 1.31315I 3.11319 − 5.85317I
u = −0.525813 − 0.373412I
a = −0.094058 − 1.038330I
b = 0.733120 − 0.760322I
1.13890 − 1.31315I 3.11319 + 5.85317I
u = −0.160803 + 0.538431I
a = 0.823656 − 0.894795I
b = −0.721771 − 0.493724I
0.05463 − 1.88803I 0.05102 + 3.76347I
u = −0.160803 − 0.538431I
a = 0.823656 + 0.894795I
b = −0.721771 + 0.493724I
0.05463 + 1.88803I 0.05102 − 3.76347I
u = 0.295011 + 0.434696I
a = −1.38778 + 0.73289I
b = 0.681477 − 0.043588I
2.53395 + 0.36100I 2.22031 + 1.00355I
u = 0.295011 − 0.434696I
a = −1.38778 − 0.73289I
b = 0.681477 + 0.043588I
2.53395 − 0.36100I 2.22031 − 1.00355I
9
II. I
u
2
= hb − 1, a − u, u
3
+ u
2
− 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
6
=
−u
u
2
+ u − 1
a
9
=
u
1
a
10
=
u
1
a
4
=
−u
2
+ 1
u
2
a
7
=
−1
0
a
8
=
u
1
a
11
=
u + 1
1
a
11
=
u + 1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
2
− u − 2
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ u
2
− 1
c
2
, c
6
u
3
+ u
2
+ 2u + 1
c
3
, c
8
, c
9
u
3
c
4
u
3
− u
2
+ 2u − 1
c
5
u
3
− u
2
+ 1
c
7
(u + 1)
3
c
10
, c
11
(u − 1)
3
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
3
− y
2
+ 2y −1
c
2
, c
4
, c
6
y
3
+ 3y
2
+ 2y −1
c
3
, c
8
, c
9
y
3
c
7
, c
10
, c
11
(y −1)
3
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = −0.877439 + 0.744862I
b = 1.00000
4.66906 + 2.82812I −0.69240 − 3.35914I
u = −0.877439 − 0.744862I
a = −0.877439 − 0.744862I
b = 1.00000
4.66906 − 2.82812I −0.69240 + 3.35914I
u = 0.754878
a = 0.754878
b = 1.00000
0.531480 −1.61520
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
3
+ u
2
− 1)(u
47
+ 2u
46
+ ··· − 2u
2
+ 1)
c
2
, c
6
(u
3
+ u
2
+ 2u + 1)(u
47
+ 12u
46
+ ··· + 4u + 1)
c
3
, c
9
u
3
(u
47
+ u
46
+ ··· + 28u + 8)
c
4
(u
3
− u
2
+ 2u − 1)(u
47
+ 12u
46
+ ··· + 4u + 1)
c
5
(u
3
− u
2
+ 1)(u
47
+ 2u
46
+ ··· − 2u
2
+ 1)
c
7
((u + 1)
3
)(u
47
+ 4u
46
+ ··· + 5u + 1)
c
8
u
3
(u
47
− 21u
46
+ ··· − 112u + 64)
c
10
, c
11
((u − 1)
3
)(u
47
+ 4u
46
+ ··· + 5u + 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
3
− y
2
+ 2y −1)(y
47
− 12y
46
+ ··· + 4y −1)
c
2
, c
4
, c
6
(y
3
+ 3y
2
+ 2y −1)(y
47
+ 48y
46
+ ··· − 20y −1)
c
3
, c
9
y
3
(y
47
+ 21y
46
+ ··· − 112y −64)
c
7
, c
10
, c
11
((y −1)
3
)(y
47
− 42y
46
+ ··· + 53y −1)
c
8
y
3
(y
47
+ 5y
46
+ ··· + 249088y −4096)
15
