11a
206
(K11a
206
)
A knot diagram
1
Linearized knot diagam
7 1 9 10 11 2 6 3 4 5 8
Solving Sequence
2,7
1 3 6 8 9 4 11 5 10
c
1
c
2
c
6
c
7
c
8
c
3
c
11
c
5
c
10
c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
23
+ u
22
+ ··· − 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 23 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
23
+ u
22
+ · · · − 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
6
=
−u
u
a
8
=
−u
3
u
3
+ u
a
9
=
u
9
+ 2u
7
+ 3u
5
+ 2u
3
+ u
u
11
+ u
9
+ 2u
7
+ u
5
+ u
3
+ u
a
4
=
−u
16
− 3u
14
− 7u
12
− 10u
10
− 11u
8
− 8u
6
− 4u
4
+ 1
−u
18
− 2u
16
− 5u
14
− 6u
12
− 7u
10
− 6u
8
− 4u
6
− 2u
4
− u
2
a
11
=
−u
8
− u
6
− u
4
+ 1
u
8
+ 2u
6
+ 2u
4
+ 2u
2
a
5
=
u
15
+ 2u
13
+ 4u
11
+ 4u
9
+ 2u
7
− 2u
3
− 2u
−u
15
− 3u
13
− 6u
11
− 9u
9
− 8u
7
− 6u
5
− 2u
3
+ u
a
10
=
u
22
+ 3u
20
+ ··· − 2u
2
+ 1
−u
22
− 4u
20
+ ··· + 2u
4
+ 3u
2
a
10
=
u
22
+ 3u
20
+ ··· − 2u
2
+ 1
−u
22
− 4u
20
+ ··· + 2u
4
+ 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
21
−4u
20
−12u
19
−12u
18
−36u
17
−32u
16
−60u
15
−52u
14
−
88u
13
−64u
12
−88u
11
−60u
10
−68u
9
−32u
8
−28u
7
−4u
6
+ 12u
4
+ 16u
3
+ 16u
2
+ 4u + 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
23
+ u
22
+ ··· − 2u + 1
c
2
, c
7
u
23
+ 7u
22
+ ··· + 8u − 1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
23
+ u
22
+ ··· − 4u
2
+ 1
c
11
u
23
− 5u
22
+ ··· − 136u + 39
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
23
+ 7y
22
+ ··· + 8y −1
c
2
, c
7
y
23
+ 19y
22
+ ··· + 116y −1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
23
− 33y
22
+ ··· + 8y −1
c
11
y
23
− 13y
22
+ ··· + 17092y −1521
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.227985 + 0.971221I
2.66448 − 2.76032I 9.49755 + 4.44807I
u = −0.227985 − 0.971221I
2.66448 + 2.76032I 9.49755 − 4.44807I
u = −0.731982 + 0.784107I
3.25860 − 0.02327I 13.38062 − 2.15520I
u = −0.731982 − 0.784107I
3.25860 + 0.02327I 13.38062 + 2.15520I
u = 0.268514 + 1.049110I
13.20350 + 3.30165I 10.15005 − 3.37633I
u = 0.268514 − 1.049110I
13.20350 − 3.30165I 10.15005 + 3.37633I
u = 0.078829 + 0.893980I
−1.87270 + 1.23334I 3.38642 − 5.87652I
u = 0.078829 − 0.893980I
−1.87270 − 1.23334I 3.38642 + 5.87652I
u = 0.683177 + 0.873071I
1.27817 + 2.63439I 7.17328 − 2.59344I
u = 0.683177 − 0.873071I
1.27817 − 2.63439I 7.17328 + 2.59344I
u = 0.815519 + 0.753290I
9.35127 − 1.67104I 15.7595 + 0.7836I
u = 0.815519 − 0.753290I
9.35127 + 1.67104I 15.7595 − 0.7836I
u = −0.862702 + 0.746175I
−18.8163 + 2.5543I 15.9877 − 0.1490I
u = −0.862702 − 0.746175I
−18.8163 − 2.5543I 15.9877 + 0.1490I
u = −0.714154 + 0.939346I
2.78784 − 5.50013I 11.6998 + 7.9457I
u = −0.714154 − 0.939346I
2.78784 + 5.50013I 11.6998 − 7.9457I
u = 0.749494 + 0.981641I
8.65288 + 7.54251I 14.3885 − 6.0343I
u = 0.749494 − 0.981641I
8.65288 − 7.54251I 14.3885 + 6.0343I
u = −0.769773 + 1.006750I
−19.6232 − 8.6288I 14.6907 + 4.9949I
u = −0.769773 − 1.006750I
−19.6232 + 8.6288I 14.6907 − 4.9949I
u = 0.723840
16.6303 16.0670
u = −0.612110
5.70319 16.3480
u = 0.310396
0.571551 17.3560
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
23
+ u
22
+ ··· − 2u + 1
c
2
, c
7
u
23
+ 7u
22
+ ··· + 8u − 1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
23
+ u
22
+ ··· − 4u
2
+ 1
c
11
u
23
− 5u
22
+ ··· − 136u + 39
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
23
+ 7y
22
+ ··· + 8y −1
c
2
, c
7
y
23
+ 19y
22
+ ··· + 116y −1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
23
− 33y
22
+ ··· + 8y −1
c
11
y
23
− 13y
22
+ ··· + 17092y −1521
7
