11a
224
(K11a
224
)
A knot diagram
1
Linearized knot diagam
6 1 10 9 8 2 11 5 3 4 7
Solving Sequence
3,9
10 4 5 11 8 6 7 1 2
c
9
c
3
c
4
c
10
c
8
c
5
c
7
c
11
c
2
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
44
− u
43
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 44 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
44
− u
43
+ · · · + 2u − 1i
(i) Arc colorings
a
3
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
4
=
−u
−u
3
+ u
a
5
=
u
3
− 2u
−u
3
+ u
a
11
=
−u
2
+ 1
−u
4
+ 2u
2
a
8
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
6
+ 2u
4
− u
2
a
6
=
u
9
− 4u
7
+ 5u
5
− 3u
−u
9
+ 3u
7
− 3u
5
+ u
a
7
=
u
12
− 5u
10
+ 9u
8
− 4u
6
− 6u
4
+ 5u
2
+ 1
u
14
− 6u
12
+ 13u
10
− 10u
8
− 4u
6
+ 8u
4
− u
2
a
1
=
−u
22
+ 9u
20
+ ··· + 2u
2
+ 1
−u
24
+ 10u
22
+ ··· − 4u
4
+ 2u
2
a
2
=
u
42
− 17u
40
+ ··· − u
2
+ 1
−u
42
+ 16u
40
+ ··· + 4u
4
+ 3u
2
a
2
=
u
42
− 17u
40
+ ··· − u
2
+ 1
−u
42
+ 16u
40
+ ··· + 4u
4
+ 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
41
− 64u
39
+ ··· + 4u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
44
− u
43
+ ··· + u
2
− 1
c
2
u
44
+ 23u
43
+ ··· + 2u + 1
c
3
, c
9
, c
10
u
44
+ u
43
+ ··· − 2u − 1
c
4
, c
5
, c
8
u
44
− 3u
43
+ ··· − 10u + 5
c
7
, c
11
u
44
− 3u
43
+ ··· + 70u − 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
44
− 23y
43
+ ··· − 2y + 1
c
2
y
44
− 3y
43
+ ··· − 10y + 1
c
3
, c
9
, c
10
y
44
− 35y
43
+ ··· − 2y + 1
c
4
, c
5
, c
8
y
44
+ 41y
43
+ ··· − 270y + 25
c
7
, c
11
y
44
+ 29y
43
+ ··· − 6454y + 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.136420 + 0.070861I
−1.83859 − 0.36732I −5.44983 + 0.09330I
u = 1.136420 − 0.070861I
−1.83859 + 0.36732I −5.44983 − 0.09330I
u = 0.011664 + 0.857762I
7.59511 − 2.36662I −0.82199 + 3.38645I
u = 0.011664 − 0.857762I
7.59511 + 2.36662I −0.82199 − 3.38645I
u = −0.072887 + 0.852785I
2.26398 + 8.63330I −5.49078 − 6.17544I
u = −0.072887 − 0.852785I
2.26398 − 8.63330I −5.49078 + 6.17544I
u = 0.058073 + 0.845269I
5.01784 − 3.75852I −2.18404 + 2.68935I
u = 0.058073 − 0.845269I
5.01784 + 3.75852I −2.18404 − 2.68935I
u = −0.066510 + 0.814340I
0.820194 + 0.338577I −7.27786 − 0.02628I
u = −0.066510 − 0.814340I
0.820194 − 0.338577I −7.27786 + 0.02628I
u = −1.209090 + 0.176546I
−3.07255 + 4.10165I −9.63918 − 6.97252I
u = −1.209090 − 0.176546I
−3.07255 − 4.10165I −9.63918 + 6.97252I
u = −1.207320 + 0.344488I
−2.67222 + 3.85231I −10.89580 − 3.96243I
u = −1.207320 − 0.344488I
−2.67222 − 3.85231I −10.89580 + 3.96243I
u = −1.199240 + 0.400757I
−1.19898 − 4.13238I −8.61614 + 2.75656I
u = −1.199240 − 0.400757I
−1.19898 + 4.13238I −8.61614 − 2.75656I
u = 1.216460 + 0.389904I
1.45135 − 0.67916I −5.37325 + 0.I
u = 1.216460 − 0.389904I
1.45135 + 0.67916I −5.37325 + 0.I
u = −1.28385
−5.57163 −16.6130
u = 1.261750 + 0.397871I
3.71994 − 2.13541I 0
u = 1.261750 − 0.397871I
3.71994 + 2.13541I 0
u = −1.280990 + 0.395746I
3.57613 + 6.86218I 0
u = −1.280990 − 0.395746I
3.57613 − 6.86218I 0
u = −1.336030 + 0.128402I
−5.89939 + 3.18300I −11.60255 + 0.I
u = −1.336030 − 0.128402I
−5.89939 − 3.18300I −11.60255 + 0.I
u = 1.353960 + 0.106974I
−9.55253 + 0.87557I −15.7624 + 0.I
u = 1.353960 − 0.106974I
−9.55253 − 0.87557I −15.7624 + 0.I
u = 1.354080 + 0.142889I
−9.09797 − 7.70313I −14.6073 + 0.I
u = 1.354080 − 0.142889I
−9.09797 + 7.70313I −14.6073 + 0.I
u = 1.314770 + 0.363443I
−3.50174 − 4.58387I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.314770 − 0.363443I
−3.50174 + 4.58387I 0
u = −1.312960 + 0.381210I
0.73171 + 8.16553I 0
u = −1.312960 − 0.381210I
0.73171 − 8.16553I 0
u = 1.322850 + 0.383944I
−2.10496 − 13.07590I 0
u = 1.322850 − 0.383944I
−2.10496 + 13.07590I 0
u = −0.371942 + 0.476818I
−3.72132 + 5.60891I −9.34455 − 7.77746I
u = −0.371942 − 0.476818I
−3.72132 − 5.60891I −9.34455 + 7.77746I
u = −0.442174 + 0.385790I
−4.03922 − 2.47426I −10.82917 − 0.27323I
u = −0.442174 − 0.385790I
−4.03922 + 2.47426I −10.82917 + 0.27323I
u = 0.334945 + 0.405418I
−0.74838 − 1.34331I −6.21576 + 4.98012I
u = 0.334945 − 0.405418I
−0.74838 + 1.34331I −6.21576 − 4.98012I
u = 0.101961 + 0.483460I
0.81833 − 1.69616I −1.98579 + 6.04080I
u = 0.101961 − 0.483460I
0.81833 + 1.69616I −1.98579 − 6.04080I
u = 0.348278
−0.869874 −12.9060
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
44
− u
43
+ ··· + u
2
− 1
c
2
u
44
+ 23u
43
+ ··· + 2u + 1
c
3
, c
9
, c
10
u
44
+ u
43
+ ··· − 2u − 1
c
4
, c
5
, c
8
u
44
− 3u
43
+ ··· − 10u + 5
c
7
, c
11
u
44
− 3u
43
+ ··· + 70u − 7
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
44
− 23y
43
+ ··· − 2y + 1
c
2
y
44
− 3y
43
+ ··· − 10y + 1
c
3
, c
9
, c
10
y
44
− 35y
43
+ ··· − 2y + 1
c
4
, c
5
, c
8
y
44
+ 41y
43
+ ··· − 270y + 25
c
7
, c
11
y
44
+ 29y
43
+ ··· − 6454y + 49
8
