11a
339
(K11a
339
)
A knot diagram
1
Linearized knot diagam
7 8 1 11 10 9 2 3 6 4 5
Solving Sequence
4,10
11 5 6 1 3 9 7 8 2
c
10
c
4
c
5
c
11
c
3
c
9
c
6
c
8
c
2
c
1
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
27
− u
26
+ ··· − 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 27 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
27
− u
26
+ · · · − 2u + 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
5
=
−u
−u
3
+ u
a
6
=
u
3
− 2u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
9
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
6
+ 2u
4
− u
2
a
7
=
u
9
− 4u
7
+ 5u
5
− 3u
−u
9
+ 3u
7
− 3u
5
+ u
a
8
=
−u
18
+ 7u
16
− 20u
14
+ 27u
12
− 11u
10
− 13u
8
+ 16u
6
− 6u
4
+ u
2
+ 1
−u
20
+ 8u
18
− 26u
16
+ 40u
14
− 19u
12
− 24u
10
+ 30u
8
− 2u
6
− 5u
4
− 2u
2
a
2
=
u
22
− 9u
20
+ ··· − 4u
2
+ 1
−u
22
+ 8u
20
+ ··· + 4u
4
+ 3u
2
a
2
=
u
22
− 9u
20
+ ··· − 4u
2
+ 1
−u
22
+ 8u
20
+ ··· + 4u
4
+ 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes =
−4u
24
+36u
22
+4u
21
−140u
20
−32u
19
+284u
18
+108u
17
−256u
16
−180u
15
−96u
14
+104u
13
+
440u
12
+120u
11
−296u
10
−216u
9
−112u
8
+56u
7
+192u
6
+80u
5
−16u
4
−36u
3
−32u
2
−8u−14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u
27
+ u
26
+ ··· − 2u − 1
c
3
, c
5
, c
6
c
9
u
27
− 3u
26
+ ··· + 4u − 1
c
4
, c
10
, c
11
u
27
+ u
26
+ ··· − 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
y
27
− 29y
26
+ ··· + 10y −1
c
3
, c
5
, c
6
c
9
y
27
+ 31y
26
+ ··· + 22y −1
c
4
, c
10
, c
11
y
27
− 21y
26
+ ··· + 10y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.013123 + 0.894482I
9.43523 − 2.24680I −6.17904 + 3.02780I
u = 0.013123 − 0.894482I
9.43523 + 2.24680I −6.17904 − 3.02780I
u = −0.041452 + 0.892930I
2.82267 + 5.43200I −9.64025 − 3.04274I
u = −0.041452 − 0.892930I
2.82267 − 5.43200I −9.64025 + 3.04274I
u = 1.162550 + 0.167516I
−1.60577 − 1.16599I −9.70330 + 0.15957I
u = 1.162550 − 0.167516I
−1.60577 + 1.16599I −9.70330 − 0.15957I
u = −0.781754 + 0.091734I
−6.68333 − 0.00498I −14.6673 − 0.4486I
u = −0.781754 − 0.091734I
−6.68333 + 0.00498I −14.6673 + 0.4486I
u = −1.25317
−4.90599 −20.0000
u = −1.255670 + 0.210110I
−2.66095 + 4.20438I −14.1782 − 7.6940I
u = −1.255670 − 0.210110I
−2.66095 − 4.20438I −14.1782 + 7.6940I
u = −1.243220 + 0.434957I
−0.891189 − 0.687706I −12.83371 − 0.18639I
u = −1.243220 − 0.434957I
−0.891189 + 0.687706I −12.83371 + 0.18639I
u = 1.33611
−12.4088 −20.5520
u = 1.319890 + 0.213766I
−9.80481 − 5.99282I −17.3414 + 5.5228I
u = 1.319890 − 0.213766I
−9.80481 + 5.99282I −17.3414 − 5.5228I
u = 1.269780 + 0.428859I
5.53802 − 2.48385I −9.46346 + 0.15279I
u = 1.269780 − 0.428859I
5.53802 + 2.48385I −9.46346 − 0.15279I
u = −1.290860 + 0.422984I
5.37877 + 6.95944I −9.93623 − 6.05202I
u = −1.290860 − 0.422984I
5.37877 − 6.95944I −9.93623 + 6.05202I
u = −0.232231 + 0.591655I
−4.98362 + 3.14884I −11.41725 − 4.81307I
u = −0.232231 − 0.591655I
−4.98362 − 3.14884I −11.41725 + 4.81307I
u = 1.310480 + 0.415835I
−1.39565 − 10.11710I −13.4570 + 5.7483I
u = 1.310480 − 0.415835I
−1.39565 + 10.11710I −13.4570 − 5.7483I
u = 0.090324 + 0.551346I
1.43201 − 1.45915I −6.27932 + 5.94435I
u = 0.090324 − 0.551346I
1.43201 + 1.45915I −6.27932 − 5.94435I
u = 0.275134
−0.522013 −19.2550
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u
27
+ u
26
+ ··· − 2u − 1
c
3
, c
5
, c
6
c
9
u
27
− 3u
26
+ ··· + 4u − 1
c
4
, c
10
, c
11
u
27
+ u
26
+ ··· − 2u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
y
27
− 29y
26
+ ··· + 10y −1
c
3
, c
5
, c
6
c
9
y
27
+ 31y
26
+ ··· + 22y −1
c
4
, c
10
, c
11
y
27
− 21y
26
+ ··· + 10y −1
7
