11a
193
(K11a
193
)
A knot diagram
1
Linearized knot diagam
7 1 11 10 9 2 3 6 4 5 8
Solving Sequence
4,9
10 5 6 11 3 8 1 2 7
c
9
c
4
c
5
c
10
c
3
c
8
c
11
c
2
c
7
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
47
+ u
46
+ ··· − 4u
3
+ 1i
* 1 irreducible components of dim
C
= 0, with total 47 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
47
+ u
46
+ · · · − 4u
3
+ 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
5
=
u
−u
3
+ u
a
6
=
−u
3
+ 2u
−u
3
+ u
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
3
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
8
=
u
6
− 3u
4
+ 2u
2
+ 1
u
6
− 2u
4
+ u
2
a
1
=
−u
16
+ 7u
14
− 19u
12
+ 22u
10
− 3u
8
− 14u
6
+ 6u
4
+ 2u
2
+ 1
−u
16
+ 6u
14
− 14u
12
+ 14u
10
− 2u
8
− 6u
6
+ 4u
4
− 2u
2
a
2
=
u
39
− 16u
37
+ ··· + 24u
5
+ 6u
3
u
39
− 15u
37
+ ··· − 3u
5
+ u
a
7
=
u
18
− 7u
16
+ 20u
14
− 27u
12
+ 11u
10
+ 13u
8
− 14u
6
+ 3u
2
+ 1
−u
20
+ 8u
18
− 26u
16
+ 40u
14
− 19u
12
− 24u
10
+ 30u
8
− 9u
4
a
7
=
u
18
− 7u
16
+ 20u
14
− 27u
12
+ 11u
10
+ 13u
8
− 14u
6
+ 3u
2
+ 1
−u
20
+ 8u
18
− 26u
16
+ 40u
14
− 19u
12
− 24u
10
+ 30u
8
− 9u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
44
+ 68u
42
+ ··· − 8u
2
+ 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
47
+ u
46
+ ··· − 2u
4
− 1
c
2
u
47
+ 23u
46
+ ··· − 4u
2
− 1
c
3
, c
5
, c
8
u
47
+ 3u
46
+ ··· + 8u + 1
c
4
, c
9
, c
10
u
47
− u
46
+ ··· − 4u
3
− 1
c
7
u
47
− u
46
+ ··· − 22u − 53
c
11
u
47
+ 5u
46
+ ··· − 64u − 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
47
+ 23y
46
+ ··· − 4y
2
− 1
c
2
y
47
+ 3y
46
+ ··· − 8y −1
c
3
, c
5
, c
8
y
47
+ 47y
46
+ ··· − 8y −1
c
4
, c
9
, c
10
y
47
− 37y
46
+ ··· − 16y
2
− 1
c
7
y
47
− 17y
46
+ ··· + 47124y −2809
c
11
y
47
− 5y
46
+ ··· + 1312y −256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.006280 + 0.120689I
−0.91501 + 3.60507I 1.64705 − 4.50144I
u = 1.006280 − 0.120689I
−0.91501 − 3.60507I 1.64705 + 4.50144I
u = −1.10074
1.86864 5.66480
u = 0.030039 + 0.875142I
−10.56620 + 0.61135I −3.63402 + 0.19416I
u = 0.030039 − 0.875142I
−10.56620 − 0.61135I −3.63402 − 0.19416I
u = 0.055754 + 0.872511I
−8.79586 + 8.79339I −1.19946 − 6.11283I
u = 0.055754 − 0.872511I
−8.79586 − 8.79339I −1.19946 + 6.11283I
u = −0.047289 + 0.862249I
−6.19361 − 3.85394I 1.82254 + 2.54256I
u = −0.047289 − 0.862249I
−6.19361 + 3.85394I 1.82254 − 2.54256I
u = −0.021231 + 0.815572I
−3.88334 − 2.31182I 2.62267 + 3.54472I
u = −0.021231 − 0.815572I
−3.88334 + 2.31182I 2.62267 − 3.54472I
u = −1.257110 + 0.182931I
1.02961 − 1.77431I 0
u = −1.257110 − 0.182931I
1.02961 + 1.77431I 0
u = 1.223180 + 0.419244I
−5.19614 − 4.16894I 0
u = 1.223180 − 0.419244I
−5.19614 + 4.16894I 0
u = −1.230390 + 0.406583I
−2.54267 − 0.69419I 0
u = −1.230390 − 0.406583I
−2.54267 + 0.69419I 0
u = −1.259550 + 0.357794I
−0.05039 − 1.90652I 0
u = −1.259550 − 0.357794I
−0.05039 + 1.90652I 0
u = 1.249070 + 0.416752I
−6.79512 + 4.01291I 0
u = 1.249070 − 0.416752I
−6.79512 − 4.01291I 0
u = 1.316370 + 0.096272I
5.85726 + 2.05767I 0
u = 1.316370 − 0.096272I
5.85726 − 2.05767I 0
u = −1.324170 + 0.059973I
4.48508 + 2.49902I 0
u = −1.324170 − 0.059973I
4.48508 − 2.49902I 0
u = 1.319560 + 0.153160I
5.16266 + 3.85903I 0
u = 1.319560 − 0.153160I
5.16266 − 3.85903I 0
u = 1.288740 + 0.366736I
0.19960 + 6.56847I 0
u = 1.288740 − 0.366736I
0.19960 − 6.56847I 0
u = −1.331010 + 0.174169I
3.09173 − 8.65002I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.331010 − 0.174169I
3.09173 + 8.65002I 0
u = −1.298060 + 0.405269I
−6.42755 − 5.19896I 0
u = −1.298060 − 0.405269I
−6.42755 + 5.19896I 0
u = 1.308420 + 0.393753I
−1.96046 + 8.36038I 0
u = 1.308420 − 0.393753I
−1.96046 − 8.36038I 0
u = −1.315440 + 0.399117I
−4.51106 − 13.35320I 0
u = −1.315440 − 0.399117I
−4.51106 + 13.35320I 0
u = 0.283978 + 0.527411I
−1.92558 + 6.21305I 1.17116 − 8.71697I
u = 0.283978 − 0.527411I
−1.92558 − 6.21305I 1.17116 + 8.71697I
u = 0.146756 + 0.548854I
−3.20832 − 0.82330I −2.58409 − 0.88162I
u = 0.146756 − 0.548854I
−3.20832 + 0.82330I −2.58409 + 0.88162I
u = 0.519306 + 0.197953I
−0.86762 − 3.28146I 4.49365 + 2.23360I
u = 0.519306 − 0.197953I
−0.86762 + 3.28146I 4.49365 − 2.23360I
u = −0.266858 + 0.458418I
0.27118 − 1.71840I 4.99592 + 5.33344I
u = −0.266858 − 0.458418I
0.27118 + 1.71840I 4.99592 − 5.33344I
u = −0.345961 + 0.277574I
0.861649 − 0.739192I 8.37308 + 5.15460I
u = −0.345961 − 0.277574I
0.861649 + 0.739192I 8.37308 − 5.15460I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
47
+ u
46
+ ··· − 2u
4
− 1
c
2
u
47
+ 23u
46
+ ··· − 4u
2
− 1
c
3
, c
5
, c
8
u
47
+ 3u
46
+ ··· + 8u + 1
c
4
, c
9
, c
10
u
47
− u
46
+ ··· − 4u
3
− 1
c
7
u
47
− u
46
+ ··· − 22u − 53
c
11
u
47
+ 5u
46
+ ··· − 64u − 16
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
47
+ 23y
46
+ ··· − 4y
2
− 1
c
2
y
47
+ 3y
46
+ ··· − 8y −1
c
3
, c
5
, c
8
y
47
+ 47y
46
+ ··· − 8y −1
c
4
, c
9
, c
10
y
47
− 37y
46
+ ··· − 16y
2
− 1
c
7
y
47
− 17y
46
+ ··· + 47124y −2809
c
11
y
47
− 5y
46
+ ··· + 1312y −256
8
