11a
110
(K11a
110
)
A knot diagram
1
Linearized knot diagam
5 1 9 10 2 11 3 4 8 7 6
Solving Sequence
2,6
5 1 3 11 7 8 10 4 9
c
5
c
1
c
2
c
11
c
6
c
7
c
10
c
4
c
9
c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
48
− u
47
+ ··· − 4u
3
+ 1i
* 1 irreducible components of dim
C
= 0, with total 48 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
48
− u
47
+ · · · − 4u
3
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
3
u
5
− u
3
+ u
a
11
=
u
3
−u
3
+ u
a
7
=
u
6
− u
4
+ 1
−u
6
+ 2u
4
− u
2
a
8
=
u
14
− 3u
12
+ 4u
10
− u
8
+ 1
−u
16
+ 4u
14
− 8u
12
+ 8u
10
− 4u
8
− 2u
6
+ 4u
4
− 2u
2
a
10
=
u
9
− 2u
7
+ u
5
+ 2u
3
− u
−u
9
+ 3u
7
− 3u
5
+ u
a
4
=
u
20
− 5u
18
+ 11u
16
− 10u
14
− 2u
12
+ 13u
10
− 9u
8
+ 3u
4
− u
2
+ 1
−u
20
+ 6u
18
− 16u
16
+ 22u
14
− 13u
12
− 4u
10
+ 10u
8
− 4u
6
− u
4
a
9
=
−u
39
+ 10u
37
+ ··· + 4u
3
− 2u
u
41
− 11u
39
+ ··· + 2u
3
+ u
a
9
=
−u
39
+ 10u
37
+ ··· + 4u
3
− 2u
u
41
− 11u
39
+ ··· + 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
47
− 56u
45
+ ··· − 8u
2
− 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
48
+ u
47
+ ··· + 4u
3
+ 1
c
2
u
48
+ 27u
47
+ ··· + 28u
3
+ 1
c
3
, c
8
u
48
− u
47
+ ··· − 2u
4
+ 1
c
4
, c
7
u
48
+ u
47
+ ··· − 44u + 17
c
6
, c
10
, c
11
u
48
+ 3u
47
+ ··· + 8u + 1
c
9
u
48
− 25u
47
+ ··· − 4u
2
+ 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
48
− 27y
47
+ ··· − 28y
3
+ 1
c
2
y
48
− 11y
47
+ ··· + 308y
2
+ 1
c
3
, c
8
y
48
+ 25y
47
+ ··· − 4y
2
+ 1
c
4
, c
7
y
48
− 31y
47
+ ··· + 2620y + 289
c
6
, c
10
, c
11
y
48
+ 49y
47
+ ··· + 56y + 1
c
9
y
48
− 3y
47
+ ··· − 8y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.958219 + 0.143307I
−1.66920 − 0.31218I −6.04929 + 0.55460I
u = 0.958219 − 0.143307I
−1.66920 + 0.31218I −6.04929 − 0.55460I
u = 0.914661 + 0.504015I
4.41403 − 0.70127I 5.15173 + 2.65109I
u = 0.914661 − 0.504015I
4.41403 + 0.70127I 5.15173 − 2.65109I
u = −1.046740 + 0.068635I
0.77690 − 3.72476I −1.95300 + 3.66807I
u = −1.046740 − 0.068635I
0.77690 + 3.72476I −1.95300 − 3.66807I
u = 1.011960 + 0.286206I
−2.55221 − 0.92643I −6.15695 + 0.73591I
u = 1.011960 − 0.286206I
−2.55221 + 0.92643I −6.15695 − 0.73591I
u = −0.950614 + 0.484261I
0.72805 + 4.58119I 0.34102 − 6.39238I
u = −0.950614 − 0.484261I
0.72805 − 4.58119I 0.34102 + 6.39238I
u = −1.021410 + 0.380117I
−1.89118 + 4.83513I −2.88338 − 8.66489I
u = −1.021410 − 0.380117I
−1.89118 − 4.83513I −2.88338 + 8.66489I
u = 0.963622 + 0.510991I
3.78897 − 9.13187I 3.52711 + 9.35882I
u = 0.963622 − 0.510991I
3.78897 + 9.13187I 3.52711 − 9.35882I
u = 0.080810 + 0.850812I
−0.65137 + 8.58815I 2.17259 − 5.82135I
u = 0.080810 − 0.850812I
−0.65137 − 8.58815I 2.17259 + 5.82135I
u = −0.013057 + 0.852192I
−5.99169 − 2.35954I −2.55512 + 3.34973I
u = −0.013057 − 0.852192I
−5.99169 + 2.35954I −2.55512 − 3.34973I
u = −0.065516 + 0.840970I
−3.41452 − 3.72023I −1.09842 + 2.42491I
u = −0.065516 − 0.840970I
−3.41452 + 3.72023I −1.09842 − 2.42491I
u = −0.757474 + 0.366588I
1.28610 + 1.69703I 6.44180 − 4.95354I
u = −0.757474 − 0.366588I
1.28610 − 1.69703I 6.44180 + 4.95354I
u = 0.079356 + 0.807965I
0.763972 + 0.284532I 4.14710 + 0.31000I
u = 0.079356 − 0.807965I
0.763972 − 0.284532I 4.14710 − 0.31000I
u = 0.546437 + 0.541746I
5.44153 − 3.53716I 7.56794 + 3.98603I
u = 0.546437 − 0.541746I
5.44153 + 3.53716I 7.56794 − 3.98603I
u = 0.468200 + 0.569910I
5.17049 + 4.81347I 6.85493 − 3.77558I
u = 0.468200 − 0.569910I
5.17049 − 4.81347I 6.85493 + 3.77558I
u = −1.214630 + 0.420476I
−3.06688 + 3.96905I 0
u = −1.214630 − 0.420476I
−3.06688 − 3.96905I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.484203 + 0.509344I
2.02079 − 0.49000I 3.99733 + 0.21349I
u = −0.484203 − 0.509344I
2.02079 + 0.49000I 3.99733 − 0.21349I
u = 1.209970 + 0.489477I
−2.57490 − 5.01368I 0
u = 1.209970 − 0.489477I
−2.57490 + 5.01368I 0
u = 1.237110 + 0.425873I
−7.33658 − 0.70647I 0
u = 1.237110 − 0.425873I
−7.33658 + 0.70647I 0
u = −1.243170 + 0.416059I
−4.66901 − 4.18367I 0
u = −1.243170 − 0.416059I
−4.66901 + 4.18367I 0
u = −1.224430 + 0.490742I
−6.86889 + 8.53427I 0
u = −1.224430 − 0.490742I
−6.86889 − 8.53427I 0
u = 1.240090 + 0.455194I
−9.75907 − 2.28164I 0
u = 1.240090 − 0.455194I
−9.75907 + 2.28164I 0
u = −1.237470 + 0.468224I
−9.66500 + 7.07748I 0
u = −1.237470 − 0.468224I
−9.66500 − 7.07748I 0
u = 1.225480 + 0.498822I
−4.07278 − 13.47170I 0
u = 1.225480 − 0.498822I
−4.07278 + 13.47170I 0
u = −0.177212 + 0.446834I
0.31404 − 1.44403I 2.46816 + 4.79849I
u = −0.177212 − 0.446834I
0.31404 + 1.44403I 2.46816 − 4.79849I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
48
+ u
47
+ ··· + 4u
3
+ 1
c
2
u
48
+ 27u
47
+ ··· + 28u
3
+ 1
c
3
, c
8
u
48
− u
47
+ ··· − 2u
4
+ 1
c
4
, c
7
u
48
+ u
47
+ ··· − 44u + 17
c
6
, c
10
, c
11
u
48
+ 3u
47
+ ··· + 8u + 1
c
9
u
48
− 25u
47
+ ··· − 4u
2
+ 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
48
− 27y
47
+ ··· − 28y
3
+ 1
c
2
y
48
− 11y
47
+ ··· + 308y
2
+ 1
c
3
, c
8
y
48
+ 25y
47
+ ··· − 4y
2
+ 1
c
4
, c
7
y
48
− 31y
47
+ ··· + 2620y + 289
c
6
, c
10
, c
11
y
48
+ 49y
47
+ ··· + 56y + 1
c
9
y
48
− 3y
47
+ ··· − 8y + 1
8
