11a
85
(K11a
85
)
A knot diagram
1
Linearized knot diagam
5 1 11 9 2 3 10 4 8 7 6
Solving Sequence
2,6
5 1 3 7 11 4 10 8 9
c
5
c
1
c
2
c
6
c
11
c
3
c
10
c
7
c
9
c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
53
− u
52
+ ··· + 3u − 1i
* 1 irreducible components of dim
C
= 0, with total 53 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
53
− u
52
+ · · · + 3u − 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
7
=
u
8
− u
6
+ u
4
+ 1
−u
10
+ 2u
8
− 3u
6
+ 2u
4
− u
2
a
11
=
u
3
−u
3
+ u
a
4
=
u
11
− 2u
9
+ 2u
7
− u
3
−u
11
+ 3u
9
− 4u
7
+ 3u
5
− u
3
+ u
a
10
=
u
21
− 4u
19
+ 9u
17
− 12u
15
+ 12u
13
− 10u
11
+ 9u
9
− 6u
7
+ 3u
5
+ u
−u
23
+ 5u
21
+ ··· − 2u
3
+ u
a
8
=
u
34
− 7u
32
+ ··· + u
2
+ 1
−u
36
+ 8u
34
+ ··· + 4u
6
− u
4
a
9
=
u
47
− 10u
45
+ ··· + 4u
5
+ 2u
−u
49
+ 11u
47
+ ··· − 2u
3
+ u
a
9
=
u
47
− 10u
45
+ ··· + 4u
5
+ 2u
−u
49
+ 11u
47
+ ··· − 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
52
+ 52u
50
+ ··· + 12u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
53
+ u
52
+ ··· + 3u + 1
c
2
u
53
+ 25u
52
+ ··· + 3u + 1
c
3
u
53
+ 7u
52
+ ··· + 41u + 5
c
4
, c
8
u
53
− u
52
+ ··· + u + 1
c
6
u
53
− u
52
+ ··· + 149u + 97
c
7
, c
9
, c
10
u
53
+ 13u
52
+ ··· + 3u + 1
c
11
u
53
+ 3u
52
+ ··· + 213u + 39
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
53
− 25y
52
+ ··· + 3y −1
c
2
y
53
+ 7y
52
+ ··· + 3y −1
c
3
y
53
− 5y
52
+ ··· + 911y −25
c
4
, c
8
y
53
− 13y
52
+ ··· + 3y −1
c
6
y
53
− 17y
52
+ ··· + 199323y −9409
c
7
, c
9
, c
10
y
53
+ 55y
52
+ ··· − 5y −1
c
11
y
53
+ 11y
52
+ ··· − 28185y −1521
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.044500 + 0.281512I
−2.20764 − 0.64085I −5.73049 + 0.77381I
u = 1.044500 − 0.281512I
−2.20764 + 0.64085I −5.73049 − 0.77381I
u = 0.601217 + 0.686706I
8.50588 − 6.50884I 1.27031 + 5.73425I
u = 0.601217 − 0.686706I
8.50588 + 6.50884I 1.27031 − 5.73425I
u = 0.974822 + 0.492221I
−0.225106 − 0.871265I −4.08839 − 0.80386I
u = 0.974822 − 0.492221I
−0.225106 + 0.871265I −4.08839 + 0.80386I
u = −0.586774 + 0.690510I
8.78157 + 0.18779I 1.88251 − 0.64861I
u = −0.586774 − 0.690510I
8.78157 − 0.18779I 1.88251 + 0.64861I
u = 1.109660 + 0.186764I
2.94416 + 0.20510I −5.58587 + 0.61243I
u = 1.109660 − 0.186764I
2.94416 − 0.20510I −5.58587 − 0.61243I
u = −1.102420 + 0.258443I
−4.56669 − 2.49112I −11.89781 + 4.18392I
u = −1.102420 − 0.258443I
−4.56669 + 2.49112I −11.89781 − 4.18392I
u = −1.122120 + 0.196280I
2.54225 − 6.40452I −6.41624 + 4.33917I
u = −1.122120 − 0.196280I
2.54225 + 6.40452I −6.41624 − 4.33917I
u = 0.971931 + 0.595508I
7.41049 + 1.56089I 0
u = 0.971931 − 0.595508I
7.41049 − 1.56089I 0
u = 0.366014 + 0.773541I
7.29360 + 8.95041I −0.09124 − 5.62138I
u = 0.366014 − 0.773541I
7.29360 − 8.95041I −0.09124 + 5.62138I
u = −0.376178 + 0.768520I
7.69936 − 2.64631I 0.774092 + 0.704677I
u = −0.376178 − 0.768520I
7.69936 + 2.64631I 0.774092 − 0.704677I
u = −1.098220 + 0.328717I
−5.25608 + 2.82044I −13.7464 − 4.6104I
u = −1.098220 − 0.328717I
−5.25608 − 2.82044I −13.7464 + 4.6104I
u = −0.983871 + 0.595556I
7.60812 + 4.77001I 0. − 5.11123I
u = −0.983871 − 0.595556I
7.60812 − 4.77001I 0. + 5.11123I
u = 0.592887 + 0.582181I
0.88261 − 3.44954I −2.55100 + 7.40984I
u = 0.592887 − 0.582181I
0.88261 + 3.44954I −2.55100 − 7.40984I
u = −1.038830 + 0.540274I
0.66178 + 4.72185I 0. − 6.22617I
u = −1.038830 − 0.540274I
0.66178 − 4.72185I 0. + 6.22617I
u = 1.108380 + 0.429410I
0.525380 − 0.893417I −6.66537 + 0.I
u = 1.108380 − 0.429410I
0.525380 + 0.893417I −6.66537 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.117790 + 0.404581I
0.34604 + 6.68644I −7.28464 − 6.64124I
u = −1.117790 − 0.404581I
0.34604 − 6.68644I −7.28464 + 6.64124I
u = 0.332464 + 0.722196I
−0.29834 + 5.13851I −4.80621 − 6.56976I
u = 0.332464 − 0.722196I
−0.29834 − 5.13851I −4.80621 + 6.56976I
u = −0.491709 + 0.618554I
2.27338 − 0.13836I 2.37846 + 0.39315I
u = −0.491709 − 0.618554I
2.27338 + 0.13836I 2.37846 − 0.39315I
u = −0.378665 + 0.682475I
1.76473 − 1.60253I 1.33859 + 1.09595I
u = −0.378665 − 0.682475I
1.76473 + 1.60253I 1.33859 − 1.09595I
u = 1.102860 + 0.521380I
−3.95438 − 4.57454I 0
u = 1.102860 − 0.521380I
−3.95438 + 4.57454I 0
u = −1.093000 + 0.554934I
−0.31357 + 6.39150I 0
u = −1.093000 − 0.554934I
−0.31357 − 6.39150I 0
u = 1.114580 + 0.556654I
−2.57269 − 10.01430I 0
u = 1.114580 − 0.556654I
−2.57269 + 10.01430I 0
u = −1.114170 + 0.582898I
5.52079 + 7.74501I 0
u = −1.114170 − 0.582898I
5.52079 − 7.74501I 0
u = 1.119280 + 0.581631I
5.0695 − 14.0551I 0
u = 1.119280 − 0.581631I
5.0695 + 14.0551I 0
u = 0.262528 + 0.616219I
−1.62999 + 0.09542I −8.49556 + 0.70141I
u = 0.262528 − 0.616219I
−1.62999 − 0.09542I −8.49556 − 0.70141I
u = 0.022954 + 0.641795I
3.51831 − 2.96655I −2.71846 + 2.72944I
u = 0.022954 − 0.641795I
3.51831 + 2.96655I −2.71846 − 2.72944I
u = 0.559370
−1.01608 −9.59730
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
53
+ u
52
+ ··· + 3u + 1
c
2
u
53
+ 25u
52
+ ··· + 3u + 1
c
3
u
53
+ 7u
52
+ ··· + 41u + 5
c
4
, c
8
u
53
− u
52
+ ··· + u + 1
c
6
u
53
− u
52
+ ··· + 149u + 97
c
7
, c
9
, c
10
u
53
+ 13u
52
+ ··· + 3u + 1
c
11
u
53
+ 3u
52
+ ··· + 213u + 39
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
53
− 25y
52
+ ··· + 3y −1
c
2
y
53
+ 7y
52
+ ··· + 3y −1
c
3
y
53
− 5y
52
+ ··· + 911y −25
c
4
, c
8
y
53
− 13y
52
+ ··· + 3y −1
c
6
y
53
− 17y
52
+ ··· + 199323y −9409
c
7
, c
9
, c
10
y
53
+ 55y
52
+ ··· − 5y −1
c
11
y
53
+ 11y
52
+ ··· − 28185y −1521
8
