11a
225
(K11a
225
)
A knot diagram
1
Linearized knot diagam
7 1 10 11 8 2 6 5 3 4 9
Solving Sequence
4,10
11 5 3 9 1 2 8 6 7
c
10
c
4
c
3
c
9
c
11
c
2
c
8
c
5
c
7
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
26
− u
25
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 26 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
26
− u
25
+ · · · − u − 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
5
=
u
−u
3
+ u
a
3
=
−u
u
a
9
=
−u
2
+ 1
u
2
a
1
=
−u
6
+ 3u
4
− 2u
2
+ 1
u
6
− 2u
4
− u
2
a
2
=
−u
11
+ 6u
9
− 12u
7
+ 10u
5
− 5u
3
u
11
− 5u
9
+ 6u
7
+ u
5
− u
3
+ u
a
8
=
−u
6
+ 3u
4
− 2u
2
+ 1
u
8
− 4u
6
+ 4u
4
a
6
=
u
11
− 6u
9
+ 12u
7
− 10u
5
+ 5u
3
−u
13
+ 7u
11
− 17u
9
+ 16u
7
− 4u
5
− u
3
+ u
a
7
=
−u
16
+ 9u
14
− 31u
12
+ 52u
10
− 47u
8
+ 24u
6
− 2u
4
− 2u
2
+ 1
u
18
− 10u
16
+ 39u
14
− 74u
12
+ 69u
10
− 26u
8
− 4u
6
+ 8u
4
− u
2
a
7
=
−u
16
+ 9u
14
− 31u
12
+ 52u
10
− 47u
8
+ 24u
6
− 2u
4
− 2u
2
+ 1
u
18
− 10u
16
+ 39u
14
− 74u
12
+ 69u
10
− 26u
8
− 4u
6
+ 8u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
23
+56u
21
−328u
19
−4u
18
+1040u
17
+44u
16
−1936u
15
−192u
14
+2156u
13
+420u
12
−
1376u
11
−484u
10
+ 324u
9
+ 288u
8
+ 228u
7
−60u
6
−176u
5
−52u
4
+ 52u
3
+ 20u
2
+ 12u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
26
+ u
25
+ ··· + u − 1
c
2
, c
5
, c
7
c
8
u
26
+ 5u
25
+ ··· − 3u + 1
c
3
, c
4
, c
9
c
10
u
26
− u
25
+ ··· − u − 1
c
11
u
26
+ 9u
25
+ ··· − 247u − 89
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
26
+ 5y
25
+ ··· − 3y + 1
c
2
, c
5
, c
7
c
8
y
26
+ 33y
25
+ ··· − 59y + 1
c
3
, c
4
, c
9
c
10
y
26
− 31y
25
+ ··· − 3y + 1
c
11
y
26
− 19y
25
+ ··· − 92159y + 7921
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.839779 + 0.452868I
11.16140 + 0.44023I 10.10436 − 1.46145I
u = 0.839779 − 0.452868I
11.16140 − 0.44023I 10.10436 + 1.46145I
u = −0.825387 + 0.468991I
11.03030 − 7.05835I 9.75996 + 6.21969I
u = −0.825387 − 0.468991I
11.03030 + 7.05835I 9.75996 − 6.21969I
u = −0.684207 + 0.398529I
1.89109 − 4.88723I 7.24553 + 8.84366I
u = −0.684207 − 0.398529I
1.89109 + 4.88723I 7.24553 − 8.84366I
u = 0.733274 + 0.287832I
2.67984 + 0.49611I 10.71301 − 1.37639I
u = 0.733274 − 0.287832I
2.67984 − 0.49611I 10.71301 + 1.37639I
u = −0.012357 + 0.660147I
8.58736 + 3.27967I 5.99252 − 2.35106I
u = −0.012357 − 0.660147I
8.58736 − 3.27967I 5.99252 + 2.35106I
u = −0.439187 + 0.350365I
−1.41635 − 1.31903I −1.30126 + 6.10882I
u = −0.439187 − 0.350365I
−1.41635 + 1.31903I −1.30126 − 6.10882I
u = 0.525085
0.783407 12.8960
u = −0.106020 + 0.464476I
0.26125 + 1.87689I 2.74450 − 3.73316I
u = −0.106020 − 0.464476I
0.26125 − 1.87689I 2.74450 + 3.73316I
u = 1.54395 + 0.04489I
5.28037 + 2.44629I 3.67676 − 4.11819I
u = 1.54395 − 0.04489I
5.28037 − 2.44629I 3.67676 + 4.11819I
u = −1.58507
8.17274 12.1060
u = 1.59973 + 0.10370I
9.67676 + 6.71425I 9.25508 − 6.45300I
u = 1.59973 − 0.10370I
9.67676 − 6.71425I 9.25508 + 6.45300I
u = −1.61572 + 0.07479I
10.74900 − 1.83401I 11.98633 + 0.23070I
u = −1.61572 − 0.07479I
10.74900 + 1.83401I 11.98633 − 0.23070I
u = 1.64863 + 0.13284I
19.5205 + 9.3622I 11.47654 − 4.95795I
u = 1.64863 − 0.13284I
19.5205 − 9.3622I 11.47654 + 4.95795I
u = −1.65250 + 0.12610I
19.7312 − 2.6570I 11.84579 + 0.35212I
u = −1.65250 − 0.12610I
19.7312 + 2.6570I 11.84579 − 0.35212I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
26
+ u
25
+ ··· + u − 1
c
2
, c
5
, c
7
c
8
u
26
+ 5u
25
+ ··· − 3u + 1
c
3
, c
4
, c
9
c
10
u
26
− u
25
+ ··· − u − 1
c
11
u
26
+ 9u
25
+ ··· − 247u − 89
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
26
+ 5y
25
+ ··· − 3y + 1
c
2
, c
5
, c
7
c
8
y
26
+ 33y
25
+ ··· − 59y + 1
c
3
, c
4
, c
9
c
10
y
26
− 31y
25
+ ··· − 3y + 1
c
11
y
26
− 19y
25
+ ··· − 92159y + 7921
7
