11a
226
(K11a
226
)
A knot diagram
1
Linearized knot diagam
7 1 11 10 8 2 6 5 3 4 9
Solving Sequence
2,6
7 8 1 3 5 9 10 4 11
c
6
c
7
c
1
c
2
c
5
c
8
c
9
c
4
c
11
c
3
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
35
+ u
34
+ ··· + u
2
− 1i
* 1 irreducible components of dim
C
= 0, with total 35 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
35
+ u
34
+ · · · + u
2
− 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
8
=
u
2
+ 1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
5
=
u
4
+ u
2
+ 1
−u
4
a
9
=
u
6
+ u
4
+ 2u
2
+ 1
−u
6
− u
2
a
10
=
u
14
+ u
12
+ 4u
10
+ 3u
8
+ 4u
6
+ 2u
4
+ 2u
2
+ 1
−u
16
− 2u
14
− 6u
12
− 8u
10
− 10u
8
− 8u
6
− 4u
4
− 2u
2
a
4
=
−u
34
− 3u
32
+ ··· − u
2
+ 1
u
34
+ u
33
+ ··· + u − 1
a
11
=
−u
15
− 2u
13
− 6u
11
− 8u
9
− 10u
7
− 8u
5
− 4u
3
− 2u
u
15
+ u
13
+ 4u
11
+ 3u
9
+ 4u
7
+ 2u
5
+ 2u
3
+ u
a
11
=
−u
15
− 2u
13
− 6u
11
− 8u
9
− 10u
7
− 8u
5
− 4u
3
− 2u
u
15
+ u
13
+ 4u
11
+ 3u
9
+ 4u
7
+ 2u
5
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
33
+ 4u
32
+ 16u
31
+ 12u
30
+ 72u
29
+ 56u
28
+ 188u
27
+ 124u
26
+
464u
25
+ 300u
24
+ 860u
23
+ 500u
22
+ 1432u
21
+ 800u
20
+ 1936u
19
+ 1004u
18
+
2280u
17
+ 1148u
16
+ 2236u
15
+ 1076u
14
+ 1848u
13
+ 896u
12
+ 1280u
11
+ 620u
10
+
724u
9
+ 360u
8
+ 348u
7
+ 168u
6
+ 128u
5
+ 56u
4
+ 36u
3
+ 12u
2
+ 4u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
35
+ u
34
+ ··· + u
2
− 1
c
2
, c
5
, c
7
c
8
u
35
+ 7u
34
+ ··· + 2u − 1
c
3
, c
4
, c
10
u
35
+ u
34
+ ··· − 2u − 1
c
9
u
35
− u
34
+ ··· − 6u − 1
c
11
u
35
+ 9u
34
+ ··· + 8u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
35
+ 7y
34
+ ··· + 2y −1
c
2
, c
5
, c
7
c
8
y
35
+ 43y
34
+ ··· + 34y −1
c
3
, c
4
, c
10
y
35
+ 31y
34
+ ··· + 2y −1
c
9
y
35
− 5y
34
+ ··· + 2y −1
c
11
y
35
− y
34
+ ··· + 66y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.543476 + 0.874447I
1.82954 − 5.19769I 6.15709 + 8.44602I
u = −0.543476 − 0.874447I
1.82954 + 5.19769I 6.15709 − 8.44602I
u = 0.619141 + 0.725788I
0.22503 + 2.28348I 5.46937 − 4.01207I
u = 0.619141 − 0.725788I
0.22503 − 2.28348I 5.46937 + 4.01207I
u = −0.370456 + 0.868836I
−5.30643 − 0.72543I −2.57924 + 3.52341I
u = −0.370456 − 0.868836I
−5.30643 + 0.72543I −2.57924 − 3.52341I
u = 0.530210 + 0.918792I
−3.36171 + 8.57781I 0.89148 − 8.59823I
u = 0.530210 − 0.918792I
−3.36171 − 8.57781I 0.89148 + 8.59823I
u = 0.499339 + 0.766815I
0.29678 + 1.94361I 2.76791 − 3.40470I
u = 0.499339 − 0.766815I
0.29678 − 1.94361I 2.76791 + 3.40470I
u = −0.086945 + 0.906060I
−6.77422 − 3.97739I −5.33902 + 4.43736I
u = −0.086945 − 0.906060I
−6.77422 + 3.97739I −5.33902 − 4.43736I
u = −0.633646 + 0.581658I
2.77033 + 0.77167I 9.84736 − 1.25670I
u = −0.633646 − 0.581658I
2.77033 − 0.77167I 9.84736 + 1.25670I
u = 0.669966 + 0.509743I
−2.05362 − 4.10467I 4.51219 + 2.60017I
u = 0.669966 − 0.509743I
−2.05362 + 4.10467I 4.51219 − 2.60017I
u = 0.084712 + 0.809947I
−1.49083 + 1.38540I −1.60809 − 5.67489I
u = 0.084712 − 0.809947I
−1.49083 − 1.38540I −1.60809 + 5.67489I
u = 0.854791 + 0.915240I
1.86062 + 3.17602I 1.83589 − 2.52504I
u = 0.854791 − 0.915240I
1.86062 − 3.17602I 1.83589 + 2.52504I
u = −0.914545 + 0.890982I
6.06012 + 4.90822I 4.65952 − 2.34927I
u = −0.914545 − 0.890982I
6.06012 − 4.90822I 4.65952 + 2.34927I
u = 0.910016 + 0.903339I
11.15980 − 1.02259I 9.09851 + 1.19971I
u = 0.910016 − 0.903339I
11.15980 + 1.02259I 9.09851 − 1.19971I
u = −0.898949 + 0.919422I
9.01203 − 3.04738I 6.19226 + 3.43104I
u = −0.898949 − 0.919422I
9.01203 + 3.04738I 6.19226 − 3.43104I
u = −0.887948 + 0.940225I
8.94377 − 3.54704I 6.02010 + 1.31518I
u = −0.887948 − 0.940225I
8.94377 + 3.54704I 6.02010 − 1.31518I
u = 0.883193 + 0.957672I
10.98400 + 7.63582I 8.68172 − 5.95948I
u = 0.883193 − 0.957672I
10.98400 − 7.63582I 8.68172 + 5.95948I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877042 + 0.967333I
5.81346 − 11.51440I 4.18005 + 6.99402I
u = −0.877042 − 0.967333I
5.81346 + 11.51440I 4.18005 − 6.99402I
u = −0.536023 + 0.185938I
−3.38342 − 2.39890I 4.22780 + 3.04888I
u = −0.536023 − 0.185938I
−3.38342 + 2.39890I 4.22780 − 3.04888I
u = 0.395324
0.851596 11.9700
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
35
+ u
34
+ ··· + u
2
− 1
c
2
, c
5
, c
7
c
8
u
35
+ 7u
34
+ ··· + 2u − 1
c
3
, c
4
, c
10
u
35
+ u
34
+ ··· − 2u − 1
c
9
u
35
− u
34
+ ··· − 6u − 1
c
11
u
35
+ 9u
34
+ ··· + 8u − 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
35
+ 7y
34
+ ··· + 2y −1
c
2
, c
5
, c
7
c
8
y
35
+ 43y
34
+ ··· + 34y −1
c
3
, c
4
, c
10
y
35
+ 31y
34
+ ··· + 2y −1
c
9
y
35
− 5y
34
+ ··· + 2y −1
c
11
y
35
− y
34
+ ··· + 66y −1
8
