11a
220
(K11a
220
)
A knot diagram
1
Linearized knot diagam
6 1 10 9 7 2 5 11 3 4 8
Solving Sequence
4,11
10 3 9 5 8 1 2 7 6
c
10
c
3
c
9
c
4
c
8
c
11
c
2
c
7
c
6
c
1
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
42
+ u
41
+ ··· − 3u − 1i
* 1 irreducible components of dim
C
= 0, with total 42 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
42
+ u
41
+ · · · − 3u − 1i
(i) Arc colorings
a
4
=
0
u
a
11
=
1
0
a
10
=
1
−u
2
a
3
=
u
−u
3
+ u
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
8
=
−u
4
+ u
2
+ 1
u
4
− 2u
2
a
1
=
u
8
− 3u
6
+ u
4
+ 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
2
=
−u
19
+ 8u
17
− 24u
15
+ 30u
13
− 7u
11
− 10u
9
− 4u
7
+ 6u
5
+ 3u
3
+ 2u
u
19
− 9u
17
+ 32u
15
− 55u
13
+ 43u
11
− 9u
9
− 4u
5
− u
3
+ u
a
7
=
−u
16
+ 7u
14
− 19u
12
+ 24u
10
− 13u
8
+ 2u
6
− 2u
4
+ 2u
2
+ 1
u
18
− 8u
16
+ 25u
14
− 36u
12
+ 19u
10
+ 4u
8
− 2u
6
− 2u
4
− 3u
2
a
6
=
−u
27
+ 12u
25
+ ··· − u
3
− 2u
u
29
− 13u
27
+ ··· + 5u
3
+ u
a
6
=
−u
27
+ 12u
25
+ ··· − u
3
− 2u
u
29
− 13u
27
+ ··· + 5u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
39
+ 72u
37
− 4u
36
− 584u
35
+ 68u
34
+ 2804u
33
− 516u
32
− 8800u
31
+ 2288u
30
+
18804u
29
−6508u
28
−27664u
27
+12240u
26
+27920u
25
−15080u
24
−19668u
23
+11628u
22
+
11364u
21
−5344u
20
−7448u
19
+2056u
18
+4732u
17
−1372u
16
−1840u
15
+300u
14
+420u
13
+
420u
12
−76u
11
−200u
10
−84u
9
+160u
8
+76u
7
−112u
6
−52u
5
−20u
4
+24u
3
−24u
2
−12u−14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
42
− u
41
+ ··· − u − 1
c
2
, c
5
, c
7
u
42
+ 11u
41
+ ··· + 3u + 1
c
3
, c
9
, c
10
u
42
+ u
41
+ ··· − 3u − 1
c
4
u
42
− 3u
41
+ ··· + 61u + 39
c
8
, c
11
u
42
+ 7u
41
+ ··· + 279u + 23
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
42
− 11y
41
+ ··· − 3y + 1
c
2
, c
5
, c
7
y
42
+ 41y
41
+ ··· − 11y + 1
c
3
, c
9
, c
10
y
42
− 39y
41
+ ··· − 3y + 1
c
4
y
42
− 11y
41
+ ··· − 25951y + 1521
c
8
, c
11
y
42
+ 29y
41
+ ··· − 14039y + 529
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.196810 + 0.224203I
4.01809 + 0.23438I −4.86393 − 0.79093I
u = −1.196810 − 0.224203I
4.01809 − 0.23438I −4.86393 + 0.79093I
u = 0.356883 + 0.692055I
3.38201 − 9.13654I −5.22617 + 8.05199I
u = 0.356883 − 0.692055I
3.38201 + 9.13654I −5.22617 − 8.05199I
u = −0.341594 + 0.685182I
3.89441 + 3.00577I −4.12276 − 3.17486I
u = −0.341594 − 0.685182I
3.89441 − 3.00577I −4.12276 + 3.17486I
u = −1.233130 + 0.069457I
−2.15848 + 0.53603I −5.34890 + 0.I
u = −1.233130 − 0.069457I
−2.15848 − 0.53603I −5.34890 + 0.I
u = 1.217450 + 0.233216I
3.86157 − 6.43991I −5.27816 + 6.02462I
u = 1.217450 − 0.233216I
3.86157 + 6.43991I −5.27816 − 6.02462I
u = 0.396277 + 0.634373I
−3.48205 − 4.78463I −11.04017 + 7.62920I
u = 0.396277 − 0.634373I
−3.48205 + 4.78463I −11.04017 − 7.62920I
u = 0.556137 + 0.493828I
2.57048 + 5.10842I −7.05988 − 2.20532I
u = 0.556137 − 0.493828I
2.57048 − 5.10842I −7.05988 + 2.20532I
u = 0.454805 + 0.560740I
−3.76676 + 0.88407I −12.38985 − 0.56473I
u = 0.454805 − 0.560740I
−3.76676 − 0.88407I −12.38985 + 0.56473I
u = −0.553895 + 0.455920I
3.00179 + 0.90271I −6.25769 − 2.96370I
u = −0.553895 − 0.455920I
3.00179 − 0.90271I −6.25769 + 2.96370I
u = 1.305380 + 0.145441I
−3.32923 − 3.99615I −9.76353 + 7.26560I
u = 1.305380 − 0.145441I
−3.32923 + 3.99615I −9.76353 − 7.26560I
u = −0.011445 + 0.679358I
7.60462 + 3.09519I −0.01509 − 2.78190I
u = −0.011445 − 0.679358I
7.60462 − 3.09519I −0.01509 + 2.78190I
u = −0.361045 + 0.570627I
−0.76961 + 1.72495I −4.78052 − 3.91512I
u = −0.361045 − 0.570627I
−0.76961 − 1.72495I −4.78052 + 3.91512I
u = 1.34637
−5.74682 −16.7140
u = 1.44469 + 0.15665I
−3.29340 − 3.04757I 0
u = 1.44469 − 0.15665I
−3.29340 + 3.04757I 0
u = 1.43643 + 0.22136I
−6.53816 − 4.66456I 0
u = 1.43643 − 0.22136I
−6.53816 + 4.66456I 0
u = 1.43871 + 0.26142I
−1.81787 − 6.45853I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.43871 − 0.26142I
−1.81787 + 6.45853I 0
u = −0.098085 + 0.527806I
1.00543 + 1.56832I −1.50314 − 6.19843I
u = −0.098085 − 0.527806I
1.00543 − 1.56832I −1.50314 + 6.19843I
u = −1.44577 + 0.26317I
−2.40746 + 12.62150I 0
u = −1.44577 − 0.26317I
−2.40746 − 12.62150I 0
u = −1.46178 + 0.16297I
−3.85638 − 2.79254I 0
u = −1.46178 − 0.16297I
−3.85638 + 2.79254I 0
u = −1.45781 + 0.20477I
−9.89796 + 1.92247I 0
u = −1.45781 − 0.20477I
−9.89796 − 1.92247I 0
u = −1.45327 + 0.23647I
−9.43094 + 7.97441I 0
u = −1.45327 − 0.23647I
−9.43094 − 7.97441I 0
u = −0.330600
−0.781422 −13.7110
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
42
− u
41
+ ··· − u − 1
c
2
, c
5
, c
7
u
42
+ 11u
41
+ ··· + 3u + 1
c
3
, c
9
, c
10
u
42
+ u
41
+ ··· − 3u − 1
c
4
u
42
− 3u
41
+ ··· + 61u + 39
c
8
, c
11
u
42
+ 7u
41
+ ··· + 279u + 23
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
42
− 11y
41
+ ··· − 3y + 1
c
2
, c
5
, c
7
y
42
+ 41y
41
+ ··· − 11y + 1
c
3
, c
9
, c
10
y
42
− 39y
41
+ ··· − 3y + 1
c
4
y
42
− 11y
41
+ ··· − 25951y + 1521
c
8
, c
11
y
42
+ 29y
41
+ ··· − 14039y + 529
8
