11a
98
(K11a
98
)
A knot diagram
1
Linearized knot diagam
6 1 10 9 2 3 11 5 4 8 7
Solving Sequence
5,8
9 4 10 11 3 7 1 2 6
c
8
c
4
c
9
c
10
c
3
c
7
c
11
c
2
c
6
c
1
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
38
− u
37
+ ··· − u + 1i
* 1 irreducible components of dim
C
= 0, with total 38 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
38
− u
37
+ · · · − u + 1i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
4
=
−u
u
3
+ u
a
10
=
u
2
+ 1
−u
4
− 2u
2
a
11
=
u
4
+ 3u
2
+ 1
−u
4
− 2u
2
a
3
=
−u
3
− 2u
u
5
+ 3u
3
+ u
a
7
=
u
8
+ 5u
6
+ 7u
4
+ 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
a
1
=
u
12
+ 7u
10
+ 17u
8
+ 16u
6
+ 6u
4
+ 5u
2
+ 1
−u
12
− 6u
10
− 12u
8
− 8u
6
− u
4
− 2u
2
a
2
=
u
29
+ 16u
27
+ ··· + 8u
3
− u
−u
29
− 15u
27
+ ··· + u
3
+ u
a
6
=
u
16
+ 9u
14
+ 31u
12
+ 50u
10
+ 39u
8
+ 22u
6
+ 18u
4
+ 4u
2
+ 1
−u
18
− 10u
16
− 39u
14
− 74u
12
− 71u
10
− 40u
8
− 26u
6
− 12u
4
− u
2
a
6
=
u
16
+ 9u
14
+ 31u
12
+ 50u
10
+ 39u
8
+ 22u
6
+ 18u
4
+ 4u
2
+ 1
−u
18
− 10u
16
− 39u
14
− 74u
12
− 71u
10
− 40u
8
− 26u
6
− 12u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
37
+4u
36
−84u
35
+76u
34
−788u
33
+640u
32
−4348u
31
+3136u
30
−15652u
29
+9876u
28
−
38648u
27
+20892u
26
−67496u
25
+30388u
24
−86252u
23
+31308u
22
−85720u
21
+24576u
20
−
72004u
19
+ 16236u
18
−52428u
17
+ 8440u
16
−31340u
15
+ 2244u
14
−15844u
13
−364u
12
−
7264u
11
−736u
10
−2476u
9
−656u
8
−756u
7
−360u
6
−144u
5
−84u
4
−52u
3
−12u
2
−12u+2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
38
− u
37
+ ··· − u + 1
c
2
u
38
+ 17u
37
+ ··· + 3u + 1
c
3
, c
4
, c
8
c
9
u
38
− u
37
+ ··· − u + 1
c
6
u
38
+ u
37
+ ··· + u + 1
c
7
, c
10
, c
11
u
38
− 5u
37
+ ··· − 25u + 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
38
+ 17y
37
+ ··· + 3y + 1
c
2
y
38
+ 9y
37
+ ··· + 19y + 1
c
3
, c
4
, c
8
c
9
y
38
+ 41y
37
+ ··· + 3y + 1
c
6
y
38
+ y
37
+ ··· + 35y + 1
c
7
, c
10
, c
11
y
38
+ 37y
37
+ ··· + 59y + 9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.635381 + 0.544778I
4.89318 + 8.99255I 2.54683 − 8.05726I
u = 0.635381 − 0.544778I
4.89318 − 8.99255I 2.54683 + 8.05726I
u = −0.637190 + 0.525254I
6.72503 − 3.70347I 5.40296 + 3.46584I
u = −0.637190 − 0.525254I
6.72503 + 3.70347I 5.40296 − 3.46584I
u = −0.646186 + 0.476105I
6.87083 − 0.63435I 5.86902 + 2.86167I
u = −0.646186 − 0.476105I
6.87083 + 0.63435I 5.86902 − 2.86167I
u = 0.651941 + 0.454511I
5.16060 − 4.64389I 3.40172 + 1.99685I
u = 0.651941 − 0.454511I
5.16060 + 4.64389I 3.40172 − 1.99685I
u = 0.587799 + 0.498634I
1.34506 + 2.00929I −0.48209 − 3.49556I
u = 0.587799 − 0.498634I
1.34506 − 2.00929I −0.48209 + 3.49556I
u = −0.330816 + 0.636061I
−2.01726 − 5.47617I −3.09870 + 9.17486I
u = −0.330816 − 0.636061I
−2.01726 + 5.47617I −3.09870 − 9.17486I
u = −0.144727 + 0.660329I
−3.03329 + 1.00909I −7.12564 + 0.28235I
u = −0.144727 − 0.660329I
−3.03329 − 1.00909I −7.12564 − 0.28235I
u = 0.301795 + 0.520951I
−0.018847 + 1.384110I 1.16696 − 5.74622I
u = 0.301795 − 0.520951I
−0.018847 − 1.384110I 1.16696 + 5.74622I
u = 0.03046 + 1.45212I
−4.91125 + 2.21769I 0
u = 0.03046 − 1.45212I
−4.91125 − 2.21769I 0
u = 0.19314 + 1.48235I
−1.12742 − 1.62626I 0
u = 0.19314 − 1.48235I
−1.12742 + 1.62626I 0
u = −0.19488 + 1.49761I
0.43075 − 3.64794I 0
u = −0.19488 − 1.49761I
0.43075 + 3.64794I 0
u = 0.379571 + 0.296373I
0.630271 + 1.053360I 5.17597 − 5.21367I
u = 0.379571 − 0.296373I
0.630271 − 1.053360I 5.17597 + 5.21367I
u = 0.17234 + 1.52286I
−5.33654 + 4.72378I 0
u = 0.17234 − 1.52286I
−5.33654 − 4.72378I 0
u = −0.448691 + 0.124937I
−0.48331 + 2.76150I 3.31371 − 3.04166I
u = −0.448691 − 0.124937I
−0.48331 − 2.76150I 3.31371 + 3.04166I
u = 0.06806 + 1.53625I
−6.95274 + 2.61432I 0
u = 0.06806 − 1.53625I
−6.95274 − 2.61432I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.19702 + 1.52628I
−0.02756 − 6.72233I 0
u = −0.19702 − 1.52628I
−0.02756 + 6.72233I 0
u = 0.19796 + 1.53605I
−1.97382 + 12.02170I 0
u = 0.19796 − 1.53605I
−1.97382 − 12.02170I 0
u = −0.03796 + 1.56118I
−10.49980 + 0.35836I 0
u = −0.03796 − 1.56118I
−10.49980 − 0.35836I 0
u = −0.08099 + 1.56107I
−9.41307 − 6.91152I 0
u = −0.08099 − 1.56107I
−9.41307 + 6.91152I 0
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
38
− u
37
+ ··· − u + 1
c
2
u
38
+ 17u
37
+ ··· + 3u + 1
c
3
, c
4
, c
8
c
9
u
38
− u
37
+ ··· − u + 1
c
6
u
38
+ u
37
+ ··· + u + 1
c
7
, c
10
, c
11
u
38
− 5u
37
+ ··· − 25u + 3
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
38
+ 17y
37
+ ··· + 3y + 1
c
2
y
38
+ 9y
37
+ ··· + 19y + 1
c
3
, c
4
, c
8
c
9
y
38
+ 41y
37
+ ··· + 3y + 1
c
6
y
38
+ y
37
+ ··· + 35y + 1
c
7
, c
10
, c
11
y
38
+ 37y
37
+ ··· + 59y + 9
8
