10
19
(K10a
108
)
A knot diagram
1
Linearized knot diagam
7 8 6 9 10 1 2 5 4 3
Solving Sequence
4,10
9 5 6 3 1 8 2 7
c
9
c
4
c
5
c
3
c
10
c
8
c
2
c
7
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
25
− u
24
+ ··· − u + 1i
* 1 irreducible components of dim
C
= 0, with total 25 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
25
− u
24
+ · · · − u + 1i
(i) Arc colorings
a
4
=
0
u
a
10
=
1
0
a
9
=
1
u
2
a
5
=
u
u
3
+ u
a
6
=
u
3
+ 2u
u
3
+ u
a
3
=
−u
7
− 4u
5
− 4u
3
−u
7
− 3u
5
− 2u
3
+ u
a
1
=
u
14
+ 7u
12
+ 18u
10
+ 19u
8
+ 4u
6
− 4u
4
+ 1
u
14
+ 6u
12
+ 13u
10
+ 10u
8
− 2u
6
− 4u
4
+ u
2
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
2
=
u
13
+ 6u
11
+ 13u
9
+ 10u
7
− 2u
5
− 4u
3
+ u
u
15
+ 7u
13
+ 18u
11
+ 19u
9
+ 4u
7
− 4u
5
+ u
a
7
=
−u
24
− 11u
22
+ ··· + 5u
4
+ 1
−u
24
+ u
23
+ ··· − 2u
3
+ 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
24
+ 4u
23
−48u
22
+ 40u
21
−240u
20
+ 164u
19
−636u
18
+ 340u
17
−920u
16
+ 332u
15
−
620u
14
+36u
13
−12u
12
−184u
11
+140u
10
−80u
9
−56u
8
+36u
7
−60u
6
+12u
4
−12u
3
+4u
2
+2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
u
25
− u
24
+ ··· + u + 1
c
3
u
25
+ 5u
24
+ ··· − 47u − 11
c
4
, c
8
, c
9
u
25
− u
24
+ ··· − u + 1
c
5
u
25
+ u
24
+ ··· + 3u + 2
c
10
u
25
− 7u
24
+ ··· + 41u − 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
y
25
− 29y
24
+ ··· + y −1
c
3
y
25
+ 11y
24
+ ··· − 827y −121
c
4
, c
8
, c
9
y
25
+ 23y
24
+ ··· + y −1
c
5
y
25
+ 3y
24
+ ··· − 31y −4
c
10
y
25
− 5y
24
+ ··· + 197y −49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.083328 + 1.136530I
−1.41378 + 1.61686I −0.87509 − 4.54712I
u = 0.083328 − 1.136530I
−1.41378 − 1.61686I −0.87509 + 4.54712I
u = −0.226231 + 1.195340I
−7.69988 − 3.32898I −4.74899 + 3.47484I
u = −0.226231 − 1.195340I
−7.69988 + 3.32898I −4.74899 − 3.47484I
u = 0.700117 + 0.334469I
−7.82366 + 6.30957I −3.83367 − 5.57691I
u = 0.700117 − 0.334469I
−7.82366 − 6.30957I −3.83367 + 5.57691I
u = 0.461544 + 0.584785I
−8.81533 − 2.31852I −6.07988 − 0.26267I
u = 0.461544 − 0.584785I
−8.81533 + 2.31852I −6.07988 + 0.26267I
u = −0.652943 + 0.287492I
−0.14392 − 4.18290I −0.98515 + 7.72660I
u = −0.652943 − 0.287492I
−0.14392 + 4.18290I −0.98515 − 7.72660I
u = −0.677492
−4.07756 0.217760
u = 0.580674 + 0.194968I
1.16471 + 0.92486I 4.08147 − 1.66278I
u = 0.580674 − 0.194968I
1.16471 − 0.92486I 4.08147 + 1.66278I
u = 0.224985 + 1.385120I
−3.90410 + 3.87050I −2.00448 − 2.43861I
u = 0.224985 − 1.385120I
−3.90410 − 3.87050I −2.00448 + 2.43861I
u = −0.15893 + 1.40888I
−6.93669 − 1.11527I −8.41631 − 0.71281I
u = −0.15893 − 1.40888I
−6.93669 + 1.11527I −8.41631 + 0.71281I
u = −0.333053 + 0.458284I
−1.19946 + 0.82124I −4.96410 − 1.46331I
u = −0.333053 − 0.458284I
−1.19946 − 0.82124I −4.96410 + 1.46331I
u = −0.25437 + 1.41342I
−5.58181 − 7.50021I −5.62573 + 7.29113I
u = −0.25437 − 1.41342I
−5.58181 + 7.50021I −5.62573 − 7.29113I
u = 0.26972 + 1.43636I
−13.4988 + 9.8448I −7.88321 − 5.59341I
u = 0.26972 − 1.43636I
−13.4988 − 9.8448I −7.88321 + 5.59341I
u = 0.14391 + 1.45939I
−15.3081 − 0.2303I −9.77375 − 0.13265I
u = 0.14391 − 1.45939I
−15.3081 + 0.2303I −9.77375 + 0.13265I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
u
25
− u
24
+ ··· + u + 1
c
3
u
25
+ 5u
24
+ ··· − 47u − 11
c
4
, c
8
, c
9
u
25
− u
24
+ ··· − u + 1
c
5
u
25
+ u
24
+ ··· + 3u + 2
c
10
u
25
− 7u
24
+ ··· + 41u − 7
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
y
25
− 29y
24
+ ··· + y −1
c
3
y
25
+ 11y
24
+ ··· − 827y −121
c
4
, c
8
, c
9
y
25
+ 23y
24
+ ··· + y −1
c
5
y
25
+ 3y
24
+ ··· − 31y −4
c
10
y
25
− 5y
24
+ ··· + 197y −49
7
