10
36
(K10a
5
)
A knot diagram
1
Linearized knot diagam
8 7 6 9 4 3 10 1 5 2
Solving Sequence
4,9
5 6 10 3 7 2 1 8
c
4
c
5
c
9
c
3
c
6
c
2
c
10
c
8
c
1
, c
7
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
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
6
=
−u
2
+ 1
u
2
a
10
=
−u
−u
3
+ u
a
3
=
u
4
− u
2
+ 1
−u
4
a
7
=
−u
6
+ u
4
− 2u
2
+ 1
u
6
+ u
2
a
2
=
u
8
− u
6
+ 3u
4
− 2u
2
+ 1
−u
8
− 2u
4
a
1
=
u
19
− 2u
17
+ 8u
15
− 12u
13
+ 21u
11
− 22u
9
+ 20u
7
− 12u
5
+ 5u
3
− 2u
−u
19
+ u
17
− 6u
15
+ 5u
13
− 11u
11
+ 7u
9
− 6u
7
+ 2u
5
− u
3
+ u
a
8
=
−u
10
+ u
8
− 4u
6
+ 3u
4
− 3u
2
+ 1
−u
12
+ 2u
10
− 4u
8
+ 6u
6
− 3u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
23
−4u
22
+8u
21
+12u
20
−36u
19
−40u
18
+56u
17
+80u
16
−116u
15
−132u
14
+136u
13
+
168u
12
−168u
11
−164u
10
+ 144u
9
+ 112u
8
−116u
7
−56u
6
+ 76u
5
+ 12u
4
−32u
3
+ 8u −10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
25
+ u
24
+ ··· + 3u + 1
c
2
, c
3
, c
5
c
6
u
25
+ 5u
24
+ ··· + u + 1
c
4
, c
9
u
25
− u
24
+ ··· + u + 1
c
7
u
25
− u
24
+ ··· − 5u + 2
c
10
u
25
+ 11u
24
+ ··· + u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
25
+ 11y
24
+ ··· + y −1
c
2
, c
3
, c
5
c
6
y
25
+ 31y
24
+ ··· + 5y −1
c
4
, c
9
y
25
− 5y
24
+ ··· + y −1
c
7
y
25
+ 3y
24
+ ··· − 31y −4
c
10
y
25
+ 7y
24
+ ··· + 21y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.832690 + 0.557074I
1.88922 + 3.01264I −1.96862 − 4.46588I
u = −0.832690 − 0.557074I
1.88922 − 3.01264I −1.96862 + 4.46588I
u = 0.907947 + 0.537572I
−0.01805 − 7.68313I −5.93165 + 8.92800I
u = 0.907947 − 0.537572I
−0.01805 + 7.68313I −5.93165 − 8.92800I
u = 0.832562 + 0.375712I
−2.08350 − 1.12769I −10.19939 + 3.41549I
u = 0.832562 − 0.375712I
−2.08350 + 1.12769I −10.19939 − 3.41549I
u = −0.646586 + 0.624531I
2.49752 + 1.43161I 0.07046 − 3.44213I
u = −0.646586 − 0.624531I
2.49752 − 1.43161I 0.07046 + 3.44213I
u = −0.885238 + 0.093706I
−3.47336 + 3.28459I −12.75115 − 5.14665I
u = −0.885238 − 0.093706I
−3.47336 − 3.28459I −12.75115 + 5.14665I
u = 0.532954 + 0.662656I
1.18303 + 3.19832I −2.28028 − 2.80466I
u = 0.532954 − 0.662656I
1.18303 − 3.19832I −2.28028 + 2.80466I
u = −0.918325 + 0.864773I
5.28985 + 3.20690I −5.88987 − 2.45318I
u = −0.918325 − 0.864773I
5.28985 − 3.20690I −5.88987 + 2.45318I
u = −0.895269 + 0.914484I
9.42796 − 3.86019I −2.25009 + 2.37671I
u = −0.895269 − 0.914484I
9.42796 + 3.86019I −2.25009 − 2.37671I
u = 0.714675
−1.05962 −9.24230
u = 0.912390 + 0.907488I
11.15260 − 1.58500I 0.08176 + 2.23225I
u = 0.912390 − 0.907488I
11.15260 + 1.58500I 0.08176 − 2.23225I
u = 0.950797 + 0.888223I
11.02790 − 5.03718I −0.15373 + 2.54574I
u = 0.950797 − 0.888223I
11.02790 + 5.03718I −0.15373 − 2.54574I
u = −0.965119 + 0.879930I
9.20201 + 10.47620I −2.72320 − 7.02847I
u = −0.965119 − 0.879930I
9.20201 − 10.47620I −2.72320 + 7.02847I
u = 0.149237 + 0.487637I
−0.32971 − 1.74239I −2.38307 + 3.79759I
u = 0.149237 − 0.487637I
−0.32971 + 1.74239I −2.38307 − 3.79759I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
u
25
+ u
24
+ ··· + 3u + 1
c
2
, c
3
, c
5
c
6
u
25
+ 5u
24
+ ··· + u + 1
c
4
, c
9
u
25
− u
24
+ ··· + u + 1
c
7
u
25
− u
24
+ ··· − 5u + 2
c
10
u
25
+ 11u
24
+ ··· + u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
25
+ 11y
24
+ ··· + y −1
c
2
, c
3
, c
5
c
6
y
25
+ 31y
24
+ ··· + 5y −1
c
4
, c
9
y
25
− 5y
24
+ ··· + y −1
c
7
y
25
+ 3y
24
+ ··· − 31y −4
c
10
y
25
+ 7y
24
+ ··· + 21y −1
7
