10
24
(K10a
71
)
A knot diagram
1
Linearized knot diagam
7 5 9 3 2 10 1 4 6 8
Solving Sequence
2,7
1 8 10 6 5 3 4 9
c
1
c
7
c
10
c
6
c
5
c
2
c
4
c
9
c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
27
+ u
26
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 27 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
27
+ u
26
+ · · · + 2u − 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
1
=
1
−u
2
a
8
=
−u
u
3
+ u
a
10
=
u
2
+ 1
−u
4
− 2u
2
a
6
=
u
5
+ 2u
3
+ u
−u
7
− 3u
5
− 2u
3
+ u
a
5
=
−u
7
− 2u
5
+ 2u
−u
7
− 3u
5
− 2u
3
+ u
a
3
=
u
14
+ 5u
12
+ 8u
10
+ u
8
− 8u
6
− 4u
4
+ 2u
2
+ 1
u
14
+ 6u
12
+ 13u
10
+ 10u
8
− 2u
6
− 4u
4
+ u
2
a
4
=
−u
21
− 8u
19
− 25u
17
− 34u
15
− 6u
13
+ 34u
11
+ 27u
9
− 8u
7
− 13u
5
+ 3u
−u
21
− 9u
19
+ ··· − u
3
+ u
a
9
=
−u
8
− 3u
6
− 3u
4
+ 1
u
10
+ 4u
8
+ 5u
6
− 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
25
− 4u
24
− 44u
23
− 40u
22
− 208u
21
− 168u
20
− 536u
19
−
372u
18
− 772u
17
− 432u
16
− 508u
15
− 184u
14
+ 100u
13
+ 92u
12
+ 340u
11
+ 72u
10
+
68u
9
− 48u
8
− 144u
7
− 28u
6
− 76u
5
+ 12u
4
+ 16u
3
+ 20u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
10
u
27
− u
26
+ ··· + 2u + 1
c
2
, c
4
, c
5
u
27
+ 7u
26
+ ··· − 2u − 1
c
3
, c
8
u
27
+ u
26
+ ··· + u
2
+ 1
c
6
, c
9
u
27
+ u
26
+ ··· + 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
10
y
27
+ 23y
26
+ ··· − 2y −1
c
2
, c
4
, c
5
y
27
+ 27y
26
+ ··· + 14y −1
c
3
, c
8
y
27
+ 7y
26
+ ··· − 2y −1
c
6
, c
9
y
27
− 13y
26
+ ··· − 2y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.278071 + 0.956556I
4.70022 − 3.05015I −2.91169 + 1.99178I
u = −0.278071 − 0.956556I
4.70022 + 3.05015I −2.91169 − 1.99178I
u = 0.260338 + 0.833668I
4.87925 − 2.83072I −2.20196 + 3.74350I
u = 0.260338 − 0.833668I
4.87925 + 2.83072I −2.20196 − 3.74350I
u = −0.768863 + 0.186622I
2.29246 + 7.02686I −6.18454 − 6.08794I
u = −0.768863 − 0.186622I
2.29246 − 7.02686I −6.18454 + 6.08794I
u = 0.738973 + 0.201195I
2.75404 − 0.96140I −5.27084 + 1.18503I
u = 0.738973 − 0.201195I
2.75404 + 0.96140I −5.27084 − 1.18503I
u = −0.291604 + 1.207020I
−0.823094 + 0.986974I −8.82659 + 0.25321I
u = −0.291604 − 1.207020I
−0.823094 − 0.986974I −8.82659 − 0.25321I
u = −0.750412 + 0.064416I
−4.29886 + 2.79673I −12.25981 − 4.61920I
u = −0.750412 − 0.064416I
−4.29886 − 2.79673I −12.25981 + 4.61920I
u = 0.082485 + 1.285040I
4.34194 − 2.01066I 0.08108 + 3.90758I
u = 0.082485 − 1.285040I
4.34194 + 2.01066I 0.08108 − 3.90758I
u = 0.257867 + 1.292320I
2.54425 − 3.27708I −0.72206 + 2.87566I
u = 0.257867 − 1.292320I
2.54425 + 3.27708I −0.72206 − 2.87566I
u = −0.317436 + 1.304880I
−0.01754 + 6.65682I −6.80212 − 7.22011I
u = −0.317436 − 1.304880I
−0.01754 − 6.65682I −6.80212 + 7.22011I
u = 0.649647
−1.51171 −6.25830
u = 0.307012 + 1.374630I
7.73615 − 4.75862I −0.67410 + 2.41055I
u = 0.307012 − 1.374630I
7.73615 + 4.75862I −0.67410 − 2.41055I
u = −0.322115 + 1.372980I
7.22305 + 10.97750I −1.68833 − 7.27184I
u = −0.322115 − 1.372980I
7.22305 − 10.97750I −1.68833 + 7.27184I
u = 0.01000 + 1.42794I
11.72200 − 3.15301I 1.82291 + 2.60032I
u = 0.01000 − 1.42794I
11.72200 + 3.15301I 1.82291 − 2.60032I
u = 0.247000 + 0.300914I
−0.352229 − 0.953640I −6.23281 + 7.10310I
u = 0.247000 − 0.300914I
−0.352229 + 0.953640I −6.23281 − 7.10310I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
10
u
27
− u
26
+ ··· + 2u + 1
c
2
, c
4
, c
5
u
27
+ 7u
26
+ ··· − 2u − 1
c
3
, c
8
u
27
+ u
26
+ ··· + u
2
+ 1
c
6
, c
9
u
27
+ u
26
+ ··· + 4u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
10
y
27
+ 23y
26
+ ··· − 2y −1
c
2
, c
4
, c
5
y
27
+ 27y
26
+ ··· + 14y −1
c
3
, c
8
y
27
+ 7y
26
+ ··· − 2y −1
c
6
, c
9
y
27
− 13y
26
+ ··· − 2y −1
7
