11a
308
(K11a
308
)
A knot diagram
1
Linearized knot diagam
6 7 1 10 9 2 3 11 4 5 8
Solving Sequence
5,11
10 4 9 6 8 1 2 3 7
c
10
c
4
c
9
c
5
c
8
c
11
c
1
c
3
c
7
c
2
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
35
− u
34
+ ··· − 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 35 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
35
− u
34
+ · · · − 2u − 1i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
10
=
1
−u
2
a
4
=
u
−u
3
+ u
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
6
=
−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
20
+ 9u
18
+ ··· + u
2
+ 1
u
22
− 10u
20
+ ··· + 2u
4
+ u
2
a
3
=
−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
34
− 15u
32
+ ··· − u
2
+ 1
−u
34
+ 16u
32
+ ··· − 2u
4
− 3u
2
a
7
=
u
34
− 15u
32
+ ··· − u
2
+ 1
−u
34
+ 16u
32
+ ··· − 2u
4
− 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
33
+64u
31
−452u
29
−4u
28
+1840u
27
+52u
26
−4728u
25
−292u
24
+7904u
23
+916u
22
−
8628u
21
−1732u
20
+6320u
19
+1988u
18
−3804u
17
−1360u
16
+2528u
15
+636u
14
−1276u
13
−
364u
12
+276u
11
+144u
10
−180u
9
+64u
8
+96u
7
−24u
6
+36u
5
−8u
4
+24u
3
−20u
2
−4u−14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
u
35
− u
34
+ ··· − 2u − 1
c
3
u
35
− 11u
34
+ ··· + 444u − 113
c
4
, c
9
, c
10
u
35
− u
34
+ ··· − 2u − 1
c
5
u
35
+ 3u
34
+ ··· + 54u + 9
c
8
, c
11
u
35
+ 5u
34
+ ··· + 4u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
y
35
− 41y
34
+ ··· + 6y −1
c
3
y
35
− 17y
34
+ ··· + 162106y −12769
c
4
, c
9
, c
10
y
35
− 33y
34
+ ··· + 6y −1
c
5
y
35
− 13y
34
+ ··· + 3618y −81
c
8
, c
11
y
35
+ 31y
34
+ ··· + 298y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.09220
−7.72425 −11.4230
u = −0.416127 + 0.687266I
−11.53560 + 7.43008I −13.0479 − 5.8668I
u = −0.416127 − 0.687266I
−11.53560 − 7.43008I −13.0479 + 5.8668I
u = −0.525382 + 0.592520I
−11.96020 − 3.16210I −14.1562 − 0.1993I
u = −0.525382 − 0.592520I
−11.96020 + 3.16210I −14.1562 + 0.1993I
u = 0.404028 + 0.654601I
−3.38071 − 5.28518I −11.19312 + 7.66639I
u = 0.404028 − 0.654601I
−3.38071 + 5.28518I −11.19312 − 7.66639I
u = −1.245760 + 0.112991I
−2.03937 + 0.97518I −7.22361 + 0.37761I
u = −1.245760 − 0.112991I
−2.03937 − 0.97518I −7.22361 − 0.37761I
u = 0.478538 + 0.569763I
−3.71886 + 1.25391I −12.53849 − 1.04095I
u = 0.478538 − 0.569763I
−3.71886 − 1.25391I −12.53849 + 1.04095I
u = −0.401418 + 0.595064I
−1.30259 + 1.88118I −7.16532 − 3.48234I
u = −0.401418 − 0.595064I
−1.30259 − 1.88118I −7.16532 + 3.48234I
u = 1.284920 + 0.176915I
−2.74426 − 4.13151I −10.06219 + 7.59188I
u = 1.284920 − 0.176915I
−2.74426 + 4.13151I −10.06219 − 7.59188I
u = −1.313190 + 0.225618I
−9.81072 + 5.98333I −13.3282 − 5.5351I
u = −1.313190 − 0.225618I
−9.81072 − 5.98333I −13.3282 + 5.5351I
u = 0.140885 + 0.636642I
−5.27877 − 2.85435I −7.73114 + 4.21990I
u = 0.140885 − 0.636642I
−5.27877 + 2.85435I −7.73114 − 4.21990I
u = 0.650180
−7.56446 −13.6890
u = 1.35428
−5.67856 −17.2470
u = −1.42496
−13.8091 −17.9870
u = −0.062444 + 0.564757I
1.40484 + 1.42814I −2.59292 − 5.83605I
u = −0.062444 − 0.564757I
1.40484 − 1.42814I −2.59292 + 5.83605I
u = 1.45233 + 0.22468I
−7.26272 − 4.90638I −11.00863 + 2.94514I
u = 1.45233 − 0.22468I
−7.26272 + 4.90638I −11.00863 − 2.94514I
u = −1.46000 + 0.24290I
−9.38489 + 8.56887I −14.7051 − 7.1915I
u = −1.46000 − 0.24290I
−9.38489 − 8.56887I −14.7051 + 7.1915I
u = −1.46668 + 0.20359I
−9.96671 + 1.56878I −15.9909 + 0.I
u = −1.46668 − 0.20359I
−9.96671 − 1.56878I −15.9909 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.46917 + 0.25360I
−17.6166 − 10.8655I −16.5622 + 5.6789I
u = 1.46917 − 0.25360I
−17.6166 + 10.8655I −16.5622 − 5.6789I
u = 1.48595 + 0.19714I
−18.4666 + 0.3155I −17.6053 + 0.I
u = 1.48595 − 0.19714I
−18.4666 − 0.3155I −17.6053 + 0.I
u = −0.321346
−0.640564 −15.8310
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
u
35
− u
34
+ ··· − 2u − 1
c
3
u
35
− 11u
34
+ ··· + 444u − 113
c
4
, c
9
, c
10
u
35
− u
34
+ ··· − 2u − 1
c
5
u
35
+ 3u
34
+ ··· + 54u + 9
c
8
, c
11
u
35
+ 5u
34
+ ··· + 4u − 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
y
35
− 41y
34
+ ··· + 6y −1
c
3
y
35
− 17y
34
+ ··· + 162106y −12769
c
4
, c
9
, c
10
y
35
− 33y
34
+ ··· + 6y −1
c
5
y
35
− 13y
34
+ ··· + 3618y −81
c
8
, c
11
y
35
+ 31y
34
+ ··· + 298y −1
8
