11a
238
(K11a
238
)
A knot diagram
1
Linearized knot diagam
7 1 11 10 9 8 2 3 5 4 6
Solving Sequence
2,7
8 1 3 9 6 5 11 4 10
c
7
c
1
c
2
c
8
c
6
c
5
c
11
c
3
c
10
c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
32
− u
31
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 32 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
32
− u
31
+ · · · + 2u − 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
1
=
u
u
a
3
=
−u
3
−u
3
+ u
a
9
=
−u
8
+ u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
+ 2u
2
a
6
=
−u
2
+ 1
−u
4
a
5
=
−u
20
+ 3u
18
− 7u
16
+ 10u
14
− 10u
12
+ 7u
10
− u
8
− 2u
6
+ 3u
4
− 3u
2
+ 1
−u
20
+ 4u
18
− 10u
16
+ 18u
14
− 23u
12
+ 24u
10
− 18u
8
+ 10u
6
− 5u
4
a
11
=
−u
7
+ 2u
5
− 2u
3
+ 2u
−u
9
+ u
7
− u
5
+ u
a
4
=
−u
19
+ 4u
17
− 10u
15
+ 18u
13
− 23u
11
+ 24u
9
− 18u
7
+ 10u
5
− 5u
3
−u
21
+ 3u
19
− 7u
17
+ 10u
15
− 10u
13
+ 7u
11
− u
9
− 2u
7
+ 3u
5
− 3u
3
+ u
a
10
=
−u
31
+ 6u
29
+ ··· − 2u
3
+ 2u
−u
31
+ u
30
+ ··· + 2u − 1
a
10
=
−u
31
+ 6u
29
+ ··· − 2u
3
+ 2u
−u
31
+ u
30
+ ··· + 2u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
31
+ 24u
29
−4u
28
−88u
27
+ 20u
26
+ 228u
25
−72u
24
−456u
23
+ 180u
22
+ 736u
21
−
356u
20
− 976u
19
+ 568u
18
+ 1080u
17
− 740u
16
− 996u
15
+ 812u
14
+ 760u
13
− 736u
12
−
468u
11
+ 564u
10
+ 220u
9
− 356u
8
− 68u
7
+ 176u
6
+ 8u
5
− 76u
4
+ 4u
3
+ 20u
2
− 4u − 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
32
+ u
31
+ ··· − 2u − 1
c
2
, c
6
u
32
+ 11u
31
+ ··· + 8u + 1
c
3
, c
4
, c
5
c
9
, c
10
u
32
− u
31
+ ··· − 2u − 1
c
8
, c
11
u
32
− u
31
+ ··· + 8u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
32
− 11y
31
+ ··· − 8y + 1
c
2
, c
6
y
32
+ 21y
31
+ ··· − 8y + 1
c
3
, c
4
, c
5
c
9
, c
10
y
32
+ 41y
31
+ ··· − 8y + 1
c
8
, c
11
y
32
− 15y
31
+ ··· − 280y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.645707 + 0.769221I
3.20190 − 3.54493I −5.40363 + 3.59501I
u = −0.645707 − 0.769221I
3.20190 + 3.54493I −5.40363 − 3.59501I
u = −0.766364 + 0.598235I
1.37609 + 2.05463I −7.69647 − 5.64619I
u = −0.766364 − 0.598235I
1.37609 − 2.05463I −7.69647 + 5.64619I
u = 0.650134 + 0.810724I
12.44820 + 5.14177I −4.17146 − 2.01638I
u = 0.650134 − 0.810724I
12.44820 − 5.14177I −4.17146 + 2.01638I
u = −1.05287
−5.13714 −18.4380
u = 1.056330 + 0.061026I
−2.61740 − 3.12405I −13.03032 + 4.71506I
u = 1.056330 − 0.061026I
−2.61740 + 3.12405I −13.03032 − 4.71506I
u = 0.636819 + 0.693070I
0.007012 + 0.662924I −11.48005 − 1.53290I
u = 0.636819 − 0.693070I
0.007012 − 0.662924I −11.48005 + 1.53290I
u = −1.082110 + 0.105469I
6.12682 + 4.72021I −11.09441 − 3.42797I
u = −1.082110 − 0.105469I
6.12682 − 4.72021I −11.09441 + 3.42797I
u = 0.858044 + 0.724840I
6.28397 − 2.75786I −2.60459 + 3.27604I
u = 0.858044 − 0.724840I
6.28397 + 2.75786I −2.60459 − 3.27604I
u = 0.989901 + 0.536666I
8.67678 − 1.64389I −8.39822 + 2.78158I
u = 0.989901 − 0.536666I
8.67678 + 1.64389I −8.39822 − 2.78158I
u = −0.971964 + 0.621405I
0.65027 + 2.73837I −9.34927 − 0.96616I
u = −0.971964 − 0.621405I
0.65027 − 2.73837I −9.34927 + 0.96616I
u = −0.869866 + 0.770916I
16.1380 + 2.8994I −2.41783 − 2.82935I
u = −0.869866 − 0.770916I
16.1380 − 2.8994I −2.41783 + 2.82935I
u = 1.002990 + 0.660346I
−1.07052 − 5.91452I −13.1301 + 6.2502I
u = 1.002990 − 0.660346I
−1.07052 + 5.91452I −13.1301 − 6.2502I
u = −1.016710 + 0.688378I
2.09241 + 9.07761I −7.53326 − 8.39661I
u = −1.016710 − 0.688378I
2.09241 − 9.07761I −7.53326 + 8.39661I
u = 1.028400 + 0.706586I
11.3054 − 10.8467I −6.07367 + 6.73348I
u = 1.028400 − 0.706586I
11.3054 + 10.8467I −6.07367 − 6.73348I
u = 0.283633 + 0.646722I
10.54710 − 2.61943I −4.33176 + 2.54357I
u = 0.283633 − 0.646722I
10.54710 + 2.61943I −4.33176 − 2.54357I
u = −0.343359 + 0.506821I
1.71293 + 1.66616I −5.31847 − 4.81567I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.343359 − 0.506821I
1.71293 − 1.66616I −5.31847 + 4.81567I
u = 0.432503
−0.576779 −17.4950
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
32
+ u
31
+ ··· − 2u − 1
c
2
, c
6
u
32
+ 11u
31
+ ··· + 8u + 1
c
3
, c
4
, c
5
c
9
, c
10
u
32
− u
31
+ ··· − 2u − 1
c
8
, c
11
u
32
− u
31
+ ··· + 8u − 4
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
32
− 11y
31
+ ··· − 8y + 1
c
2
, c
6
y
32
+ 21y
31
+ ··· − 8y + 1
c
3
, c
4
, c
5
c
9
, c
10
y
32
+ 41y
31
+ ··· − 8y + 1
c
8
, c
11
y
32
− 15y
31
+ ··· − 280y + 16
8
