11a
161
(K11a
161
)
A knot diagram
1
Linearized knot diagam
6 1 10 7 2 5 4 11 3 8 9
Solving Sequence
2,6
1
3,9
10 5 7 4 11 8
c
1
c
2
c
9
c
5
c
6
c
4
c
11
c
8
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
20
− 2u
18
+ ··· + b − 2u, u
28
+ u
27
+ ··· + a + 2, u
32
+ 2u
31
+ ··· + 4u + 1i
I
u
2
= hu
2
+ b, −u
2
+ a + u, u
4
− u
3
+ u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 36 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
= h−u
20
−2u
18
+· · ·+b−2u, u
28
+u
27
+· · ·+a+2, u
32
+2u
31
+· · ·+4u+1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
9
=
−u
28
− u
27
+ ··· − 6u − 2
u
20
+ 2u
18
+ ··· + 2u
2
+ 2u
a
10
=
−2u
30
− u
29
+ ··· − 7u − 3
2u
31
+ 4u
30
+ ··· + 9u + 2
a
5
=
−u
u
a
7
=
−u
3
u
3
+ u
a
4
=
−u
5
− u
u
5
+ u
3
+ u
a
11
=
u
30
+ u
29
+ ··· + 7u + 3
−u
31
− 2u
30
+ ··· − 5u − 1
a
8
=
−u
7
− 2u
3
u
7
+ u
5
+ 2u
3
+ u
a
8
=
−u
7
− 2u
3
u
7
+ u
5
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
31
+8u
30
+19u
29
+22u
28
+72u
27
+97u
26
+199u
25
+195u
24
+434u
23
+440u
22
+814u
21
+
663u
20
+1230u
19
+979u
18
+1669u
17
+1135u
16
+1826u
15
+1208u
14
+1820u
13
+1120u
12
+
1432u
11
+910u
10
+996u
9
+668u
8
+516u
7
+390u
6
+216u
5
+187u
4
+58u
3
+55u
2
+13u+11
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
32
− 2u
31
+ ··· − 4u + 1
c
2
, c
4
, c
6
c
7
u
32
+ 6u
31
+ ··· − 56u
2
+ 1
c
3
, c
9
u
32
− u
31
+ ··· + 24u − 16
c
8
, c
10
, c
11
u
32
+ 5u
31
+ ··· − 4u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
32
+ 6y
31
+ ··· − 56y
2
+ 1
c
2
, c
4
, c
6
c
7
y
32
+ 42y
31
+ ··· − 112y + 1
c
3
, c
9
y
32
− 27y
31
+ ··· + 448y + 256
c
8
, c
10
, c
11
y
32
− 35y
31
+ ··· − 22y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.213719 + 0.980461I
a = 0.92583 − 1.26296I
b = 0.082336 + 0.696499I
4.40938 − 2.90320I 5.62644 + 3.88291I
u = −0.213719 − 0.980461I
a = 0.92583 + 1.26296I
b = 0.082336 − 0.696499I
4.40938 + 2.90320I 5.62644 − 3.88291I
u = −0.644830 + 0.775185I
a = 2.23380 + 1.34488I
b = −0.42916 − 2.42515I
4.97796 − 2.41324I 9.06378 + 3.46829I
u = −0.644830 − 0.775185I
a = 2.23380 − 1.34488I
b = −0.42916 + 2.42515I
4.97796 + 2.41324I 9.06378 − 3.46829I
u = 0.798476 + 0.579251I
a = −1.76126 + 0.16137I
b = 0.88715 − 1.74244I
10.60130 − 2.72339I 11.99326 + 0.76740I
u = 0.798476 − 0.579251I
a = −1.76126 − 0.16137I
b = 0.88715 + 1.74244I
10.60130 + 2.72339I 11.99326 − 0.76740I
u = 0.601316 + 0.841196I
a = 0.867822 − 0.956388I
b = 0.193771 + 0.505942I
2.73490 + 4.63620I 7.44058 − 7.48323I
u = 0.601316 − 0.841196I
a = 0.867822 + 0.956388I
b = 0.193771 − 0.505942I
2.73490 − 4.63620I 7.44058 + 7.48323I
u = 0.645468 + 0.683845I
a = 0.0195996 − 0.1036640I
b = −0.539124 + 0.646751I
3.24411 + 0.05063I 9.93222 + 0.12660I
u = 0.645468 − 0.683845I
a = 0.0195996 + 0.1036640I
b = −0.539124 − 0.646751I
3.24411 − 0.05063I 9.93222 − 0.12660I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.614078 + 0.966359I
a = −1.02310 + 2.02918I
b = −0.31554 − 2.13236I
9.31106 + 7.91275I 9.40540 − 6.63145I
u = 0.614078 − 0.966359I
a = −1.02310 − 2.02918I
b = −0.31554 + 2.13236I
9.31106 − 7.91275I 9.40540 + 6.63145I
u = −0.423229 + 0.733264I
a = −0.896141 − 0.367650I
b = 0.294342 + 0.546654I
0.00047 − 1.65514I 0.39437 + 4.54470I
u = −0.423229 − 0.733264I
a = −0.896141 + 0.367650I
b = 0.294342 − 0.546654I
0.00047 + 1.65514I 0.39437 − 4.54470I
u = −0.145430 + 0.769393I
a = −0.613814 + 1.208160I
b = 0.426833 − 0.149998I
−1.08342 − 1.49550I −1.76412 + 6.31671I
u = −0.145430 − 0.769393I
a = −0.613814 − 1.208160I
b = 0.426833 + 0.149998I
−1.08342 + 1.49550I −1.76412 − 6.31671I
u = 0.866691 + 0.917191I
a = −0.900315 + 0.319705I
b = 0.08960 − 1.43559I
7.59385 + 3.21086I 2.30282 − 2.66372I
u = 0.866691 − 0.917191I
a = −0.900315 − 0.319705I
b = 0.08960 + 1.43559I
7.59385 − 3.21086I 2.30282 + 2.66372I
u = −0.705788
a = −1.72336
b = 0.673766
7.74304 12.4360
u = −0.918056 + 0.925441I
a = 0.220309 + 0.450379I
b = 0.124115 − 1.293980I
12.49900 − 0.30826I 9.65224 − 0.25325I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.918056 − 0.925441I
a = 0.220309 − 0.450379I
b = 0.124115 + 1.293980I
12.49900 + 0.30826I 9.65224 + 0.25325I
u = −0.945672 + 0.902976I
a = −1.81639 − 0.29726I
b = 0.97029 + 3.38005I
−19.5223 + 4.2287I 11.43737 − 1.00370I
u = −0.945672 − 0.902976I
a = −1.81639 + 0.29726I
b = 0.97029 − 3.38005I
−19.5223 − 4.2287I 11.43737 + 1.00370I
u = 0.915023 + 0.941366I
a = 2.39534 − 0.89971I
b = −0.12103 + 4.15879I
14.7168 + 3.3681I 10.32984 − 2.30184I
u = 0.915023 − 0.941366I
a = 2.39534 + 0.89971I
b = −0.12103 − 4.15879I
14.7168 − 3.3681I 10.32984 + 2.30184I
u = −0.903860 + 0.952544I
a = 1.222940 + 0.282890I
b = −0.231803 − 1.207090I
12.41050 − 6.40086I 9.40627 + 4.90251I
u = −0.903860 − 0.952544I
a = 1.222940 − 0.282890I
b = −0.231803 + 1.207090I
12.41050 + 6.40086I 9.40627 − 4.90251I
u = −0.900364 + 0.984023I
a = −1.99724 − 1.52148I
b = −0.77261 + 3.46344I
19.6887 − 11.0126I 11.01976 + 5.54593I
u = −0.900364 − 0.984023I
a = −1.99724 + 1.52148I
b = −0.77261 − 3.46344I
19.6887 + 11.0126I 11.01976 − 5.54593I
u = 0.161526 + 0.565105I
a = 0.28634 − 2.32243I
b = −0.713364 + 0.589378I
1.29270 + 0.72541I 4.11413 + 2.96939I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.161526 − 0.565105I
a = 0.28634 + 2.32243I
b = −0.713364 − 0.589378I
1.29270 − 0.72541I 4.11413 − 2.96939I
u = −0.309046
a = −0.604076
b = −0.565378
0.870053 11.8550
8
II. I
u
2
= hu
2
+ b, −u
2
+ a + u, u
4
− u
3
+ u
2
+ 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
3
− u
2
− 1
a
9
=
u
2
− u
−u
2
a
10
=
u
2
− u
−u
2
a
5
=
−u
u
a
7
=
−u
3
u
3
+ u
a
4
=
u
2
+ 1
u
3
− u
2
− 1
a
11
=
u
2
− u + 1
0
a
8
=
−1
−u
2
a
8
=
−1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
2
+ 6u + 7
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− u
3
+ u
2
+ 1
c
2
, c
6
, c
7
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
3
, c
9
u
4
c
4
u
4
− u
3
+ 3u
2
− 2u + 1
c
5
u
4
+ u
3
+ u
2
+ 1
c
8
(u + 1)
4
c
10
, c
11
(u − 1)
4
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
2
, c
4
, c
6
c
7
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
3
, c
9
y
4
c
8
, c
10
, c
11
(y −1)
4
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.351808 + 0.720342I
a = −0.043315 − 1.227190I
b = 0.395123 + 0.506844I
1.43393 − 1.41510I 6.86477 + 6.85627I
u = −0.351808 − 0.720342I
a = −0.043315 + 1.227190I
b = 0.395123 − 0.506844I
1.43393 + 1.41510I 6.86477 − 6.85627I
u = 0.851808 + 0.911292I
a = −0.956685 + 0.641200I
b = 0.10488 − 1.55249I
8.43568 + 3.16396I 12.63523 − 2.29471I
u = 0.851808 − 0.911292I
a = −0.956685 − 0.641200I
b = 0.10488 + 1.55249I
8.43568 − 3.16396I 12.63523 + 2.29471I
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
4
− u
3
+ u
2
+ 1)(u
32
− 2u
31
+ ··· − 4u + 1)
c
2
, c
6
, c
7
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
32
+ 6u
31
+ ··· − 56u
2
+ 1)
c
3
, c
9
u
4
(u
32
− u
31
+ ··· + 24u − 16)
c
4
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
32
+ 6u
31
+ ··· − 56u
2
+ 1)
c
5
(u
4
+ u
3
+ u
2
+ 1)(u
32
− 2u
31
+ ··· − 4u + 1)
c
8
((u + 1)
4
)(u
32
+ 5u
31
+ ··· − 4u − 1)
c
10
, c
11
((u − 1)
4
)(u
32
+ 5u
31
+ ··· − 4u − 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
32
+ 6y
31
+ ··· − 56y
2
+ 1)
c
2
, c
4
, c
6
c
7
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
32
+ 42y
31
+ ··· − 112y + 1)
c
3
, c
9
y
4
(y
32
− 27y
31
+ ··· + 448y + 256)
c
8
, c
10
, c
11
((y −1)
4
)(y
32
− 35y
31
+ ··· − 22y + 1)
14
