11a
9
(K11a
9
)
A knot diagram
1
Linearized knot diagam
5 1 9 2 3 10 11 4 6 7 8
Solving Sequence
7,10
11 8
1,3
2 6 5 9 4
c
10
c
7
c
11
c
2
c
6
c
5
c
9
c
3
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
35
+ u
34
+ ··· + 2b − 1, 3u
35
+ 4u
34
+ ··· + 2a − 2, u
36
+ 3u
35
+ ··· − 3u
2
− 1i
I
u
2
= h−au + b, a
2
+ a + 1, u
2
− u − 1i
* 2 irreducible components of dim
C
= 0, with total 40 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
+· · ·+2b−1, 3u
35
+4u
34
+· · ·+2a−2, u
36
+3u
35
+· · ·−3u
2
−1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
8
=
−u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
−
3
2
u
35
− 2u
34
+ ··· −
5
2
u + 1
−
1
2
u
35
−
1
2
u
34
+ ··· + 4u
2
+
1
2
a
2
=
5u
35
+
13
2
u
34
+ ··· +
1
2
u −
5
2
8u
35
+ 10u
34
+ ··· + 3u − 5
a
6
=
u
u
a
5
=
−
1
2
u
35
− u
34
+ ··· +
11
2
u + 1
−
1
2
u
35
−
1
2
u
34
+ ··· − 2u
2
+
1
2
a
9
=
−u
2
+ 1
−u
2
a
4
=
11
2
u
35
+ 7u
34
+ ··· −
1
2
u − 3
19
2
u
35
+
23
2
u
34
+ ··· + 3u −
11
2
a
4
=
11
2
u
35
+ 7u
34
+ ··· −
1
2
u − 3
19
2
u
35
+
23
2
u
34
+ ··· + 3u −
11
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
5
2
u
35
− 3u
34
+ ··· +
23
2
u
2
+
5
2
u
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
36
+ 3u
35
+ ··· + 2u + 1
c
2
u
36
+ 19u
35
+ ··· + 2u + 1
c
3
, c
8
u
36
+ u
35
+ ··· − 32u − 16
c
5
u
36
− 3u
35
+ ··· − 156u + 41
c
6
, c
7
, c
9
c
10
, c
11
u
36
+ 3u
35
+ ··· − 3u
2
− 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
36
+ 19y
35
+ ··· + 2y + 1
c
2
y
36
− y
35
+ ··· − 46y + 1
c
3
, c
8
y
36
+ 25y
35
+ ··· + 896y + 256
c
5
y
36
− 21y
35
+ ··· + 12482y + 1681
c
6
, c
7
, c
9
c
10
, c
11
y
36
− 49y
35
+ ··· + 6y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.025520 + 0.116463I
a = −1.031170 + 0.432608I
b = −2.09741 + 0.72386I
−4.16025 + 3.63915I −10.15018 − 4.27650I
u = −1.025520 − 0.116463I
a = −1.031170 − 0.432608I
b = −2.09741 − 0.72386I
−4.16025 − 3.63915I −10.15018 + 4.27650I
u = 0.917325 + 0.063901I
a = −0.133059 − 1.056750I
b = 0.317589 + 0.408768I
−2.00047 − 2.57631I −10.63302 + 4.45192I
u = 0.917325 − 0.063901I
a = −0.133059 + 1.056750I
b = 0.317589 − 0.408768I
−2.00047 + 2.57631I −10.63302 − 4.45192I
u = 1.065990 + 0.299185I
a = 0.322094 − 0.440855I
b = 1.56593 − 0.19350I
−5.13782 − 4.39791I −8.11131 + 3.98843I
u = 1.065990 − 0.299185I
a = 0.322094 + 0.440855I
b = 1.56593 + 0.19350I
−5.13782 + 4.39791I −8.11131 − 3.98843I
u = 1.082360 + 0.370781I
a = −0.558691 + 0.183985I
b = −2.00888 + 0.15748I
−8.00799 − 9.41273I −10.73207 + 7.33022I
u = 1.082360 − 0.370781I
a = −0.558691 − 0.183985I
b = −2.00888 − 0.15748I
−8.00799 + 9.41273I −10.73207 − 7.33022I
u = −0.852163
a = 0.572389
b = 1.20255
−1.51344 −5.97070
u = 1.178870 + 0.253014I
a = −0.540902 + 0.868497I
b = −1.39570 + 0.91291I
−9.53106 − 0.77090I −13.03537 + 0.66876I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.178870 − 0.253014I
a = −0.540902 − 0.868497I
b = −1.39570 − 0.91291I
−9.53106 + 0.77090I −13.03537 − 0.66876I
u = −0.465838 + 0.569982I
a = −0.135891 − 0.713585I
b = 0.582474 + 0.680739I
−4.25762 − 2.03075I −9.39588 + 0.30706I
u = −0.465838 − 0.569982I
a = −0.135891 + 0.713585I
b = 0.582474 − 0.680739I
−4.25762 + 2.03075I −9.39588 − 0.30706I
u = −0.680312 + 0.218264I
a = 0.215818 − 0.256120I
b = 0.392517 − 0.767490I
−1.43730 + 0.46103I −9.15571 − 0.89205I
u = −0.680312 − 0.218264I
a = 0.215818 + 0.256120I
b = 0.392517 + 0.767490I
−1.43730 − 0.46103I −9.15571 + 0.89205I
u = −0.294050 + 0.635512I
a = −0.93728 − 1.18603I
b = 0.435962 + 0.264963I
−3.72424 + 5.98943I −7.50022 − 6.65502I
u = −0.294050 − 0.635512I
a = −0.93728 + 1.18603I
b = 0.435962 − 0.264963I
−3.72424 − 5.98943I −7.50022 + 6.65502I
u = −0.300828 + 0.511616I
a = 0.900271 + 0.580279I
b = −0.322840 − 0.451012I
−0.88449 + 1.61128I −3.96504 − 4.05315I
u = −0.300828 − 0.511616I
a = 0.900271 − 0.580279I
b = −0.322840 + 0.451012I
−0.88449 − 1.61128I −3.96504 + 4.05315I
u = 1.60354 + 0.03866I
a = −0.577687 − 1.062600I
b = −0.73772 − 1.35775I
−9.29333 − 1.36083I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.60354 − 0.03866I
a = −0.577687 + 1.062600I
b = −0.73772 + 1.35775I
−9.29333 + 1.36083I 0
u = 0.003501 + 0.334247I
a = 2.06412 − 0.29075I
b = −0.222553 − 0.457483I
0.57956 + 1.37320I 1.27470 − 4.45868I
u = 0.003501 − 0.334247I
a = 2.06412 + 0.29075I
b = −0.222553 + 0.457483I
0.57956 − 1.37320I 1.27470 + 4.45868I
u = 0.220883 + 0.210533I
a = −2.72148 + 0.23613I
b = 0.536583 + 0.437480I
−0.27564 − 2.47765I 1.24066 + 5.09366I
u = 0.220883 − 0.210533I
a = −2.72148 − 0.23613I
b = 0.536583 − 0.437480I
−0.27564 + 2.47765I 1.24066 − 5.09366I
u = 1.70560
a = −2.31988
b = −2.94838
−10.7808 0
u = −1.71389 + 0.01340I
a = −0.457517 + 0.775429I
b = −0.66586 + 1.78211I
−11.48460 + 2.85990I 0
u = −1.71389 − 0.01340I
a = −0.457517 − 0.775429I
b = −0.66586 − 1.78211I
−11.48460 − 2.85990I 0
u = 1.73373 + 0.02857I
a = 2.85868 + 0.56360I
b = 3.62671 + 0.70465I
−14.0947 − 4.2255I 0
u = 1.73373 − 0.02857I
a = 2.85868 − 0.56360I
b = 3.62671 − 0.70465I
−14.0947 + 4.2255I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.74040 + 0.07931I
a = −2.19385 − 0.26897I
b = −3.06657 + 0.17165I
−15.1592 + 5.9753I 0
u = −1.74040 − 0.07931I
a = −2.19385 + 0.26897I
b = −3.06657 − 0.17165I
−15.1592 − 5.9753I 0
u = −1.74533 + 0.09973I
a = 2.64626 + 0.43864I
b = 3.66599 + 0.11964I
−18.0669 + 11.3850I 0
u = −1.74533 − 0.09973I
a = 2.64626 − 0.43864I
b = 3.66599 − 0.11964I
−18.0669 − 11.3850I 0
u = −1.76676 + 0.06022I
a = 1.65403 + 0.87991I
b = 2.26669 + 0.61564I
19.3219 + 2.0938I 0
u = −1.76676 − 0.06022I
a = 1.65403 − 0.87991I
b = 2.26669 − 0.61564I
19.3219 − 2.0938I 0
8
II. I
u
2
= h−au + b, a
2
+ a + 1, u
2
− u − 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
u + 1
a
8
=
−u
−u − 1
a
1
=
−u
−u
a
3
=
a
au
a
2
=
au + a
2au
a
6
=
u
u
a
5
=
a + u + 1
au + 2u
a
9
=
−u
−u − 1
a
4
=
a
au
a
4
=
a
au
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2au − 3a − u − 8
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
(u
2
+ u + 1)
2
c
3
, c
8
u
4
c
4
(u
2
− u + 1)
2
c
6
, c
7
(u
2
+ u − 1)
2
c
9
, c
10
, c
11
(u
2
− u − 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y
2
+ y + 1)
2
c
3
, c
8
y
4
c
6
, c
7
, c
9
c
10
, c
11
(y
2
− 3y + 1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = −0.500000 + 0.866025I
b = 0.309017 − 0.535233I
−0.98696 + 2.02988I −6.50000 − 1.52761I
u = −0.618034
a = −0.500000 − 0.866025I
b = 0.309017 + 0.535233I
−0.98696 − 2.02988I −6.50000 + 1.52761I
u = 1.61803
a = −0.500000 + 0.866025I
b = −0.80902 + 1.40126I
−8.88264 + 2.02988I −6.50000 − 5.40059I
u = 1.61803
a = −0.500000 − 0.866025I
b = −0.80902 − 1.40126I
−8.88264 − 2.02988I −6.50000 + 5.40059I
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u + 1)
2
)(u
36
+ 3u
35
+ ··· + 2u + 1)
c
2
((u
2
+ u + 1)
2
)(u
36
+ 19u
35
+ ··· + 2u + 1)
c
3
, c
8
u
4
(u
36
+ u
35
+ ··· − 32u − 16)
c
4
((u
2
− u + 1)
2
)(u
36
+ 3u
35
+ ··· + 2u + 1)
c
5
((u
2
+ u + 1)
2
)(u
36
− 3u
35
+ ··· − 156u + 41)
c
6
, c
7
((u
2
+ u − 1)
2
)(u
36
+ 3u
35
+ ··· − 3u
2
− 1)
c
9
, c
10
, c
11
((u
2
− u − 1)
2
)(u
36
+ 3u
35
+ ··· − 3u
2
− 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y
2
+ y + 1)
2
)(y
36
+ 19y
35
+ ··· + 2y + 1)
c
2
((y
2
+ y + 1)
2
)(y
36
− y
35
+ ··· − 46y + 1)
c
3
, c
8
y
4
(y
36
+ 25y
35
+ ··· + 896y + 256)
c
5
((y
2
+ y + 1)
2
)(y
36
− 21y
35
+ ··· + 12482y + 1681)
c
6
, c
7
, c
9
c
10
, c
11
((y
2
− 3y + 1)
2
)(y
36
− 49y
35
+ ··· + 6y + 1)
14
