11n
70
(K11n
70
)
A knot diagram
1
Linearized knot diagam
4 1 8 2 10 11 4 1 7 6 9
Solving Sequence
1,8 4,9
3 2 5 7 11 6 10
c
8
c
3
c
2
c
4
c
7
c
11
c
6
c
10
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h34u
10
− 4u
9
+ 399u
8
− 28u
7
+ 1229u
6
− 12u
5
+ 313u
4
+ 20u
3
− 168u
2
+ 161b − 217u − 33,
− 122u
10
− 33u
9
+ ··· + 161a + 412, u
11
+ 12u
9
+ 38u
7
+ 10u
5
− 11u
3
− 2u + 1i
I
u
2
= hb, u
4
− u
3
+ 2u
2
+ a − u + 1, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 16 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
= h34u
10
− 4u
9
+ · · · + 161b − 33, −122u
10
− 33u
9
+ · · · + 161a +
412, u
11
+ 12u
9
+ 38u
7
+ 10u
5
− 11u
3
− 2u + 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
0.757764u
10
+ 0.204969u
9
+ ··· − 2.13043u − 2.55901
−0.211180u
10
+ 0.0248447u
9
+ ··· + 1.34783u + 0.204969
a
9
=
1
−u
2
a
3
=
0.968944u
10
+ 0.180124u
9
+ ··· − 3.47826u − 2.76398
−0.211180u
10
+ 0.0248447u
9
+ ··· + 1.34783u + 0.204969
a
2
=
0.968944u
10
+ 0.180124u
9
+ ··· − 3.47826u − 2.76398
−0.366460u
10
− 0.0745342u
9
+ ··· + 1.95652u + 0.385093
a
5
=
−0.577640u
10
− 0.0496894u
9
+ ··· + 2.30435u + 0.590062
0.478261u
10
− 0.173913u
9
+ ··· − 0.434783u − 0.434783
a
7
=
0.385093u
10
+ 0.366460u
9
+ ··· − 1.86957u − 0.726708
−0.0496894u
10
− 0.111801u
9
+ ··· − 0.565217u + 0.577640
a
11
=
−u
u
3
+ u
a
6
=
0.335404u
10
+ 0.254658u
9
+ ··· − 1.43478u − 1.14907
−0.248447u
10
− 0.559006u
9
+ ··· − 0.826087u + 0.888199
a
10
=
u
7
− u
6
+ 7u
5
− 6u
4
+ 7u
3
− u
2
+ u
−u
9
+ u
8
− 8u
7
+ 7u
6
− 13u
5
+ 7u
4
− 2u
3
+ u
2
a
10
=
u
7
− u
6
+ 7u
5
− 6u
4
+ 7u
3
− u
2
+ u
−u
9
+ u
8
− 8u
7
+ 7u
6
− 13u
5
+ 7u
4
− 2u
3
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
265
161
u
10
−
88
161
u
9
+
449
23
u
8
−
157
23
u
7
+
9650
161
u
6
−
3162
161
u
5
+
1412
161
u
4
+
1728
161
u
3
−
436
23
u
2
+
215
23
u−
1048
161
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
11
− 6u
10
+ ··· + 2u − 1
c
2
u
11
+ 24u
10
+ ··· − 2u + 1
c
3
, c
7
u
11
− u
10
+ ··· − 64u − 32
c
5
, c
6
, c
10
u
11
+ 2u
10
− 4u
9
− 8u
8
+ 6u
7
+ 8u
6
− 8u
5
+ 9u
3
+ 2u
2
− 1
c
8
, c
11
u
11
+ 12u
9
+ 38u
7
+ 10u
5
− 11u
3
− 2u − 1
c
9
u
11
− 6u
10
+ ··· + 20u − 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
11
− 24y
10
+ ··· − 2y −1
c
2
y
11
− 116y
10
+ ··· + 306y −1
c
3
, c
7
y
11
+ 33y
10
+ ··· + 3584y −1024
c
5
, c
6
, c
10
y
11
− 12y
10
+ ··· + 4y −1
c
8
, c
11
y
11
+ 24y
10
+ ··· + 4y −1
c
9
y
11
− 12y
10
+ ··· + 540y −49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.038253 + 0.855092I
a = 0.943582 + 0.148881I
b = 0.736543 + 0.902004I
−5.67466 + 3.04693I −7.70492 − 3.06297I
u = 0.038253 − 0.855092I
a = 0.943582 − 0.148881I
b = 0.736543 − 0.902004I
−5.67466 − 3.04693I −7.70492 + 3.06297I
u = −0.723670
a = 2.50476
b = −2.03541
−8.89454 −10.0850
u = 0.652390
a = 0.388538
b = 0.487023
−2.74892 −1.30150
u = −0.167337 + 0.482250I
a = −0.485416 + 0.373126I
b = −0.326857 + 0.480234I
−0.105049 − 1.037840I −1.85452 + 6.48223I
u = −0.167337 − 0.482250I
a = −0.485416 − 0.373126I
b = −0.326857 − 0.480234I
−0.105049 + 1.037840I −1.85452 − 6.48223I
u = 0.330126
a = −3.63442
b = 0.726217
−2.26362 −4.99860
u = −0.00594 + 2.39914I
a = −0.131668 − 0.965580I
b = −0.73626 − 3.16232I
14.4281 + 6.7220I −9.53086 − 2.63003I
u = −0.00594 − 2.39914I
a = −0.131668 + 0.965580I
b = −0.73626 + 3.16232I
14.4281 − 6.7220I −9.53086 + 2.63003I
u = 0.00560 + 2.41642I
a = 0.044064 − 0.931881I
b = 0.23766 − 3.02607I
−18.1442 − 2.6778I −6.71737 + 2.37407I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.00560 − 2.41642I
a = 0.044064 + 0.931881I
b = 0.23766 + 3.02607I
−18.1442 + 2.6778I −6.71737 − 2.37407I
6
II. I
u
2
= hb, u
4
− u
3
+ 2u
2
+ a − u + 1, u
5
− u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
1
=
0
u
a
8
=
1
0
a
4
=
−u
4
+ u
3
− 2u
2
+ u − 1
0
a
9
=
1
−u
2
a
3
=
−u
4
+ u
3
− 2u
2
+ u − 1
0
a
2
=
−u
4
+ u
3
− 2u
2
+ u − 1
u
a
5
=
0
−u
a
7
=
1
0
a
11
=
−u
u
3
+ u
a
6
=
u
4
+ u
2
+ 1
−u
4
+ u
3
− u
2
− 1
a
10
=
u
2
+ 1
−u
2
a
10
=
u
2
+ 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
4
+ 4u
3
− 6u
2
+ 3u − 10
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
5
c
2
, c
4
(u + 1)
5
c
3
, c
7
u
5
c
5
, c
6
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
8
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
9
u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1
c
10
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
11
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
7
y
5
c
5
, c
6
, c
10
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
8
, c
11
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
9
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.339110 + 0.822375I
a = 0.428550 + 1.039280I
b = 0
−1.97403 − 1.53058I −5.05737 + 4.09764I
u = −0.339110 − 0.822375I
a = 0.428550 − 1.039280I
b = 0
−1.97403 + 1.53058I −5.05737 − 4.09764I
u = 0.766826
a = −1.30408
b = 0
−4.04602 −9.76980
u = 0.455697 + 1.200150I
a = −0.276511 + 0.728237I
b = 0
−7.51750 + 4.40083I −9.05774 − 4.18967I
u = 0.455697 − 1.200150I
a = −0.276511 − 0.728237I
b = 0
−7.51750 − 4.40083I −9.05774 + 4.18967I
10
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
11
− 6u
10
+ ··· + 2u − 1)
c
2
((u + 1)
5
)(u
11
+ 24u
10
+ ··· − 2u + 1)
c
3
, c
7
u
5
(u
11
− u
10
+ ··· − 64u − 32)
c
4
((u + 1)
5
)(u
11
− 6u
10
+ ··· + 2u − 1)
c
5
, c
6
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
· (u
11
+ 2u
10
− 4u
9
− 8u
8
+ 6u
7
+ 8u
6
− 8u
5
+ 9u
3
+ 2u
2
− 1)
c
8
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
11
+ 12u
9
+ ··· − 2u − 1)
c
9
(u
5
+ 3u
4
+ 4u
3
+ u
2
− u − 1)(u
11
− 6u
10
+ ··· + 20u − 7)
c
10
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
· (u
11
+ 2u
10
− 4u
9
− 8u
8
+ 6u
7
+ 8u
6
− 8u
5
+ 9u
3
+ 2u
2
− 1)
c
11
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
11
+ 12u
9
+ ··· − 2u − 1)
11
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
5
)(y
11
− 24y
10
+ ··· − 2y −1)
c
2
((y −1)
5
)(y
11
− 116y
10
+ ··· + 306y −1)
c
3
, c
7
y
5
(y
11
+ 33y
10
+ ··· + 3584y −1024)
c
5
, c
6
, c
10
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
11
− 12y
10
+ ··· + 4y −1)
c
8
, c
11
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
11
+ 24y
10
+ ··· + 4y −1)
c
9
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)(y
11
− 12y
10
+ ··· + 540y −49)
12
