11n
95
(K11n
95
)
A knot diagram
1
Linearized knot diagam
5 1 9 7 2 11 3 1 7 5 9
Solving Sequence
1,5
2 3
6,8
9 7 4 11 10
c
1
c
2
c
5
c
8
c
7
c
4
c
11
c
10
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
10
− 4u
9
+ 5u
8
+ 4u
7
− 20u
6
+ 24u
5
− 8u
4
− 8u
3
+ 7u
2
+ b − 1,
u
11
− 7u
10
+ 18u
9
− 12u
8
− 36u
7
+ 95u
6
− 84u
5
− 2u
4
+ 59u
3
− 31u
2
+ 2a − 9u + 9,
u
12
− 5u
11
+ 10u
10
− 4u
9
− 22u
8
+ 51u
7
− 48u
6
+ 10u
5
+ 23u
4
− 21u
3
+ 3u
2
+ 5u − 2i
I
u
2
= hu
5
+ 2u
4
− 2u
2
+ b − u + 1, −3u
5
− 5u
4
+ 2u
3
+ 8u
2
+ a + 2u − 6, u
6
+ 2u
5
− 3u
3
− 2u
2
+ 2u + 1i
I
u
3
= h−4u
4
a − 5u
3
a − 10u
4
− 4u
2
a − 7u
3
+ 3au + u
2
+ 11b + 5a + 13u − 4,
− 6u
4
+ u
2
a − 2u
3
+ a
2
+ 2au + 3u
2
+ a + 9u − 11, u
5
+ u
4
− u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 28 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
10
−4u
9
+· · ·+b −1, u
11
−7u
10
+· · ·+2a +9, u
12
−5u
11
+· · ·+5u −2i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
8
=
−
1
2
u
11
+
7
2
u
10
+ ··· +
9
2
u −
9
2
−u
10
+ 4u
9
− 5u
8
− 4u
7
+ 20u
6
− 24u
5
+ 8u
4
+ 8u
3
− 7u
2
+ 1
a
9
=
−
1
2
u
11
+
5
2
u
10
+ ··· +
9
2
u −
7
2
−u
10
+ 4u
9
− 5u
8
− 4u
7
+ 20u
6
− 24u
5
+ 8u
4
+ 8u
3
− 7u
2
+ 1
a
7
=
−
3
2
u
11
+
13
2
u
10
+ ··· +
11
2
u −
7
2
u
11
− 4u
10
+ 6u
9
+ u
8
− 18u
7
+ 30u
6
− 22u
5
+ 2u
4
+ 9u
3
− 6u
2
+ 1
a
4
=
−
1
2
u
11
+
3
2
u
10
+ ··· +
1
2
u +
1
2
u
10
− 3u
9
+ 2u
8
+ 6u
7
− 14u
6
+ 11u
5
+ 2u
4
− 8u
3
+ 4u
2
+ 2u − 1
a
11
=
3
2
u
11
−
13
2
u
10
+ ··· −
11
2
u +
7
2
−u
11
+ 4u
10
+ ··· + 3u − 1
a
10
=
3
2
u
11
−
13
2
u
10
+ ··· −
11
2
u +
7
2
−u
11
+ 5u
10
+ ··· + 5u − 3
a
10
=
3
2
u
11
−
13
2
u
10
+ ··· −
11
2
u +
7
2
−u
11
+ 5u
10
+ ··· + 5u − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −u
11
+ 6u
10
− 14u
9
+ 9u
8
+ 27u
7
− 75u
6
+ 75u
5
− 10u
4
− 49u
3
+ 40u
2
− 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
12
+ 5u
11
+ ··· − 5u − 2
c
2
u
12
+ 5u
11
+ ··· + 37u + 4
c
3
, c
4
, c
10
u
12
− u
11
+ ··· − 2u − 1
c
6
u
12
+ 12u
11
+ ··· + 240u + 32
c
7
u
12
+ 5u
10
+ ··· + 4u + 1
c
8
, c
11
u
12
+ 2u
11
+ ··· + 3u + 1
c
9
u
12
− 7u
11
+ ··· − 15u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
12
− 5y
11
+ ··· − 37y + 4
c
2
y
12
+ 7y
11
+ ··· − 353y + 16
c
3
, c
4
, c
10
y
12
− 19y
11
+ ··· + 2y + 1
c
6
y
12
− 6y
11
+ ··· − 7936y + 1024
c
7
y
12
+ 10y
11
+ ··· − 10y + 1
c
8
, c
11
y
12
− 6y
11
+ ··· − 25y + 1
c
9
y
12
− 3y
11
+ ··· − 689y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.634055 + 0.761588I
a = 2.40907 − 0.56101I
b = −1.061820 + 0.403224I
2.28232 − 3.09531I −6.37045 + 4.07458I
u = 0.634055 − 0.761588I
a = 2.40907 + 0.56101I
b = −1.061820 − 0.403224I
2.28232 + 3.09531I −6.37045 − 4.07458I
u = 0.706953 + 1.119620I
a = −2.03790 − 1.24403I
b = 1.33004 + 0.60517I
−1.55271 + 4.05634I −6.99284 − 2.54487I
u = 0.706953 − 1.119620I
a = −2.03790 + 1.24403I
b = 1.33004 − 0.60517I
−1.55271 − 4.05634I −6.99284 + 2.54487I
u = 1.184170 + 0.621257I
a = 1.075910 + 0.634900I
b = −0.732377 + 0.158790I
0.53240 − 2.26677I −5.92780 + 2.45213I
u = 1.184170 − 0.621257I
a = 1.075910 − 0.634900I
b = −0.732377 − 0.158790I
0.53240 + 2.26677I −5.92780 − 2.45213I
u = −0.585422 + 0.102144I
a = 0.251345 − 0.127948I
b = −0.388763 − 1.056570I
−0.76434 + 2.25567I −2.25761 − 1.65555I
u = −0.585422 − 0.102144I
a = 0.251345 + 0.127948I
b = −0.388763 + 1.056570I
−0.76434 − 2.25567I −2.25761 + 1.65555I
u = 1.13630 + 0.87513I
a = −2.57645 + 0.49107I
b = 1.35172 − 1.03292I
−2.90723 − 11.19710I −8.74463 + 6.08532I
u = 1.13630 − 0.87513I
a = −2.57645 − 0.49107I
b = 1.35172 + 1.03292I
−2.90723 + 11.19710I −8.74463 − 6.08532I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.531194
a = −1.14054
b = 0.227398
−0.766539 −13.0250
u = −1.68330
a = −0.603416
b = 0.774996
−10.8637 −2.38840
6
II. I
u
2
= hu
5
+ 2u
4
− 2u
2
+ b − u + 1, −3u
5
− 5u
4
+ 2u
3
+ 8u
2
+ a + 2u −
6, u
6
+ 2u
5
− 3u
3
− 2u
2
+ 2u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
8
=
3u
5
+ 5u
4
− 2u
3
− 8u
2
− 2u + 6
−u
5
− 2u
4
+ 2u
2
+ u − 1
a
9
=
2u
5
+ 3u
4
− 2u
3
− 6u
2
− u + 5
−u
5
− 2u
4
+ 2u
2
+ u − 1
a
7
=
2u
5
+ 3u
4
− u
3
− 5u
2
− 2u + 4
−u
5
− 2u
4
− u
3
+ 2u
2
+ 2u − 1
a
4
=
−3u
5
− 5u
4
+ 2u
3
+ 8u
2
+ 3u − 7
u
5
+ 2u
4
− 2u
2
− u + 2
a
11
=
−2u
5
− 3u
4
+ u
3
+ 5u
2
+ 2u − 4
−u
2
− u + 1
a
10
=
−2u
5
− 3u
4
+ u
3
+ 5u
2
+ 2u − 4
u
5
+ u
4
− u
3
− 3u
2
− u + 2
a
10
=
−2u
5
− 3u
4
+ u
3
+ 5u
2
+ 2u − 4
u
5
+ u
4
− u
3
− 3u
2
− u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
5
+ 7u
4
+ 4u
3
− 6u
2
− 9u − 7
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
+ 2u
5
− 3u
3
− 2u
2
+ 2u + 1
c
2
u
6
+ 4u
5
+ 8u
4
+ 15u
3
+ 16u
2
+ 8u + 1
c
3
u
6
+ u
5
− 2u
4
− 3u
3
− 5u
2
− 4u − 1
c
4
, c
10
u
6
− u
5
− 2u
4
+ 3u
3
− 5u
2
+ 4u − 1
c
5
u
6
− 2u
5
+ 3u
3
− 2u
2
− 2u + 1
c
6
u
6
+ u
5
− 2u
4
+ 2u
3
− 2u + 1
c
7
u
6
− 4u
3
− 5u
2
− 2u − 1
c
8
u
6
+ 2u
5
− 2u
3
− 2u
2
− u + 1
c
9
u
6
+ 4u
5
+ 5u
4
+ 2u
3
− u
2
− u + 1
c
11
u
6
− 2u
5
+ 2u
3
− 2u
2
+ u + 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
6
− 4y
5
+ 8y
4
− 15y
3
+ 16y
2
− 8y + 1
c
2
y
6
− 24y
4
− 31y
3
+ 32y
2
− 32y + 1
c
3
, c
4
, c
10
y
6
− 5y
5
+ 17y
3
+ 5y
2
− 6y + 1
c
6
y
6
− 5y
5
+ 2y
3
+ 4y
2
− 4y + 1
c
7
y
6
− 10y
4
− 18y
3
+ 9y
2
+ 6y + 1
c
8
, c
11
y
6
− 4y
5
+ 4y
4
+ 2y
3
− 5y + 1
c
9
y
6
− 6y
5
+ 7y
4
− 4y
3
+ 15y
2
− 3y + 1
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.907957 + 0.227043I
a = −0.348496 + 0.361180I
b = 0.355765 − 0.898533I
−1.45069 − 2.49752I −13.4121 + 4.8455I
u = 0.907957 − 0.227043I
a = −0.348496 − 0.361180I
b = 0.355765 + 0.898533I
−1.45069 + 2.49752I −13.4121 − 4.8455I
u = −0.934823 + 0.946305I
a = −2.43499 + 0.27700I
b = 1.42809 + 0.28813I
5.64849 + 3.45368I −2.17386 − 2.96497I
u = −0.934823 − 0.946305I
a = −2.43499 − 0.27700I
b = 1.42809 − 0.28813I
5.64849 − 3.45368I −2.17386 + 2.96497I
u = −1.52247
a = −0.116304
b = −0.452275
−11.4632 −16.4310
u = −0.423796
a = 5.68327
b = −1.11543
−6.80200 −4.39680
10
III.
I
u
3
= h−4u
4
a−10u
4
+· · ·+5a−4, −6u
4
−2u
3
+· · ·+a−11, u
5
+u
4
−u
2
+u+1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
8
=
a
0.363636au
4
+ 0.909091u
4
+ ··· − 0.454545a + 0.363636
a
9
=
0.363636au
4
+ 0.909091u
4
+ ··· + 0.545455a + 0.363636
0.363636au
4
+ 0.909091u
4
+ ··· − 0.454545a + 0.363636
a
7
=
0.272727au
4
+ 0.181818u
4
+ ··· + 0.909091a + 0.272727
0.181818au
4
+ 1.45455u
4
+ ··· − 0.727273a + 0.181818
a
4
=
−0.454545au
4
− 3.63636u
4
+ ··· − 0.181818a − 2.45455
0.0909091au
4
+ 1.72727u
4
+ ··· − 0.363636a + 1.09091
a
11
=
0.272727au
4
+ 0.181818u
4
+ ··· + 0.909091a + 0.272727
0.181818au
4
+ 1.45455u
4
+ ··· − 0.727273a + 0.181818
a
10
=
0.272727au
4
+ 0.181818u
4
+ ··· + 0.909091a + 0.272727
−0.272727au
4
+ 0.818182u
4
+ ··· − 0.909091a + 0.727273
a
10
=
0.272727au
4
+ 0.181818u
4
+ ··· + 0.909091a + 0.272727
−0.272727au
4
+ 0.818182u
4
+ ··· − 0.909091a + 0.727273
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
4
+ 4u
2
+ 4u − 18
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
5
− u
4
+ u
2
+ u − 1)
2
c
2
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
2
c
3
, c
4
, c
10
u
10
+ u
9
− 4u
8
− 4u
7
− 2u
6
+ 2u
5
+ 29u
4
+ 7u
3
− 48u
2
+ 12u − 1
c
6
(u − 1)
10
c
7
u
10
+ u
9
+ 2u
8
+ 6u
7
− 14u
6
+ 28u
5
− 59u
4
+ 53u
3
− 82u
2
+ 34u − 13
c
8
, c
11
u
10
+ 3u
9
+ 2u
8
− 8u
7
− 24u
6
− 16u
5
+ 25u
4
+ 71u
3
+ 78u
2
+ 40u + 7
c
9
(u
5
+ 3u
4
− 5u
2
− u + 3)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)
2
c
2
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
2
c
3
, c
4
, c
10
y
10
− 9y
9
+ ··· − 48y + 1
c
6
(y −1)
10
c
7
y
10
+ 3y
9
+ ··· + 976y + 169
c
8
, c
11
y
10
− 5y
9
+ ··· − 508y + 49
c
9
(y
5
− 9y
4
+ 28y
3
− 43y
2
+ 31y −9)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.758138 + 0.584034I
a = −1.87197 − 0.03044I
b = 0.452332 − 1.123840I
−4.75993 − 2.21397I −11.11432 + 4.22289I
u = 0.758138 + 0.584034I
a = −0.87798 − 2.02319I
b = 0.81806 + 1.53771I
−4.75993 − 2.21397I −11.11432 + 4.22289I
u = 0.758138 − 0.584034I
a = −1.87197 + 0.03044I
b = 0.452332 + 1.123840I
−4.75993 + 2.21397I −11.11432 − 4.22289I
u = 0.758138 − 0.584034I
a = −0.87798 + 2.02319I
b = 0.81806 − 1.53771I
−4.75993 + 2.21397I −11.11432 − 4.22289I
u = −0.935538 + 0.903908I
a = −1.88766 + 0.16400I
b = 0.868620 + 0.215856I
4.37856 + 3.33174I −10.08126 − 2.36228I
u = −0.935538 + 0.903908I
a = 2.70055 − 0.28054I
b = −1.72566 − 0.41266I
4.37856 + 3.33174I −10.08126 − 2.36228I
u = −0.935538 − 0.903908I
a = −1.88766 − 0.16400I
b = 0.868620 − 0.215856I
4.37856 − 3.33174I −10.08126 + 2.36228I
u = −0.935538 − 0.903908I
a = 2.70055 + 0.28054I
b = −1.72566 + 0.41266I
4.37856 − 3.33174I −10.08126 + 2.36228I
u = −0.645200
a = 3.94511
b = 0.340045
−7.46192 −19.6090
u = −0.645200
a = −4.07100
b = 1.83325
−7.46192 −19.6090
14
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
5
− u
4
+ u
2
+ u − 1)
2
(u
6
+ 2u
5
− 3u
3
− 2u
2
+ 2u + 1)
· (u
12
+ 5u
11
+ ··· − 5u − 2)
c
2
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)
2
· (u
6
+ 4u
5
+ ··· + 8u + 1)(u
12
+ 5u
11
+ ··· + 37u + 4)
c
3
(u
6
+ u
5
− 2u
4
− 3u
3
− 5u
2
− 4u − 1)
· (u
10
+ u
9
− 4u
8
− 4u
7
− 2u
6
+ 2u
5
+ 29u
4
+ 7u
3
− 48u
2
+ 12u − 1)
· (u
12
− u
11
+ ··· − 2u − 1)
c
4
, c
10
(u
6
− u
5
− 2u
4
+ 3u
3
− 5u
2
+ 4u − 1)
· (u
10
+ u
9
− 4u
8
− 4u
7
− 2u
6
+ 2u
5
+ 29u
4
+ 7u
3
− 48u
2
+ 12u − 1)
· (u
12
− u
11
+ ··· − 2u − 1)
c
5
(u
5
− u
4
+ u
2
+ u − 1)
2
(u
6
− 2u
5
+ 3u
3
− 2u
2
− 2u + 1)
· (u
12
+ 5u
11
+ ··· − 5u − 2)
c
6
((u − 1)
10
)(u
6
+ u
5
+ ··· − 2u + 1)(u
12
+ 12u
11
+ ··· + 240u + 32)
c
7
(u
6
− 4u
3
− 5u
2
− 2u − 1)
· (u
10
+ u
9
+ 2u
8
+ 6u
7
− 14u
6
+ 28u
5
− 59u
4
+ 53u
3
− 82u
2
+ 34u − 13)
· (u
12
+ 5u
10
+ ··· + 4u + 1)
c
8
(u
6
+ 2u
5
− 2u
3
− 2u
2
− u + 1)
· (u
10
+ 3u
9
+ 2u
8
− 8u
7
− 24u
6
− 16u
5
+ 25u
4
+ 71u
3
+ 78u
2
+ 40u + 7)
· (u
12
+ 2u
11
+ ··· + 3u + 1)
c
9
(u
5
+ 3u
4
− 5u
2
− u + 3)
2
(u
6
+ 4u
5
+ 5u
4
+ 2u
3
− u
2
− u + 1)
· (u
12
− 7u
11
+ ··· − 15u − 4)
c
11
(u
6
− 2u
5
+ 2u
3
− 2u
2
+ u + 1)
· (u
10
+ 3u
9
+ 2u
8
− 8u
7
− 24u
6
− 16u
5
+ 25u
4
+ 71u
3
+ 78u
2
+ 40u + 7)
· (u
12
+ 2u
11
+ ··· + 3u + 1)
15
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)
2
· (y
6
− 4y
5
+ ··· − 8y + 1)(y
12
− 5y
11
+ ··· − 37y + 4)
c
2
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)
2
· (y
6
− 24y
4
+ ··· − 32y + 1)(y
12
+ 7y
11
+ ··· − 353y + 16)
c
3
, c
4
, c
10
(y
6
− 5y
5
+ 17y
3
+ 5y
2
− 6y + 1)(y
10
− 9y
9
+ ··· − 48y + 1)
· (y
12
− 19y
11
+ ··· + 2y + 1)
c
6
(y −1)
10
(y
6
− 5y
5
+ 2y
3
+ 4y
2
− 4y + 1)
· (y
12
− 6y
11
+ ··· − 7936y + 1024)
c
7
(y
6
− 10y
4
− 18y
3
+ 9y
2
+ 6y + 1)(y
10
+ 3y
9
+ ··· + 976y + 169)
· (y
12
+ 10y
11
+ ··· − 10y + 1)
c
8
, c
11
(y
6
− 4y
5
+ 4y
4
+ 2y
3
− 5y + 1)(y
10
− 5y
9
+ ··· − 508y + 49)
· (y
12
− 6y
11
+ ··· − 25y + 1)
c
9
(y
5
− 9y
4
+ 28y
3
− 43y
2
+ 31y −9)
2
· (y
6
− 6y
5
+ ··· − 3y + 1)(y
12
− 3y
11
+ ··· − 689y + 16)
16
