11a
260
(K11a
260
)
A knot diagram
1
Linearized knot diagam
4 7 1 2 10 9 3 11 6 5 8
Solving Sequence
5,10
6
2,11
4 1 3 9 7 8
c
5
c
10
c
4
c
1
c
3
c
9
c
6
c
8
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
34
− u
33
+ ··· + b + 1, −u
37
+ 2u
36
+ ··· + a − 1, u
38
− 2u
37
+ ··· + u + 1i
I
u
2
= hb + 1, −u
3
+ u
2
+ a − 3u + 1, u
4
− u
3
+ 3u
2
− 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 42 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
34
−u
33
+· · · +b + 1, −u
37
+2u
36
+· · · +a − 1, u
38
−2u
37
+· · · +u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
2
=
u
37
− 2u
36
+ ··· + 5u + 1
−u
34
+ u
33
+ ··· − u − 1
a
11
=
−u
u
a
4
=
u
37
− 2u
36
+ ··· + 4u + 1
−u
34
+ u
33
+ ··· − 2u − 1
a
1
=
−u
9
− 4u
7
− 3u
5
+ 2u
3
− u
u
9
+ 5u
7
+ 7u
5
+ 2u
3
+ u
a
3
=
u
37
− 2u
36
+ ··· + 8u
2
+ u
−u
35
− u
34
+ ··· − 2u − 1
a
9
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
4
+ 2u
2
a
8
=
−u
5
− 2u
3
+ u
u
5
+ 3u
3
+ u
a
8
=
−u
5
− 2u
3
+ u
u
5
+ 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −u
37
+ 2u
36
+ ··· + 8u − 5
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
u
38
− 5u
37
+ ··· + 3u − 1
c
2
, c
7
u
38
− u
37
+ ··· − 8u − 16
c
5
, c
6
, c
9
c
10
u
38
− 2u
37
+ ··· + u + 1
c
8
, c
11
u
38
+ 6u
37
+ ··· + 93u + 19
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
y
38
− 39y
37
+ ··· − 23y + 1
c
2
, c
7
y
38
− 27y
37
+ ··· − 64y + 256
c
5
, c
6
, c
9
c
10
y
38
+ 42y
37
+ ··· + 3y + 1
c
8
, c
11
y
38
+ 30y
37
+ ··· − 13361y + 361
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.331390 + 0.800737I
a = −1.08027 + 1.42658I
b = 1.43349 − 0.08457I
−4.40003 + 3.17772I −9.24672 − 4.52124I
u = −0.331390 − 0.800737I
a = −1.08027 − 1.42658I
b = 1.43349 + 0.08457I
−4.40003 − 3.17772I −9.24672 + 4.52124I
u = 0.632534 + 0.587679I
a = 0.72801 − 2.04747I
b = 1.54993 + 0.28338I
−10.96810 − 8.77029I −12.03440 + 6.55590I
u = 0.632534 − 0.587679I
a = 0.72801 + 2.04747I
b = 1.54993 − 0.28338I
−10.96810 + 8.77029I −12.03440 − 6.55590I
u = 0.595823 + 0.532540I
a = −0.88414 + 1.11716I
b = −0.536492 − 0.820187I
−4.14241 − 4.72017I −10.42521 + 6.54233I
u = 0.595823 − 0.532540I
a = −0.88414 − 1.11716I
b = −0.536492 + 0.820187I
−4.14241 + 4.72017I −10.42521 − 6.54233I
u = −0.607436 + 0.495757I
a = −1.52782 − 1.27199I
b = −1.46016 + 0.02727I
−6.41754 + 2.06753I −11.71336 − 3.34688I
u = −0.607436 − 0.495757I
a = −1.52782 + 1.27199I
b = −1.46016 − 0.02727I
−6.41754 − 2.06753I −11.71336 + 3.34688I
u = 0.670848 + 0.404516I
a = 0.817417 − 0.255182I
b = 1.56238 − 0.24922I
−11.51120 + 4.37869I −13.39153 − 0.68267I
u = 0.670848 − 0.404516I
a = 0.817417 + 0.255182I
b = 1.56238 + 0.24922I
−11.51120 − 4.37869I −13.39153 + 0.68267I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.603069 + 0.453875I
a = 0.323964 − 0.069070I
b = −0.604946 + 0.776470I
−4.37423 + 0.63202I −11.49824 + 0.19498I
u = 0.603069 − 0.453875I
a = 0.323964 + 0.069070I
b = −0.604946 − 0.776470I
−4.37423 − 0.63202I −11.49824 − 0.19498I
u = −0.458515 + 0.496866I
a = 0.735714 + 0.425841I
b = 0.295812 − 0.100934I
−0.58212 + 1.61412I −3.79024 − 4.58395I
u = −0.458515 − 0.496866I
a = 0.735714 − 0.425841I
b = 0.295812 + 0.100934I
−0.58212 − 1.61412I −3.79024 + 4.58395I
u = −0.166029 + 0.605237I
a = 0.54999 − 1.37311I
b = −0.197084 + 0.433714I
0.92221 + 1.54825I −1.51822 − 6.63292I
u = −0.166029 − 0.605237I
a = 0.54999 + 1.37311I
b = −0.197084 − 0.433714I
0.92221 − 1.54825I −1.51822 + 6.63292I
u = −0.599131
a = 0.814584
b = 1.47212
−6.92604 −14.5410
u = 0.19248 + 1.43542I
a = −0.557197 − 0.105570I
b = 1.57803 − 0.19884I
−5.62113 + 1.29652I 0
u = 0.19248 − 1.43542I
a = −0.557197 + 0.105570I
b = 1.57803 + 0.19884I
−5.62113 − 1.29652I 0
u = 0.16452 + 1.49701I
a = 0.870156 − 0.798495I
b = −0.700266 + 0.746539I
2.00271 − 2.06597I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.16452 − 1.49701I
a = 0.870156 + 0.798495I
b = −0.700266 − 0.746539I
2.00271 + 2.06597I 0
u = 0.02138 + 1.51704I
a = 0.79272 + 1.61255I
b = −1.125240 − 0.315445I
5.07701 − 1.17536I 0
u = 0.02138 − 1.51704I
a = 0.79272 − 1.61255I
b = −1.125240 + 0.315445I
5.07701 + 1.17536I 0
u = −0.17777 + 1.51557I
a = −0.154126 − 1.301400I
b = −1.46693 + 0.08311I
0.19906 + 4.87289I 0
u = −0.17777 − 1.51557I
a = −0.154126 + 1.301400I
b = −1.46693 − 0.08311I
0.19906 − 4.87289I 0
u = −0.12286 + 1.53872I
a = 0.329499 + 0.682733I
b = 0.371714 − 0.234405I
6.26465 + 3.65085I 0
u = −0.12286 − 1.53872I
a = 0.329499 − 0.682733I
b = 0.371714 + 0.234405I
6.26465 − 3.65085I 0
u = 0.17843 + 1.53412I
a = −0.32146 + 1.73410I
b = −0.481260 − 0.864252I
2.69845 − 7.51312I 0
u = 0.17843 − 1.53412I
a = −0.32146 − 1.73410I
b = −0.481260 + 0.864252I
2.69845 + 7.51312I 0
u = −0.03636 + 1.55804I
a = 0.36918 − 1.51241I
b = −0.071818 + 0.599117I
8.24732 + 2.22241I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.03636 − 1.55804I
a = 0.36918 + 1.51241I
b = −0.071818 − 0.599117I
8.24732 − 2.22241I 0
u = 0.160891 + 0.403134I
a = −0.03733 + 2.61389I
b = −1.072260 − 0.128378I
−1.45280 − 0.68265I −5.04350 − 1.82049I
u = 0.160891 − 0.403134I
a = −0.03733 − 2.61389I
b = −1.072260 + 0.128378I
−1.45280 + 0.68265I −5.04350 + 1.82049I
u = 0.19856 + 1.55611I
a = −0.54782 − 2.02596I
b = 1.53547 + 0.31265I
−3.85806 − 11.81890I 0
u = 0.19856 − 1.55611I
a = −0.54782 + 2.02596I
b = 1.53547 − 0.31265I
−3.85806 + 11.81890I 0
u = −0.07622 + 1.60929I
a = −1.71521 + 1.01252I
b = 1.362500 − 0.126997I
3.79825 + 4.60582I 0
u = −0.07622 − 1.60929I
a = −1.71521 − 1.01252I
b = 1.362500 + 0.126997I
3.79825 − 4.60582I 0
u = −0.284804
a = 0.802881
b = −0.417854
−0.765706 −13.9120
8
II. I
u
2
= hb + 1, −u
3
+ u
2
+ a − 3u + 1, u
4
− u
3
+ 3u
2
− 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
2
=
u
3
− u
2
+ 3u − 1
−1
a
11
=
−u
u
a
4
=
u
3
− u
2
+ 3u
−1
a
1
=
−1
0
a
3
=
u
3
− u
2
+ 3u − 1
−1
a
9
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
3
− u
2
+ 2u − 1
a
8
=
u
2
+ 1
u
3
− u
2
+ 2u − 1
a
8
=
u
2
+ 1
u
3
− u
2
+ 2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5u
3
− 5u
2
+ 14u − 16
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
c
2
, c
7
u
4
c
3
, c
4
(u + 1)
4
c
5
, c
6
u
4
− u
3
+ 3u
2
− 2u + 1
c
8
u
4
− u
3
+ u
2
+ 1
c
9
, c
10
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
11
u
4
+ u
3
+ u
2
+ 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
(y −1)
4
c
2
, c
7
y
4
c
5
, c
6
, c
9
c
10
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
8
, c
11
y
4
+ y
3
+ 3y
2
+ 2y + 1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395123 + 0.506844I
a = 0.043315 + 1.227190I
b = −1.00000
−1.85594 − 1.41510I −11.17855 + 5.62908I
u = 0.395123 − 0.506844I
a = 0.043315 − 1.227190I
b = −1.00000
−1.85594 + 1.41510I −11.17855 − 5.62908I
u = 0.10488 + 1.55249I
a = 0.956685 + 0.641200I
b = −1.00000
5.14581 − 3.16396I −6.32145 + 1.65351I
u = 0.10488 − 1.55249I
a = 0.956685 − 0.641200I
b = −1.00000
5.14581 + 3.16396I −6.32145 − 1.65351I
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
38
− 5u
37
+ ··· + 3u − 1)
c
2
, c
7
u
4
(u
38
− u
37
+ ··· − 8u − 16)
c
3
, c
4
((u + 1)
4
)(u
38
− 5u
37
+ ··· + 3u − 1)
c
5
, c
6
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
38
− 2u
37
+ ··· + u + 1)
c
8
(u
4
− u
3
+ u
2
+ 1)(u
38
+ 6u
37
+ ··· + 93u + 19)
c
9
, c
10
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
38
− 2u
37
+ ··· + u + 1)
c
11
(u
4
+ u
3
+ u
2
+ 1)(u
38
+ 6u
37
+ ··· + 93u + 19)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
((y −1)
4
)(y
38
− 39y
37
+ ··· − 23y + 1)
c
2
, c
7
y
4
(y
38
− 27y
37
+ ··· − 64y + 256)
c
5
, c
6
, c
9
c
10
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
38
+ 42y
37
+ ··· + 3y + 1)
c
8
, c
11
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
38
+ 30y
37
+ ··· − 13361y + 361)
14
