11a
200
(K11a
200
)
A knot diagram
1
Linearized knot diagam
6 1 8 10 7 2 4 3 11 5 9
Solving Sequence
1,6
2 3 7
5,9
8 11 10 4
c
1
c
2
c
6
c
5
c
8
c
11
c
9
c
4
c
3
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
2
+ b, −u
13
+ u
11
+ u
10
− 4u
9
+ 3u
7
+ 4u
6
− 4u
5
− 2u
4
+ 3u
3
+ 3u
2
+ 2a + u − 3,
u
14
− 2u
12
+ 6u
10
− u
9
− 8u
8
+ u
7
+ 10u
6
− 2u
5
− 9u
4
+ u
3
+ 4u
2
+ u − 1i
I
u
2
= h11044796022984u
35
+ 15849610659410u
34
+ ··· + 5213417579383b − 19244867589607,
− 20597520331605u
35
− 27230487651401u
34
+ ··· + 5213417579383a + 39323690068543,
u
36
+ u
35
+ ··· − 2u + 1i
I
u
3
= hu
2
+ b, −u
2
+ a − u + 1, u
4
− u
2
+ 1i
I
u
4
= h−u
2
+ b + 1, a − u − 1, u
4
− u
2
+ 1i
* 4 irreducible components of dim
C
= 0, with total 58 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
2
+ b, −u
13
+ u
11
+ · · · + 2a − 3, u
14
− 2u
12
+ · · · + u − 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
7
=
−u
−u
3
+ u
a
5
=
u
3
u
5
− u
3
+ u
a
9
=
1
2
u
13
−
1
2
u
11
+ ··· −
1
2
u +
3
2
−u
2
a
8
=
−u
6
+ u
4
− 2u
2
+ 1
1
2
u
12
+
1
2
u
11
+ ··· − u +
1
2
a
11
=
1
2
u
13
−
1
2
u
12
+ ··· +
1
2
u + 1
−u
4
a
10
=
1
2
u
13
−
1
2
u
12
+ ··· +
1
2
u + 1
−u
6
− u
2
a
4
=
−
1
2
u
13
+
1
2
u
11
+ ··· +
1
2
u +
1
2
−u
7
+ u
5
− 2u
3
+ u
a
4
=
−
1
2
u
13
+
1
2
u
11
+ ··· +
1
2
u +
1
2
−u
7
+ u
5
− 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= u
13
+ u
11
+ u
10
+ 2u
9
− 4u
8
+ 7u
7
+ 4u
6
− 4u
5
− 10u
4
+ 11u
3
+ 5u
2
− 9u − 13
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
10
u
14
− 2u
12
+ 6u
10
+ u
9
− 8u
8
− u
7
+ 10u
6
+ 2u
5
− 9u
4
− u
3
+ 4u
2
− u − 1
c
2
, c
5
, c
9
c
11
u
14
+ 4u
13
+ ··· + 9u + 1
c
3
, c
7
, c
8
u
14
− 5u
13
+ ··· + 8u − 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
y
14
− 4y
13
+ ··· − 9y + 1
c
2
, c
5
, c
9
c
11
y
14
+ 16y
13
+ ··· − 17y + 1
c
3
, c
7
, c
8
y
14
+ 13y
13
+ ··· − 136y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.950366
a = −0.787840
b = −0.903195
−4.35310 −20.7960
u = 0.934140 + 0.165940I
a = −0.833929 − 0.848131I
b = −0.845081 − 0.310022I
−0.76895 − 3.05854I −15.2345 + 4.4220I
u = 0.934140 − 0.165940I
a = −0.833929 + 0.848131I
b = −0.845081 + 0.310022I
−0.76895 + 3.05854I −15.2345 − 4.4220I
u = −0.861511 + 0.818074I
a = −0.43826 − 2.03212I
b = −0.072957 + 1.409560I
6.31411 + 3.07801I −6.07433 − 2.66063I
u = −0.861511 − 0.818074I
a = −0.43826 + 2.03212I
b = −0.072957 − 1.409560I
6.31411 − 3.07801I −6.07433 + 2.66063I
u = 0.771614 + 0.940827I
a = −0.178207 + 1.387930I
b = 0.28977 − 1.45191I
14.2923 + 0.8767I −3.65848 + 1.44035I
u = 0.771614 − 0.940827I
a = −0.178207 − 1.387930I
b = 0.28977 + 1.45191I
14.2923 − 0.8767I −3.65848 − 1.44035I
u = 0.965155 + 0.787055I
a = −1.13614 + 2.04636I
b = −0.31207 − 1.51926I
5.64578 − 9.04247I −7.75570 + 7.54934I
u = 0.965155 − 0.787055I
a = −1.13614 − 2.04636I
b = −0.31207 + 1.51926I
5.64578 + 9.04247I −7.75570 − 7.54934I
u = −0.499772 + 0.464713I
a = 1.46491 − 0.18431I
b = −0.033814 + 0.464501I
2.42034 + 2.01219I −5.03531 − 3.18410I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.499772 − 0.464713I
a = 1.46491 + 0.18431I
b = −0.033814 − 0.464501I
2.42034 − 2.01219I −5.03531 + 3.18410I
u = −1.055500 + 0.798468I
a = −1.43912 − 1.62917I
b = −0.47652 + 1.68556I
12.4304 + 13.7591I −6.11753 − 7.81595I
u = −1.055500 − 0.798468I
a = −1.43912 + 1.62917I
b = −0.47652 − 1.68556I
12.4304 − 13.7591I −6.11753 + 7.81595I
u = 0.442106
a = 0.909335
b = −0.195458
−0.647887 −15.4520
6
II.
I
u
2
= h1.10×10
13
u
35
+1.58×10
13
u
34
+· · ·+5.21×10
12
b−1.92×10
13
, −2.06×
10
13
u
35
−2.72×10
13
u
34
+· · ·+5.21×10
12
a+3.93×10
13
, u
36
+u
35
+· · ·−2u+1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
7
=
−u
−u
3
+ u
a
5
=
u
3
u
5
− u
3
+ u
a
9
=
3.95087u
35
+ 5.22315u
34
+ ··· + 0.910129u − 7.54279
−2.11853u
35
− 3.04016u
34
+ ··· − 2.06187u + 3.69141
a
8
=
2.27927u
35
+ 2.86643u
34
+ ··· − 0.0438616u − 4.50374
−2.47612u
35
− 3.71564u
34
+ ··· − 2.03874u + 4.69444
a
11
=
−2.30128u
35
− 3.92404u
34
+ ··· + 1.16386u + 3.30524
−2.34203u
35
− 3.45720u
34
+ ··· − 1.18510u + 5.47128
a
10
=
−1.79396u
35
− 3.71712u
34
+ ··· + 0.968286u + 3.13328
−1.97576u
35
− 2.57126u
34
+ ··· − 0.845464u + 4.81490
a
4
=
4.69444u
35
+ 7.17055u
34
+ ··· − 0.960342u − 7.35013
0.587159u
35
+ 0.875255u
34
+ ··· + 0.0548089u − 2.27927
a
4
=
4.69444u
35
+ 7.17055u
34
+ ··· − 0.960342u − 7.35013
0.587159u
35
+ 0.875255u
34
+ ··· + 0.0548089u − 2.27927
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
23301194605224
5213417579383
u
35
+
35979605140824
5213417579383
u
34
+ ··· +
21746030582642
5213417579383
u −
88939694002132
5213417579383
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
10
u
36
− u
35
+ ··· + 2u + 1
c
2
, c
5
, c
9
c
11
u
36
+ 11u
35
+ ··· + 2u + 1
c
3
, c
7
, c
8
(u
18
+ 2u
17
+ ··· + 4u + 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
y
36
− 11y
35
+ ··· − 2y + 1
c
2
, c
5
, c
9
c
11
y
36
+ 29y
35
+ ··· − 86y + 1
c
3
, c
7
, c
8
(y
18
+ 20y
17
+ ··· − 6y + 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.812169 + 0.607179I
a = 0.671292 + 0.171361I
b = 0.144113 − 0.052398I
1.69238 + 2.34050I −6.11304 − 4.51747I
u = −0.812169 − 0.607179I
a = 0.671292 − 0.171361I
b = 0.144113 + 0.052398I
1.69238 − 2.34050I −6.11304 + 4.51747I
u = −0.946964 + 0.251366I
a = −1.156670 − 0.366820I
b = −0.466192 + 1.168730I
−0.82103 + 4.83091I −14.6707 − 7.5484I
u = −0.946964 − 0.251366I
a = −1.156670 + 0.366820I
b = −0.466192 − 1.168730I
−0.82103 − 4.83091I −14.6707 + 7.5484I
u = 0.730851 + 0.539733I
a = 0.924619 − 0.162335I
b = −0.543811 + 0.535375I
−0.218413 + 0.059150I −13.30450 − 1.20964I
u = 0.730851 − 0.539733I
a = 0.924619 + 0.162335I
b = −0.543811 − 0.535375I
−0.218413 − 0.059150I −13.30450 + 1.20964I
u = −0.942145 + 0.554752I
a = 0.794075 − 0.773298I
b = −0.251878 + 0.053017I
1.36390 + 2.08554I −9.56168 − 2.20642I
u = −0.942145 − 0.554752I
a = 0.794075 + 0.773298I
b = −0.251878 − 0.053017I
1.36390 − 2.08554I −9.56168 + 2.20642I
u = −0.040087 + 0.897653I
a = 0.20998 − 1.45458I
b = −0.11524 + 1.50569I
9.19677 + 3.10798I −3.50971 − 2.64457I
u = −0.040087 − 0.897653I
a = 0.20998 + 1.45458I
b = −0.11524 − 1.50569I
9.19677 − 3.10798I −3.50971 + 2.64457I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.928565 + 0.629318I
a = −0.112955 + 1.243650I
b = −0.833557 − 0.476070I
−0.82103 − 4.83091I −14.6707 + 7.5484I
u = 0.928565 − 0.629318I
a = −0.112955 − 1.243650I
b = −0.833557 + 0.476070I
−0.82103 + 4.83091I −14.6707 − 7.5484I
u = 0.808373 + 0.331144I
a = 1.193410 − 0.008565I
b = −0.242832 + 0.788929I
−0.218413 − 0.059150I −13.30450 + 1.20964I
u = 0.808373 − 0.331144I
a = 1.193410 + 0.008565I
b = −0.242832 − 0.788929I
−0.218413 + 0.059150I −13.30450 − 1.20964I
u = −0.823976 + 0.805806I
a = 0.742818 − 0.074215I
b = −1.25591 − 0.81116I
5.35610 − 1.19422I −7.28872 + 0.77166I
u = −0.823976 − 0.805806I
a = 0.742818 + 0.074215I
b = −1.25591 + 0.81116I
5.35610 + 1.19422I −7.28872 − 0.77166I
u = 0.812050 + 0.836206I
a = 0.83079 − 1.99521I
b = −0.21419 + 1.47787I
6.12069 + 2.97589I −6.53141 − 2.59059I
u = 0.812050 − 0.836206I
a = 0.83079 + 1.99521I
b = −0.21419 − 1.47787I
6.12069 − 2.97589I −6.53141 + 2.59059I
u = −0.729822 + 0.942917I
a = 0.48397 + 1.64428I
b = −0.39833 − 1.70046I
13.4573 − 7.3548I −4.66879 + 3.22304I
u = −0.729822 − 0.942917I
a = 0.48397 − 1.64428I
b = −0.39833 + 1.70046I
13.4573 + 7.3548I −4.66879 − 3.22304I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.185250 + 0.286307I
a = −0.870802 − 0.153065I
b = −0.29933 − 1.46346I
4.97567 − 7.12729I −8.35142 + 6.02297I
u = 1.185250 − 0.286307I
a = −0.870802 + 0.153065I
b = −0.29933 + 1.46346I
4.97567 + 7.12729I −8.35142 − 6.02297I
u = −0.923985 + 0.799724I
a = 1.36056 + 1.78580I
b = 0.039816 − 1.358080I
6.12069 + 2.97589I −6.53141 − 2.59059I
u = −0.923985 − 0.799724I
a = 1.36056 − 1.78580I
b = 0.039816 + 1.358080I
6.12069 − 2.97589I −6.53141 + 2.59059I
u = −0.946857 + 0.772796I
a = −0.283619 − 1.357530I
b = −1.32284 + 0.67869I
4.97567 + 7.12729I −8.35142 − 6.02297I
u = −0.946857 − 0.772796I
a = −0.283619 + 1.357530I
b = −1.32284 − 0.67869I
4.97567 − 7.12729I −8.35142 + 6.02297I
u = −1.172820 + 0.345817I
a = 1.063490 − 0.229177I
b = −0.029612 − 1.327930I
5.35610 + 1.19422I −7.28872 − 0.77166I
u = −1.172820 − 0.345817I
a = 1.063490 + 0.229177I
b = −0.029612 + 1.327930I
5.35610 − 1.19422I −7.28872 + 0.77166I
u = 0.901479 + 0.835123I
a = 0.216921 − 0.412346I
b = 0.804174 − 0.071969I
9.19677 − 3.10798I −3.50971 + 2.64457I
u = 0.901479 − 0.835123I
a = 0.216921 + 0.412346I
b = 0.804174 + 0.071969I
9.19677 + 3.10798I −3.50971 − 2.64457I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.035570 + 0.821025I
a = 1.38875 − 1.34795I
b = 0.35645 + 1.37632I
13.4573 − 7.3548I −4.66879 + 3.22304I
u = 1.035570 − 0.821025I
a = 1.38875 + 1.34795I
b = 0.35645 − 1.37632I
13.4573 + 7.3548I −4.66879 − 3.22304I
u = 0.504616 + 0.052532I
a = −2.34048 + 1.62886I
b = −0.579887 − 1.045310I
1.36390 − 2.08554I −9.56168 + 2.20642I
u = 0.504616 − 0.052532I
a = −2.34048 − 1.62886I
b = −0.579887 + 1.045310I
1.36390 + 2.08554I −9.56168 − 2.20642I
u = −0.067934 + 0.385652I
a = 1.38386 + 2.45598I
b = −0.290953 − 0.986264I
1.69238 − 2.34050I −6.11304 + 4.51747I
u = −0.067934 − 0.385652I
a = 1.38386 − 2.45598I
b = −0.290953 + 0.986264I
1.69238 + 2.34050I −6.11304 − 4.51747I
13
III. I
u
3
= hu
2
+ b, −u
2
+ a − u + 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
7
=
−u
−u
3
+ u
a
5
=
u
3
0
a
9
=
u
2
+ u − 1
−u
2
a
8
=
u
2
− 1
−u
3
− u
2
+ u
a
11
=
u
3
−u
2
+ 1
a
10
=
u
3
+ u
2
− 1
−u
2
+ 1
a
4
=
−u
2
+ u + 1
u
3
− u
a
4
=
−u
2
+ u + 1
u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8u
2
− 12
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
10
u
4
− u
2
+ 1
c
2
, c
11
(u
2
+ u + 1)
2
c
3
, c
7
, c
8
(u
2
+ 1)
2
c
5
, c
9
(u
2
− u + 1)
2
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
(y
2
− y + 1)
2
c
2
, c
5
, c
9
c
11
(y
2
+ y + 1)
2
c
3
, c
7
, c
8
(y + 1)
4
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = 0.36603 + 1.36603I
b = −0.500000 − 0.866025I
1.64493 − 4.05977I −8.00000 + 6.92820I
u = 0.866025 − 0.500000I
a = 0.36603 − 1.36603I
b = −0.500000 + 0.866025I
1.64493 + 4.05977I −8.00000 − 6.92820I
u = −0.866025 + 0.500000I
a = −1.36603 − 0.36603I
b = −0.500000 + 0.866025I
1.64493 + 4.05977I −8.00000 − 6.92820I
u = −0.866025 − 0.500000I
a = −1.36603 + 0.36603I
b = −0.500000 − 0.866025I
1.64493 − 4.05977I −8.00000 + 6.92820I
17
IV. I
u
4
= h−u
2
+ b + 1, a − u − 1, u
4
− u
2
+ 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
7
=
−u
−u
3
+ u
a
5
=
u
3
0
a
9
=
u + 1
u
2
− 1
a
8
=
1
−u
3
+ u
2
+ u − 1
a
11
=
−u
3
− u
2
+ u + 2
u
2
a
10
=
−u
3
− 2u
2
+ u + 2
u
2
a
4
=
−u
3
− u
2
+ 1
u
a
4
=
−u
3
− u
2
+ 1
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −8
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
10
u
4
− u
2
+ 1
c
2
, c
11
(u
2
+ u + 1)
2
c
3
, c
7
, c
8
(u
2
+ 1)
2
c
5
, c
9
(u
2
− u + 1)
2
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
(y
2
− y + 1)
2
c
2
, c
5
, c
9
c
11
(y
2
+ y + 1)
2
c
3
, c
7
, c
8
(y + 1)
4
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.866025 + 0.500000I
a = 1.86603 + 0.50000I
b = −0.500000 + 0.866025I
1.64493 −8.00000
u = 0.866025 − 0.500000I
a = 1.86603 − 0.50000I
b = −0.500000 − 0.866025I
1.64493 −8.00000
u = −0.866025 + 0.500000I
a = 0.133975 + 0.500000I
b = −0.500000 − 0.866025I
1.64493 −8.00000
u = −0.866025 − 0.500000I
a = 0.133975 − 0.500000I
b = −0.500000 + 0.866025I
1.64493 −8.00000
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
10
(u
4
− u
2
+ 1)
2
· (u
14
− 2u
12
+ 6u
10
+ u
9
− 8u
8
− u
7
+ 10u
6
+ 2u
5
− 9u
4
− u
3
+ 4u
2
− u − 1)
· (u
36
− u
35
+ ··· + 2u + 1)
c
2
, c
11
((u
2
+ u + 1)
4
)(u
14
+ 4u
13
+ ··· + 9u + 1)(u
36
+ 11u
35
+ ··· + 2u + 1)
c
3
, c
7
, c
8
((u
2
+ 1)
4
)(u
14
− 5u
13
+ ··· + 8u − 4)(u
18
+ 2u
17
+ ··· + 4u + 1)
2
c
5
, c
9
((u
2
− u + 1)
4
)(u
14
+ 4u
13
+ ··· + 9u + 1)(u
36
+ 11u
35
+ ··· + 2u + 1)
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
((y
2
− y + 1)
4
)(y
14
− 4y
13
+ ··· − 9y + 1)(y
36
− 11y
35
+ ··· − 2y + 1)
c
2
, c
5
, c
9
c
11
((y
2
+ y + 1)
4
)(y
14
+ 16y
13
+ ··· − 17y + 1)
· (y
36
+ 29y
35
+ ··· − 86y + 1)
c
3
, c
7
, c
8
((y + 1)
8
)(y
14
+ 13y
13
+ ··· − 136y + 16)
· (y
18
+ 20y
17
+ ··· − 6y + 1)
2
23
