9
34
(K9a
28
)
A knot diagram
1
Linearized knot diagam
7 9 8 2 3 4 1 6 5
Solving Sequence
2,7
1
5,8
4 3 6 9
c
1
c
7
c
4
c
3
c
6
c
9
c
2
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−61u
16
− 298u
15
+ ··· + 43b + 351, −107u
16
− 319u
15
+ ··· + 172a − 257,
u
17
+ 5u
16
+ ··· − 21u − 4i
I
u
2
= hu
10
a − 2u
9
a + ··· + a − 1, −u
9
a − u
10
+ ··· + a
2
+ 1,
u
11
− 3u
10
+ 8u
9
− 13u
8
+ 18u
7
− 20u
6
+ 18u
5
− 15u
4
+ 9u
3
− 5u
2
+ 2u − 1i
I
u
3
= h−u
3
+ 2u
2
+ b − 2u + 1, u
4
− u
3
+ a + u − 2, u
5
− 2u
4
+ 3u
3
− 3u
2
+ u − 1i
* 3 irreducible components of dim
C
= 0, with total 44 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
= h−61u
16
− 298u
15
+ · · · + 43b + 351, −107u
16
− 319u
15
+ · · · +
172a − 257, u
17
+ 5u
16
+ · · · − 21u − 4i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
1
=
1
u
2
a
5
=
0.622093u
16
+ 1.85465u
15
+ ··· + 5.02907u + 1.49419
1.41860u
16
+ 6.93023u
15
+ ··· − 36.1860u − 8.16279
a
8
=
u
u
3
+ u
a
4
=
2.04070u
16
+ 8.78488u
15
+ ··· − 31.1570u − 6.66860
1.41860u
16
+ 6.93023u
15
+ ··· − 36.1860u − 8.16279
a
3
=
0.901163u
16
+ 3.80814u
15
+ ··· − 14.7616u − 2.94767
0.720930u
16
+ 3.04651u
15
+ ··· − 9.20930u − 1.55814
a
6
=
−3.56395u
16
− 14.4477u
15
+ ··· + 49.8895u + 13.1221
−3.37209u
16
− 15.6047u
15
+ ··· + 62.7209u + 14.2558
a
9
=
−0.843023u
16
− 4.40116u
15
+ ··· + 26.6802u + 7.56395
−0.604651u
16
− 2.23256u
15
+ ··· + 18.0465u + 5.79070
a
9
=
−0.843023u
16
− 4.40116u
15
+ ··· + 26.6802u + 7.56395
−0.604651u
16
− 2.23256u
15
+ ··· + 18.0465u + 5.79070
(ii) Obstruction class = −1
(iii) Cusp Shapes =
441
43
u
16
+
1969
43
u
15
+ ··· −
7549
43
u −
2042
43
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
17
+ 5u
16
+ ··· − 21u − 4
c
2
, c
8
u
17
+ u
16
+ ··· − u − 1
c
3
, c
9
u
17
+ 5u
13
+ ··· + 4u − 1
c
4
, c
6
u
17
+ 2u
16
+ ··· + 8u − 1
c
5
u
17
+ 10u
16
+ ··· + 5u + 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
17
+ 9y
16
+ ··· + 17y −16
c
2
, c
8
y
17
+ 7y
16
+ ··· − 19y −1
c
3
, c
9
y
17
+ 10y
15
+ ··· + 10y −1
c
4
, c
6
y
17
− 12y
16
+ ··· + 46y −1
c
5
y
17
+ 16y
15
+ ··· − 11y −4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.048681 + 1.008070I
a = −1.66750 + 0.61626I
b = 1.134670 + 0.483593I
−3.35770 + 0.12402I −5.97884 + 0.38118I
u = 0.048681 − 1.008070I
a = −1.66750 − 0.61626I
b = 1.134670 − 0.483593I
−3.35770 − 0.12402I −5.97884 − 0.38118I
u = 0.423210 + 0.769632I
a = 0.879104 + 0.306597I
b = −0.311039 − 0.398365I
0.28619 + 1.83578I 2.59246 − 3.36751I
u = 0.423210 − 0.769632I
a = 0.879104 − 0.306597I
b = −0.311039 + 0.398365I
0.28619 − 1.83578I 2.59246 + 3.36751I
u = −1.115480 + 0.170377I
a = 0.027795 − 0.216323I
b = −0.973543 + 0.694225I
0.27750 + 8.29795I 1.06571 − 6.88359I
u = −1.115480 − 0.170377I
a = 0.027795 + 0.216323I
b = −0.973543 − 0.694225I
0.27750 − 8.29795I 1.06571 + 6.88359I
u = 1.18539
a = 0.285468
b = −0.154842
2.39123 15.5890
u = −0.546851 + 1.063670I
a = −0.818209 + 0.890659I
b = 1.249560 + 0.062335I
−3.79067 − 2.00597I −6.21078 + 1.26630I
u = −0.546851 − 1.063670I
a = −0.818209 − 0.890659I
b = 1.249560 − 0.062335I
−3.79067 + 2.00597I −6.21078 − 1.26630I
u = −0.437546 + 1.154220I
a = −1.81788 + 0.29672I
b = 1.40541 + 1.07727I
−4.31147 − 5.61068I −7.96642 + 8.06049I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.437546 − 1.154220I
a = −1.81788 − 0.29672I
b = 1.40541 − 1.07727I
−4.31147 + 5.61068I −7.96642 − 8.06049I
u = −0.582313 + 0.090917I
a = 0.732188 − 0.199615I
b = 0.842156 − 0.620975I
−1.32135 + 1.62186I −2.58195 − 4.11393I
u = −0.582313 − 0.090917I
a = 0.732188 + 0.199615I
b = 0.842156 + 0.620975I
−1.32135 − 1.62186I −2.58195 + 4.11393I
u = −0.59542 + 1.30831I
a = 1.58913 − 0.22054I
b = −1.40015 − 0.93567I
−3.3114 − 14.3446I −1.18187 + 8.40363I
u = −0.59542 − 1.30831I
a = 1.58913 + 0.22054I
b = −1.40015 + 0.93567I
−3.3114 + 14.3446I −1.18187 − 8.40363I
u = −0.28698 + 1.44004I
a = 0.807648 − 0.511056I
b = −0.869639 − 0.080492I
−5.40594 + 3.12036I −5.53287 − 3.71986I
u = −0.28698 − 1.44004I
a = 0.807648 + 0.511056I
b = −0.869639 + 0.080492I
−5.40594 − 3.12036I −5.53287 + 3.71986I
6
II.
I
u
2
= hu
10
a−2u
9
a+· · ·+a−1, −u
9
a−u
10
+· · ·+a
2
+1, u
11
−3u
10
+· · ·+2u−1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
1
=
1
u
2
a
5
=
a
−u
10
a + 2u
9
a + ··· − a + 1
a
8
=
u
u
3
+ u
a
4
=
−u
10
a + 2u
9
a + ··· − 2u + 1
−u
10
a + 2u
9
a + ··· − a + 1
a
3
=
u
9
− 2u
8
+ 4u
7
− 3u
6
+ u
5
+ u
3
a + u
4
− 4u
3
+ au + 2u
2
+ a − 3u + 1
u
10
a − 2u
9
a + ··· + a + 1
a
6
=
−u
9
a + u
9
+ ··· − a + 2
1
a
9
=
u
9
− 4u
8
+ ··· + a − 1
−u
10
a + 2u
9
a + ··· − a + 1
a
9
=
u
9
− 4u
8
+ ··· + a − 1
−u
10
a + 2u
9
a + ··· − a + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
10
− 4u
9
+ 8u
8
+ 4u
7
− 8u
6
+ 12u
5
− 12u
4
+ 4u
3
− 8u
2
+ 2
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u
11
− 3u
10
+ ··· + 2u − 1)
2
c
2
, c
8
u
22
+ 3u
21
+ ··· + 6u + 1
c
3
, c
9
u
22
+ u
21
+ ··· − 10u + 1
c
4
, c
6
u
22
− u
21
+ ··· − 4u + 1
c
5
(u
11
− 5u
10
+ 12u
9
− 15u
8
+ 8u
7
+ 4u
6
− 8u
5
+ 3u
4
+ 3u
3
− 3u
2
+ 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
11
+ 7y
10
+ ··· − 6y −1)
2
c
2
, c
8
y
22
− 5y
21
+ ··· + 72y
2
+ 1
c
3
, c
9
y
22
− y
21
+ ··· − 8y + 1
c
4
, c
6
y
22
+ 3y
21
+ ··· + 8y + 1
c
5
(y
11
− y
10
+ ··· + 6y −1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.253759 + 0.946686I
a = −0.049055 − 1.213920I
b = −0.33551 + 1.93421I
−0.13765 − 5.21629I 0.43603 + 9.01278I
u = −0.253759 + 0.946686I
a = −2.57911 − 0.36655I
b = 0.584301 + 0.546847I
−0.13765 − 5.21629I 0.43603 + 9.01278I
u = −0.253759 − 0.946686I
a = −0.049055 + 1.213920I
b = −0.33551 − 1.93421I
−0.13765 + 5.21629I 0.43603 − 9.01278I
u = −0.253759 − 0.946686I
a = −2.57911 + 0.36655I
b = 0.584301 − 0.546847I
−0.13765 + 5.21629I 0.43603 − 9.01278I
u = 1.10821
a = 0.305204 + 0.028042I
b = −0.160435 − 0.287182I
2.37876 12.2610
u = 1.10821
a = 0.305204 − 0.028042I
b = −0.160435 + 0.287182I
2.37876 12.2610
u = 0.572881 + 0.536287I
a = 0.605018 − 0.138715I
b = 0.379406 − 0.599968I
0.42400 + 2.24779I 3.63582 − 5.06360I
u = 0.572881 + 0.536287I
a = 1.12964 + 0.99333I
b = −0.960104 − 0.104756I
0.42400 + 2.24779I 3.63582 − 5.06360I
u = 0.572881 − 0.536287I
a = 0.605018 + 0.138715I
b = 0.379406 + 0.599968I
0.42400 − 2.24779I 3.63582 + 5.06360I
u = 0.572881 − 0.536287I
a = 1.12964 − 0.99333I
b = −0.960104 + 0.104756I
0.42400 − 2.24779I 3.63582 + 5.06360I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.290349 + 1.272230I
a = 1.21435 + 0.88581I
b = −0.734695 + 0.377618I
−4.63073 + 5.00074I −7.84059 − 6.22751I
u = 0.290349 + 1.272230I
a = −1.62496 + 0.36379I
b = 1.46811 − 0.97707I
−4.63073 + 5.00074I −7.84059 − 6.22751I
u = 0.290349 − 1.272230I
a = 1.21435 − 0.88581I
b = −0.734695 − 0.377618I
−4.63073 − 5.00074I −7.84059 + 6.22751I
u = 0.290349 − 1.272230I
a = −1.62496 − 0.36379I
b = 1.46811 + 0.97707I
−4.63073 − 5.00074I −7.84059 + 6.22751I
u = −0.234018 + 0.605151I
a = 0.357585 − 0.648167I
b = 0.378854 − 1.068730I
0.80290 + 2.70441I 3.46762 + 0.08333I
u = −0.234018 + 0.605151I
a = 2.61356 + 0.79794I
b = −0.866642 − 0.847442I
0.80290 + 2.70441I 3.46762 + 0.08333I
u = −0.234018 − 0.605151I
a = 0.357585 + 0.648167I
b = 0.378854 + 1.068730I
0.80290 − 2.70441I 3.46762 − 0.08333I
u = −0.234018 − 0.605151I
a = 2.61356 − 0.79794I
b = −0.866642 + 0.847442I
0.80290 − 2.70441I 3.46762 − 0.08333I
u = 0.57044 + 1.34258I
a = −0.862107 + 0.035474I
b = 0.818255 − 0.852218I
−1.76023 + 5.92443I 3.17045 − 10.02355I
u = 0.57044 + 1.34258I
a = 1.389870 + 0.219943I
b = −1.071530 + 0.524779I
−1.76023 + 5.92443I 3.17045 − 10.02355I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.57044 − 1.34258I
a = −0.862107 − 0.035474I
b = 0.818255 + 0.852218I
−1.76023 − 5.92443I 3.17045 + 10.02355I
u = 0.57044 − 1.34258I
a = 1.389870 − 0.219943I
b = −1.071530 − 0.524779I
−1.76023 − 5.92443I 3.17045 + 10.02355I
12
III.
I
u
3
= h−u
3
+ 2u
2
+ b −2u + 1, u
4
− u
3
+ a + u −2, u
5
− 2u
4
+ 3u
3
− 3u
2
+ u − 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
1
=
1
u
2
a
5
=
−u
4
+ u
3
− u + 2
u
3
− 2u
2
+ 2u − 1
a
8
=
u
u
3
+ u
a
4
=
−u
4
+ 2u
3
− 2u
2
+ u + 1
u
3
− 2u
2
+ 2u − 1
a
3
=
−u
4
+ u
3
− u
2
+ 2
−u
4
+ 2u
3
− 3u
2
+ 2u − 1
a
6
=
−u
4
+ 3u
3
− 4u
2
+ 4u − 2
u
4
− u
3
+ u
2
− 1
a
9
=
u
4
− 2u
3
+ 3u
2
− 2u
u
2
− u + 1
a
9
=
u
4
− 2u
3
+ 3u
2
− 2u
u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6u
4
+ 13u
3
− 22u
2
+ 14u − 9
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− 2u
4
+ 3u
3
− 3u
2
+ u − 1
c
2
, c
8
u
5
− u
4
− u
3
+ u
2
− 1
c
3
, c
9
u
5
− u
3
+ u
2
+ u − 1
c
4
, c
6
u
5
+ 2u
4
+ 3u
3
+ 3u
2
+ 3u + 1
c
5
u
5
− 3u
4
+ 5u
3
− 4u
2
+ 3u − 1
c
7
u
5
+ 2u
4
+ 3u
3
+ 3u
2
+ u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
5
+ 2y
4
− y
3
− 7y
2
− 5y −1
c
2
, c
8
y
5
− 3y
4
+ 3y
3
− 3y
2
+ 2y −1
c
3
, c
9
y
5
− 2y
4
+ 3y
3
− 3y
2
+ 3y −1
c
4
, c
6
y
5
+ 2y
4
+ 3y
3
+ 5y
2
+ 3y −1
c
5
y
5
+ y
4
+ 7y
3
+ 8y
2
+ y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.372466 + 1.263920I
a = −1.347300 − 0.010044I
b = 0.929085 − 0.848284I
−3.01018 + 5.17259I −1.67537 − 5.94701I
u = 0.372466 − 1.263920I
a = −1.347300 + 0.010044I
b = 0.929085 + 0.848284I
−3.01018 − 5.17259I −1.67537 + 5.94701I
u = 1.33263
a = −0.119827
b = 0.480071
2.14584 −17.5700
u = −0.038780 + 0.656277I
a = 1.90721 − 0.97967I
b = −0.169121 + 1.134660I
0.29233 − 3.70382I −0.53969 + 6.40947I
u = −0.038780 − 0.656277I
a = 1.90721 + 0.97967I
b = −0.169121 − 1.134660I
0.29233 + 3.70382I −0.53969 − 6.40947I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
5
− 2u
4
+ 3u
3
− 3u
2
+ u − 1)(u
11
− 3u
10
+ ··· + 2u − 1)
2
· (u
17
+ 5u
16
+ ··· − 21u − 4)
c
2
, c
8
(u
5
− u
4
− u
3
+ u
2
− 1)(u
17
+ u
16
+ ··· − u − 1)(u
22
+ 3u
21
+ ··· + 6u + 1)
c
3
, c
9
(u
5
− u
3
+ u
2
+ u − 1)(u
17
+ 5u
13
+ ··· + 4u − 1)
· (u
22
+ u
21
+ ··· − 10u + 1)
c
4
, c
6
(u
5
+ 2u
4
+ 3u
3
+ 3u
2
+ 3u + 1)(u
17
+ 2u
16
+ ··· + 8u − 1)
· (u
22
− u
21
+ ··· − 4u + 1)
c
5
(u
5
− 3u
4
+ 5u
3
− 4u
2
+ 3u − 1)
· (u
11
− 5u
10
+ 12u
9
− 15u
8
+ 8u
7
+ 4u
6
− 8u
5
+ 3u
4
+ 3u
3
− 3u
2
+ 1)
2
· (u
17
+ 10u
16
+ ··· + 5u + 2)
c
7
(u
5
+ 2u
4
+ 3u
3
+ 3u
2
+ u + 1)(u
11
− 3u
10
+ ··· + 2u − 1)
2
· (u
17
+ 5u
16
+ ··· − 21u − 4)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
5
+ 2y
4
− y
3
− 7y
2
− 5y −1)(y
11
+ 7y
10
+ ··· − 6y −1)
2
· (y
17
+ 9y
16
+ ··· + 17y −16)
c
2
, c
8
(y
5
− 3y
4
+ 3y
3
− 3y
2
+ 2y −1)(y
17
+ 7y
16
+ ··· − 19y −1)
· (y
22
− 5y
21
+ ··· + 72y
2
+ 1)
c
3
, c
9
(y
5
− 2y
4
+ 3y
3
− 3y
2
+ 3y −1)(y
17
+ 10y
15
+ ··· + 10y −1)
· (y
22
− y
21
+ ··· − 8y + 1)
c
4
, c
6
(y
5
+ 2y
4
+ 3y
3
+ 5y
2
+ 3y −1)(y
17
− 12y
16
+ ··· + 46y −1)
· (y
22
+ 3y
21
+ ··· + 8y + 1)
c
5
(y
5
+ y
4
+ 7y
3
+ 8y
2
+ y −1)(y
11
− y
10
+ ··· + 6y −1)
2
· (y
17
+ 16y
15
+ ··· − 11y −4)
18
