12a
0463
(K12a
0463
)
A knot diagram
1
Linearized knot diagam
3 6 11 7 8 2 5 1 12 4 10 9
Solving Sequence
3,11 4,6
2 7 5 1 10 12 9 8
c
3
c
2
c
6
c
4
c
1
c
10
c
11
c
9
c
8
c
5
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hu
58
+ 2u
57
+ ··· + b − 1, −u
57
− u
56
+ ··· + a + 1, u
59
+ 2u
58
+ ··· − 2u − 1i
I
u
2
= hb, −u
2
+ a + u − 1, u
4
− u
3
+ u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 63 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
58
+2u
57
+· · ·+b−1, −u
57
−u
56
+· · ·+a+1, u
59
+2u
58
+· · ·−2u−1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
6
=
u
57
+ u
56
+ ··· + u − 1
−u
58
− 2u
57
+ ··· + u + 1
a
2
=
−u
9
− 3u
5
− u
u
9
+ u
7
+ 3u
5
+ 2u
3
+ u
a
7
=
−u
57
− u
56
+ ··· + 3u
2
+ 2u
u
58
+ 2u
57
+ ··· − 2u − 1
a
5
=
−u
55
− u
54
+ ··· − u + 1
u
29
+ 3u
27
+ ··· + 4u
2
+ u
a
1
=
u
7
+ 2u
3
u
9
+ u
7
+ 3u
5
+ 2u
3
+ u
a
10
=
u
u
3
+ u
a
12
=
u
3
u
5
+ u
3
+ u
a
9
=
u
5
+ u
u
7
+ u
5
+ 2u
3
+ u
a
8
=
u
9
+ 3u
5
+ u
u
11
+ u
9
+ 4u
7
+ 3u
5
+ 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
58
+ 8u
57
+ ··· − 13u − 5
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
59
+ 27u
58
+ ··· − 1984u − 256
c
2
, c
6
u
59
− u
58
+ ··· − 56u + 16
c
3
, c
10
u
59
+ 2u
58
+ ··· − 2u − 1
c
4
, c
5
, c
7
u
59
− 5u
58
+ ··· + 24u
2
+ 1
c
8
, c
9
, c
11
c
12
u
59
− 12u
58
+ ··· + 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
59
+ 3y
58
+ ··· − 2207744y −65536
c
2
, c
6
y
59
+ 27y
58
+ ··· − 1984y −256
c
3
, c
10
y
59
+ 12y
58
+ ··· + 2y −1
c
4
, c
5
, c
7
y
59
− 53y
58
+ ··· − 48y −1
c
8
, c
9
, c
11
c
12
y
59
+ 72y
58
+ ··· + 50y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.343246 + 0.929430I
a = 0.23393 + 2.03837I
b = 0.385366 − 0.992201I
−2.90400 − 0.48534I −3.04622 − 0.93099I
u = −0.343246 − 0.929430I
a = 0.23393 − 2.03837I
b = 0.385366 + 0.992201I
−2.90400 + 0.48534I −3.04622 + 0.93099I
u = −0.530651 + 0.868709I
a = −1.04989 + 1.47863I
b = 0.958742 − 0.452365I
−3.01197 + 4.86238I −3.57054 − 6.43781I
u = −0.530651 − 0.868709I
a = −1.04989 − 1.47863I
b = 0.958742 + 0.452365I
−3.01197 − 4.86238I −3.57054 + 6.43781I
u = 0.512834 + 0.819534I
a = −2.07477 − 1.14802I
b = 0.344806 − 0.832765I
−2.20006 − 2.45590I −5.34282 + 5.82388I
u = 0.512834 − 0.819534I
a = −2.07477 + 1.14802I
b = 0.344806 + 0.832765I
−2.20006 + 2.45590I −5.34282 − 5.82388I
u = 0.517835 + 0.901720I
a = 2.57194 + 0.49149I
b = −0.571645 + 0.989887I
−0.05687 − 6.75762I 0. + 9.22820I
u = 0.517835 − 0.901720I
a = 2.57194 − 0.49149I
b = −0.571645 − 0.989887I
−0.05687 + 6.75762I 0. − 9.22820I
u = −0.431886 + 0.855275I
a = 0.42205 − 1.46717I
b = −0.622029 + 0.574005I
1.17445 + 2.04675I 3.24024 − 3.82120I
u = −0.431886 − 0.855275I
a = 0.42205 + 1.46717I
b = −0.622029 − 0.574005I
1.17445 − 2.04675I 3.24024 + 3.82120I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.104023 + 0.946889I
a = −2.13002 − 1.92768I
b = 0.550439 + 1.057570I
−1.60171 + 5.75877I 0.24744 − 6.03089I
u = −0.104023 − 0.946889I
a = −2.13002 + 1.92768I
b = 0.550439 − 1.057570I
−1.60171 − 5.75877I 0.24744 + 6.03089I
u = 0.731988 + 0.763169I
a = 0.800342 + 0.062233I
b = −0.112548 + 1.197950I
−9.65537 − 2.66883I −9.83468 + 3.25272I
u = 0.731988 − 0.763169I
a = 0.800342 − 0.062233I
b = −0.112548 − 1.197950I
−9.65537 + 2.66883I −9.83468 − 3.25272I
u = 0.537997 + 0.944744I
a = −2.66911 − 0.07381I
b = 0.647369 − 1.158890I
−5.25013 − 10.71760I −4.54465 + 9.45987I
u = 0.537997 − 0.944744I
a = −2.66911 + 0.07381I
b = 0.647369 + 1.158890I
−5.25013 + 10.71760I −4.54465 − 9.45987I
u = −0.057586 + 0.882777I
a = 2.31101 + 1.39500I
b = −0.592455 − 0.810374I
3.06980 + 2.34027I 6.64897 − 4.48405I
u = −0.057586 − 0.882777I
a = 2.31101 − 1.39500I
b = −0.592455 + 0.810374I
3.06980 − 2.34027I 6.64897 + 4.48405I
u = 0.714820 + 0.495375I
a = 0.447234 − 0.136210I
b = −0.585668 − 1.188170I
−6.70702 + 6.08853I −8.24622 − 3.55476I
u = 0.714820 − 0.495375I
a = 0.447234 + 0.136210I
b = −0.585668 + 1.188170I
−6.70702 − 6.08853I −8.24622 + 3.55476I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.566605 + 0.649388I
a = −0.266615 − 1.188520I
b = −0.124692 − 0.867050I
−2.75909 − 1.65966I −8.41788 + 3.66504I
u = 0.566605 − 0.649388I
a = −0.266615 + 1.188520I
b = −0.124692 + 0.867050I
−2.75909 + 1.65966I −8.41788 − 3.66504I
u = −0.611622 + 0.577390I
a = 1.131410 − 0.440626I
b = −0.956464 − 0.308436I
−3.94508 − 0.54490I −6.77151 − 0.50771I
u = −0.611622 − 0.577390I
a = 1.131410 + 0.440626I
b = −0.956464 + 0.308436I
−3.94508 + 0.54490I −6.77151 + 0.50771I
u = 0.629823 + 0.513947I
a = −0.474587 + 0.552020I
b = 0.472585 + 0.971110I
−1.28323 + 2.43963I −4.50558 − 3.22204I
u = 0.629823 − 0.513947I
a = −0.474587 − 0.552020I
b = 0.472585 − 0.971110I
−1.28323 − 2.43963I −4.50558 + 3.22204I
u = 0.050655 + 0.809073I
a = −2.80210 − 0.73123I
b = 0.654760 + 0.520162I
0.057074 − 1.043030I 3.86720 + 0.46567I
u = 0.050655 − 0.809073I
a = −2.80210 + 0.73123I
b = 0.654760 − 0.520162I
0.057074 + 1.043030I 3.86720 − 0.46567I
u = 0.802556 + 0.909873I
a = 0.645306 − 0.524552I
b = 0.073782 + 0.922649I
−9.57681 − 3.00894I 0
u = 0.802556 − 0.909873I
a = 0.645306 + 0.524552I
b = 0.073782 − 0.922649I
−9.57681 + 3.00894I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.878048 + 0.900066I
a = −0.608654 − 0.248494I
b = 0.743403 − 0.349469I
−6.92983 − 1.93819I 0
u = 0.878048 − 0.900066I
a = −0.608654 + 0.248494I
b = 0.743403 + 0.349469I
−6.92983 + 1.93819I 0
u = −0.908427 + 0.893152I
a = −0.394230 − 0.515132I
b = 0.548605 − 1.127370I
−9.26800 − 2.97267I 0
u = −0.908427 − 0.893152I
a = −0.394230 + 0.515132I
b = 0.548605 + 1.127370I
−9.26800 + 2.97267I 0
u = 0.862553 + 0.938272I
a = 0.210045 + 0.711663I
b = −0.759924 − 0.382114I
−6.80919 − 4.50807I 0
u = 0.862553 − 0.938272I
a = 0.210045 − 0.711663I
b = −0.759924 + 0.382114I
−6.80919 + 4.50807I 0
u = −0.350516 + 0.631281I
a = −0.830854 + 0.196340I
b = 0.379823 + 0.257914I
0.162716 + 1.132970I 2.90169 − 5.38040I
u = −0.350516 − 0.631281I
a = −0.830854 − 0.196340I
b = 0.379823 − 0.257914I
0.162716 − 1.132970I 2.90169 + 5.38040I
u = −0.922367 + 0.885921I
a = 0.414846 + 0.164365I
b = −0.69639 + 1.25575I
−14.8968 − 7.2841I 0
u = −0.922367 − 0.885921I
a = 0.414846 − 0.164365I
b = −0.69639 − 1.25575I
−14.8968 + 7.2841I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.906516 + 0.902473I
a = 0.880104 + 0.387890I
b = −1.146010 + 0.424597I
−12.19390 + 0.69942I 0
u = 0.906516 − 0.902473I
a = 0.880104 − 0.387890I
b = −1.146010 − 0.424597I
−12.19390 − 0.69942I 0
u = −0.899151 + 0.910017I
a = 0.012912 + 0.933912I
b = −0.290358 + 1.086540I
−11.05620 + 2.06484I 0
u = −0.899151 − 0.910017I
a = 0.012912 − 0.933912I
b = −0.290358 − 1.086540I
−11.05620 − 2.06484I 0
u = −0.881614 + 0.946166I
a = −1.35992 + 1.22851I
b = 0.320527 + 1.080930I
−10.93940 + 4.50938I 0
u = −0.881614 − 0.946166I
a = −1.35992 − 1.22851I
b = 0.320527 − 1.080930I
−10.93940 − 4.50938I 0
u = 0.880655 + 0.955668I
a = −0.445587 − 0.984412I
b = 1.141580 + 0.449582I
−12.02220 − 7.29324I 0
u = 0.880655 − 0.955668I
a = −0.445587 + 0.984412I
b = 1.141580 − 0.449582I
−12.02220 + 7.29324I 0
u = −0.875312 + 0.962071I
a = 1.78278 − 1.05080I
b = −0.569196 − 1.124490I
−9.04599 + 9.55430I 0
u = −0.875312 − 0.962071I
a = 1.78278 + 1.05080I
b = −0.569196 + 1.124490I
−9.04599 − 9.55430I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.913352 + 0.939543I
a = 0.829208 − 0.487224I
b = −0.01243 − 1.44915I
−19.6434 + 3.3613I 0
u = −0.913352 − 0.939543I
a = 0.829208 + 0.487224I
b = −0.01243 + 1.44915I
−19.6434 − 3.3613I 0
u = −0.877468 + 0.975151I
a = −1.93743 + 0.83023I
b = 0.71000 + 1.24590I
−14.6076 + 13.9156I 0
u = −0.877468 − 0.975151I
a = −1.93743 − 0.83023I
b = 0.71000 − 1.24590I
−14.6076 − 13.9156I 0
u = −0.626785 + 0.171888I
a = 0.501490 − 0.081895I
b = −0.432777 − 1.116070I
−5.26927 + 3.82540I −8.88049 − 3.82555I
u = −0.626785 − 0.171888I
a = 0.501490 + 0.081895I
b = −0.432777 + 1.116070I
−5.26927 − 3.82540I −8.88049 + 3.82555I
u = −0.424302 + 0.237848I
a = −0.692243 + 0.560199I
b = 0.363149 + 0.700644I
−0.194105 + 1.203550I −3.60543 − 5.01021I
u = −0.424302 − 0.237848I
a = −0.692243 − 0.560199I
b = 0.363149 − 0.700644I
−0.194105 − 1.203550I −3.60543 + 5.01021I
u = 0.330842
a = 2.08280
b = −0.644701
−2.22425 −4.28740
10
II. I
u
2
= hb, −u
2
+ a + u − 1, u
4
− u
3
+ u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
u
2
a
6
=
u
2
− u + 1
0
a
2
=
1
0
a
7
=
u
2
− u + 1
0
a
5
=
u
2
− u + 2
u
2
a
1
=
1
0
a
10
=
u
u
3
+ u
a
12
=
u
3
u
3
− u
2
− 1
a
9
=
−u
2
− 1
−u
2
a
8
=
−1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
2
− 2u − 1
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u
4
c
3
u
4
− u
3
+ u
2
+ 1
c
4
, c
5
(u − 1)
4
c
7
(u + 1)
4
c
8
, c
9
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
10
u
4
+ u
3
+ u
2
+ 1
c
11
, c
12
u
4
− u
3
+ 3u
2
− 2u + 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
y
4
c
3
, c
10
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
4
, c
5
, c
7
(y −1)
4
c
8
, c
9
, c
11
c
12
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.351808 + 0.720342I
a = 0.95668 − 1.22719I
b = 0
−1.43393 + 1.41510I −1.48175 − 2.96122I
u = −0.351808 − 0.720342I
a = 0.95668 + 1.22719I
b = 0
−1.43393 − 1.41510I −1.48175 + 2.96122I
u = 0.851808 + 0.911292I
a = 0.043315 + 0.641200I
b = 0
−8.43568 − 3.16396I −3.01825 + 2.83489I
u = 0.851808 − 0.911292I
a = 0.043315 − 0.641200I
b = 0
−8.43568 + 3.16396I −3.01825 − 2.83489I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
4
(u
59
+ 27u
58
+ ··· − 1984u − 256)
c
2
, c
6
u
4
(u
59
− u
58
+ ··· − 56u + 16)
c
3
(u
4
− u
3
+ u
2
+ 1)(u
59
+ 2u
58
+ ··· − 2u − 1)
c
4
, c
5
((u − 1)
4
)(u
59
− 5u
58
+ ··· + 24u
2
+ 1)
c
7
((u + 1)
4
)(u
59
− 5u
58
+ ··· + 24u
2
+ 1)
c
8
, c
9
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
59
− 12u
58
+ ··· + 2u + 1)
c
10
(u
4
+ u
3
+ u
2
+ 1)(u
59
+ 2u
58
+ ··· − 2u − 1)
c
11
, c
12
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
59
− 12u
58
+ ··· + 2u + 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
4
(y
59
+ 3y
58
+ ··· − 2207744y −65536)
c
2
, c
6
y
4
(y
59
+ 27y
58
+ ··· − 1984y −256)
c
3
, c
10
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
59
+ 12y
58
+ ··· + 2y −1)
c
4
, c
5
, c
7
((y −1)
4
)(y
59
− 53y
58
+ ··· − 48y −1)
c
8
, c
9
, c
11
c
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
59
+ 72y
58
+ ··· + 50y −1)
16
