12a
0247
(K12a
0247
)
A knot diagram
1
Linearized knot diagam
3 6 7 10 8 2 1 12 11 5 9 4
Solving Sequence
2,7
6 3 4 1 8 5 12 9 11 10
c
6
c
2
c
3
c
1
c
7
c
5
c
12
c
8
c
11
c
10
c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
81
+ u
80
+ ··· + u − 1i
* 1 irreducible components of dim
C
= 0, with total 81 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
81
+ u
80
+ · · · + u − 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
8
=
u
8
+ u
6
+ u
4
+ 1
u
10
+ 2u
8
+ 3u
6
+ 2u
4
+ u
2
a
5
=
u
16
+ 3u
14
+ 5u
12
+ 4u
10
+ 3u
8
+ 2u
6
+ 2u
4
+ 1
u
18
+ 4u
16
+ 9u
14
+ 12u
12
+ 11u
10
+ 6u
8
+ 2u
6
+ u
2
a
12
=
−u
11
− 2u
9
− 2u
7
+ u
3
u
11
+ 3u
9
+ 4u
7
+ 3u
5
+ u
3
+ u
a
9
=
−u
32
− 7u
30
+ ··· + 2u
4
+ 1
u
32
+ 8u
30
+ ··· + 4u
4
+ 2u
2
a
11
=
−u
53
− 12u
51
+ ··· + 2u
3
+ u
u
53
+ 13u
51
+ ··· + 3u
3
+ u
a
10
=
−u
74
− 17u
72
+ ··· + u
2
+ 1
u
74
+ 18u
72
+ ··· + 8u
4
+ 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
80
− 4u
79
+ ··· − 8u
2
− 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
81
+ 39u
80
+ ··· + u − 1
c
2
, c
6
u
81
− u
80
+ ··· + u + 1
c
3
u
81
+ u
80
+ ··· − 277u + 65
c
4
, c
10
u
81
− u
80
+ ··· + u + 1
c
5
, c
12
u
81
+ 7u
80
+ ··· + 2761u + 101
c
7
u
81
− 5u
80
+ ··· − 11u + 3
c
8
, c
9
, c
11
u
81
+ 21u
80
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
81
+ 7y
80
+ ··· + 17y −1
c
2
, c
6
y
81
+ 39y
80
+ ··· + y −1
c
3
y
81
− 25y
80
+ ··· − 421431y −4225
c
4
, c
10
y
81
− 21y
80
+ ··· + y −1
c
5
, c
12
y
81
+ 51y
80
+ ··· + 2274161y −10201
c
7
y
81
+ 3y
80
+ ··· − 563y −9
c
8
, c
9
, c
11
y
81
+ 79y
80
+ ··· + 9y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.330756 + 0.928246I
−1.98935 − 0.55410I 0
u = 0.330756 − 0.928246I
−1.98935 + 0.55410I 0
u = 0.555231 + 0.887447I
4.58988 − 4.17415I 0
u = 0.555231 − 0.887447I
4.58988 + 4.17415I 0
u = −0.550578 + 0.902148I
4.97491 − 1.96297I 0
u = −0.550578 − 0.902148I
4.97491 + 1.96297I 0
u = 0.021905 + 0.940885I
4.01374 − 3.02957I −4.00000 + 2.75966I
u = 0.021905 − 0.940885I
4.01374 + 3.02957I −4.00000 − 2.75966I
u = 0.631971 + 0.668959I
5.23666 + 8.85428I 0.25550 − 7.99532I
u = 0.631971 − 0.668959I
5.23666 − 8.85428I 0.25550 + 7.99532I
u = 0.483592 + 0.777442I
−2.06562 − 0.44729I −7.29217 + 1.06967I
u = 0.483592 − 0.777442I
−2.06562 + 0.44729I −7.29217 − 1.06967I
u = −0.474582 + 0.979170I
−0.31365 − 2.38173I 0
u = −0.474582 − 0.979170I
−0.31365 + 2.38173I 0
u = −0.630050 + 0.657774I
5.69407 − 2.69657I 1.28923 + 3.02747I
u = −0.630050 − 0.657774I
5.69407 + 2.69657I 1.28923 − 3.02747I
u = 0.580245 + 0.690845I
−1.70309 + 4.76740I −5.47059 − 8.11597I
u = 0.580245 − 0.690845I
−1.70309 − 4.76740I −5.47059 + 8.11597I
u = 0.446078 + 1.061030I
−3.47656 + 3.43189I 0
u = 0.446078 − 1.061030I
−3.47656 − 3.43189I 0
u = −0.519943 + 1.034750I
0.30103 − 3.37806I 0
u = −0.519943 − 1.034750I
0.30103 + 3.37806I 0
u = 0.285545 + 1.130800I
−5.01539 − 0.16721I 0
u = 0.285545 − 1.130800I
−5.01539 + 0.16721I 0
u = −0.540133 + 0.631709I
0.70198 − 1.71974I 1.35755 + 3.78809I
u = −0.540133 − 0.631709I
0.70198 + 1.71974I 1.35755 − 3.78809I
u = −0.771211 + 0.309758I
3.47094 + 10.85050I −1.26204 − 7.02651I
u = −0.771211 − 0.309758I
3.47094 − 10.85050I −1.26204 + 7.02651I
u = 0.249724 + 1.142850I
−0.48830 − 1.78736I 0
u = 0.249724 − 1.142850I
−0.48830 + 1.78736I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.683944 + 0.470341I
8.62833 − 2.03896I 3.69559 + 2.22375I
u = −0.683944 − 0.470341I
8.62833 + 2.03896I 3.69559 − 2.22375I
u = 0.689016 + 0.459096I
8.57475 − 4.19689I 3.50201 + 3.13868I
u = 0.689016 − 0.459096I
8.57475 + 4.19689I 3.50201 − 3.13868I
u = 0.765943 + 0.314154I
4.01700 − 4.68092I −0.19311 + 2.19687I
u = 0.765943 − 0.314154I
4.01700 + 4.68092I −0.19311 − 2.19687I
u = −0.250936 + 1.149570I
−1.05501 + 7.90870I 0
u = −0.250936 − 1.149570I
−1.05501 − 7.90870I 0
u = −0.275321 + 1.148290I
−7.91963 + 3.33484I 0
u = −0.275321 − 1.148290I
−7.91963 − 3.33484I 0
u = 0.333976 + 1.136910I
−1.43197 + 1.29517I 0
u = 0.333976 − 1.136910I
−1.43197 − 1.29517I 0
u = −0.301260 + 1.146810I
−8.21875 − 2.62295I 0
u = −0.301260 − 1.146810I
−8.21875 + 2.62295I 0
u = −0.755307 + 0.286115I
−3.56728 + 6.37685I −6.68349 − 6.54893I
u = −0.755307 − 0.286115I
−3.56728 − 6.37685I −6.68349 + 6.54893I
u = −0.330768 + 1.146950I
−1.97419 − 7.22380I 0
u = −0.330768 − 1.146950I
−1.97419 + 7.22380I 0
u = −0.569017 + 1.049970I
6.92763 − 2.80448I 0
u = −0.569017 − 1.049970I
6.92763 + 2.80448I 0
u = 0.569598 + 1.056390I
6.82301 + 9.05454I 0
u = 0.569598 − 1.056390I
6.82301 − 9.05454I 0
u = 0.529876 + 1.077230I
−0.50944 + 7.02202I 0
u = 0.529876 − 1.077230I
−0.50944 − 7.02202I 0
u = 0.728882 + 0.290469I
−0.81550 − 3.12081I −0.65919 + 2.66104I
u = 0.728882 − 0.290469I
−0.81550 + 3.12081I −0.65919 − 2.66104I
u = −0.732942 + 0.254989I
−4.07021 + 0.53547I −8.23201 + 1.09852I
u = −0.732942 − 0.254989I
−4.07021 − 0.53547I −8.23201 − 1.09852I
u = 0.512335 + 1.126340I
−0.22713 + 6.52430I 0
u = 0.512335 − 1.126340I
−0.22713 − 6.52430I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.578778 + 0.484061I
1.91397 − 1.02951I 2.98287 + 4.00023I
u = −0.578778 − 0.484061I
1.91397 + 1.02951I 2.98287 − 4.00023I
u = −0.515985 + 1.136090I
−0.720055 − 0.730088I 0
u = −0.515985 − 1.136090I
−0.720055 + 0.730088I 0
u = 0.546823 + 1.128660I
−3.24659 + 7.96298I 0
u = 0.546823 − 1.128660I
−3.24659 − 7.96298I 0
u = −0.537260 + 1.136870I
−6.61921 − 5.33206I 0
u = −0.537260 − 1.136870I
−6.61921 + 5.33206I 0
u = −0.708940 + 0.201872I
1.93893 − 3.88483I −3.08441 + 2.98468I
u = −0.708940 − 0.201872I
1.93893 + 3.88483I −3.08441 − 2.98468I
u = −0.551751 + 1.137250I
−6.05282 − 11.29930I 0
u = −0.551751 − 1.137250I
−6.05282 + 11.29930I 0
u = 0.563166 + 1.133120I
1.61264 + 9.68341I 0
u = 0.563166 − 1.133120I
1.61264 − 9.68341I 0
u = 0.629075 + 0.379382I
1.50547 − 2.46200I 0.64686 + 5.57955I
u = 0.629075 − 0.379382I
1.50547 + 2.46200I 0.64686 − 5.57955I
u = −0.563360 + 1.136020I
1.0430 − 15.8655I 0
u = −0.563360 − 1.136020I
1.0430 + 15.8655I 0
u = 0.684512 + 0.197850I
2.38107 − 1.99261I −2.22631 + 2.45378I
u = 0.684512 − 0.197850I
2.38107 + 1.99261I −2.22631 − 2.45378I
u = 0.407633
−1.06455 −9.20770
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
81
+ 39u
80
+ ··· + u − 1
c
2
, c
6
u
81
− u
80
+ ··· + u + 1
c
3
u
81
+ u
80
+ ··· − 277u + 65
c
4
, c
10
u
81
− u
80
+ ··· + u + 1
c
5
, c
12
u
81
+ 7u
80
+ ··· + 2761u + 101
c
7
u
81
− 5u
80
+ ··· − 11u + 3
c
8
, c
9
, c
11
u
81
+ 21u
80
+ ··· + u + 1
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
81
+ 7y
80
+ ··· + 17y −1
c
2
, c
6
y
81
+ 39y
80
+ ··· + y −1
c
3
y
81
− 25y
80
+ ··· − 421431y −4225
c
4
, c
10
y
81
− 21y
80
+ ··· + y −1
c
5
, c
12
y
81
+ 51y
80
+ ··· + 2274161y −10201
c
7
y
81
+ 3y
80
+ ··· − 563y −9
c
8
, c
9
, c
11
y
81
+ 79y
80
+ ··· + 9y −1
9
