12a
1023
(K12a
1023
)
A knot diagram
1
Linearized knot diagam
4 7 8 9 11 12 3 2 1 5 6 10
Solving Sequence
2,7
3 8 4 9 5 1 10 11 12 6
c
2
c
7
c
3
c
8
c
4
c
1
c
9
c
10
c
12
c
6
c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
63
− u
62
+ ··· + 4u
3
− 1i
* 1 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
63
− u
62
+ · · · + 4u
3
− 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
−u
2
a
8
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
9
=
−u
3
+ 2u
−u
3
+ u
a
5
=
−u
10
+ 5u
8
− 8u
6
+ 3u
4
+ u
2
+ 1
−u
10
+ 4u
8
− 5u
6
+ 2u
4
− u
2
a
1
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
10
=
u
17
− 8u
15
+ 25u
13
− 36u
11
+ 19u
9
+ 4u
7
− 2u
5
− 4u
3
+ u
−u
19
+ 9u
17
− 32u
15
+ 55u
13
− 43u
11
+ 9u
9
+ 4u
5
− u
3
+ u
a
11
=
u
39
− 18u
37
+ ··· − 6u
5
− 6u
3
u
39
− 17u
37
+ ··· + 3u
5
+ u
a
12
=
u
28
− 13u
26
+ ··· + u
2
+ 1
−u
30
+ 14u
28
+ ··· − 4u
4
− u
2
a
6
=
u
57
− 26u
55
+ ··· + 2u
3
+ u
−u
59
+ 27u
57
+ ··· − u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
61
− 112u
59
+ ··· + 4u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
63
− 13u
62
+ ··· + 5048u − 367
c
2
, c
3
, c
7
u
63
+ u
62
+ ··· + 4u
3
+ 1
c
4
u
63
− u
62
+ ··· − 16u + 1
c
5
, c
6
, c
10
c
11
u
63
+ u
62
+ ··· − 2u
4
+ 1
c
8
u
63
− 3u
62
+ ··· − 14u + 1
c
9
, c
12
u
63
− 11u
62
+ ··· + 1032u − 113
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
63
+ 23y
62
+ ··· + 185728y −134689
c
2
, c
3
, c
7
y
63
− 57y
62
+ ··· + 12y
2
− 1
c
4
y
63
− y
62
+ ··· − 64y −1
c
5
, c
6
, c
10
c
11
y
63
− 69y
62
+ ··· + 4y
2
− 1
c
8
y
63
− 5y
62
+ ··· + 96y −1
c
9
, c
12
y
63
+ 39y
62
+ ··· − 28816y −12769
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.05857
−0.871869 −9.57900
u = −1.124880 + 0.212975I
−4.94868 − 6.91271I 0
u = −1.124880 − 0.212975I
−4.94868 + 6.91271I 0
u = 1.148860 + 0.182186I
2.18519 + 4.53135I 0
u = 1.148860 − 0.182186I
2.18519 − 4.53135I 0
u = −0.830553 + 0.042703I
−8.69415 + 0.00048I −9.30642 + 0.15839I
u = −0.830553 − 0.042703I
−8.69415 − 0.00048I −9.30642 − 0.15839I
u = −1.190630 + 0.128855I
2.84482 − 1.03901I 0
u = −1.190630 − 0.128855I
2.84482 + 1.03901I 0
u = −0.307202 + 0.707160I
−5.43312 − 10.27260I −7.72829 + 7.96510I
u = −0.307202 − 0.707160I
−5.43312 + 10.27260I −7.72829 − 7.96510I
u = 0.311428 + 0.693681I
1.68556 + 7.55058I −4.18504 − 9.18442I
u = 0.311428 − 0.693681I
1.68556 − 7.55058I −4.18504 + 9.18442I
u = −0.317156 + 0.675863I
2.25968 − 3.54520I −2.30097 + 2.95262I
u = −0.317156 − 0.675863I
2.25968 + 3.54520I −2.30097 − 2.95262I
u = −0.615511 + 0.402928I
−4.21282 + 6.36699I −5.11968 − 2.58502I
u = −0.615511 − 0.402928I
−4.21282 − 6.36699I −5.11968 + 2.58502I
u = 0.336084 + 0.649282I
−3.64458 + 1.06314I −5.63466 − 3.13287I
u = 0.336084 − 0.649282I
−3.64458 − 1.06314I −5.63466 + 3.13287I
u = −0.218313 + 0.688956I
−10.70060 − 3.40629I −12.54413 + 4.55404I
u = −0.218313 − 0.688956I
−10.70060 + 3.40629I −12.54413 − 4.55404I
u = 0.577950 + 0.406867I
2.80271 − 3.72383I −1.35159 + 3.56435I
u = 0.577950 − 0.406867I
2.80271 + 3.72383I −1.35159 − 3.56435I
u = 0.229540 + 0.647261I
−2.84257 + 2.89752I −11.56820 − 6.31602I
u = 0.229540 − 0.647261I
−2.84257 − 2.89752I −11.56820 + 6.31602I
u = 0.495663 + 0.468066I
−2.93186 + 2.65024I −3.65682 − 3.70204I
u = 0.495663 − 0.468066I
−2.93186 − 2.65024I −3.65682 + 3.70204I
u = −0.533777 + 0.423287I
3.22952 − 0.19502I 0.24983 + 3.49872I
u = −0.533777 − 0.423287I
3.22952 + 0.19502I 0.24983 − 3.49872I
u = 1.303640 + 0.225472I
−3.76308 − 0.34360I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.303640 − 0.225472I
−3.76308 + 0.34360I 0
u = −0.083521 + 0.671063I
−8.05532 + 3.57894I −11.69365 − 1.74226I
u = −0.083521 − 0.671063I
−8.05532 − 3.57894I −11.69365 + 1.74226I
u = 1.32555
−2.93780 0
u = −1.350050 + 0.193271I
3.40243 − 1.30144I 0
u = −1.350050 − 0.193271I
3.40243 + 1.30144I 0
u = 0.070290 + 0.619087I
−1.00852 − 1.48110I −8.78123 + 3.67726I
u = 0.070290 − 0.619087I
−1.00852 + 1.48110I −8.78123 − 3.67726I
u = 1.389370 + 0.217872I
4.99399 + 3.97068I 0
u = 1.389370 − 0.217872I
4.99399 − 3.97068I 0
u = 1.382970 + 0.269752I
−5.61347 + 6.88488I 0
u = 1.382970 − 0.269752I
−5.61347 − 6.88488I 0
u = −1.389830 + 0.251114I
2.31904 − 6.16933I 0
u = −1.389830 − 0.251114I
2.31904 + 6.16933I 0
u = −0.214690 + 0.530628I
−0.156297 − 1.165440I −2.55431 + 5.45798I
u = −0.214690 − 0.530628I
−0.156297 + 1.165440I −2.55431 − 5.45798I
u = 1.44160 + 0.15031I
9.44187 + 2.25272I 0
u = 1.44160 − 0.15031I
9.44187 − 2.25272I 0
u = −1.44303 + 0.13785I
9.12730 + 1.82675I 0
u = −1.44303 − 0.13785I
9.12730 − 1.82675I 0
u = 1.42643 + 0.26226I
7.83985 + 6.97132I 0
u = 1.42643 − 0.26226I
7.83985 − 6.97132I 0
u = −1.42926 + 0.25015I
2.00484 − 4.35421I 0
u = −1.42926 − 0.25015I
2.00484 + 4.35421I 0
u = 1.44572 + 0.12636I
2.23352 − 4.59359I 0
u = 1.44572 − 0.12636I
2.23352 + 4.59359I 0
u = −1.42610 + 0.26976I
7.24522 − 11.06320I 0
u = −1.42610 − 0.26976I
7.24522 + 11.06320I 0
u = 1.42568 + 0.27581I
0.10974 + 13.85250I 0
u = 1.42568 − 0.27581I
0.10974 − 13.85250I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44329 + 0.16543I
3.21696 − 4.93771I 0
u = −1.44329 − 0.16543I
3.21696 + 4.93771I 0
u = 0.481012
−1.12974 −8.20090
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
63
− 13u
62
+ ··· + 5048u − 367
c
2
, c
3
, c
7
u
63
+ u
62
+ ··· + 4u
3
+ 1
c
4
u
63
− u
62
+ ··· − 16u + 1
c
5
, c
6
, c
10
c
11
u
63
+ u
62
+ ··· − 2u
4
+ 1
c
8
u
63
− 3u
62
+ ··· − 14u + 1
c
9
, c
12
u
63
− 11u
62
+ ··· + 1032u − 113
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
63
+ 23y
62
+ ··· + 185728y −134689
c
2
, c
3
, c
7
y
63
− 57y
62
+ ··· + 12y
2
− 1
c
4
y
63
− y
62
+ ··· − 64y −1
c
5
, c
6
, c
10
c
11
y
63
− 69y
62
+ ··· + 4y
2
− 1
c
8
y
63
− 5y
62
+ ··· + 96y −1
c
9
, c
12
y
63
+ 39y
62
+ ··· − 28816y −12769
9
