12a
0729
(K12a
0729
)
A knot diagram
1
Linearized knot diagam
3 8 9 10 11 1 2 7 12 6 5 4
Solving Sequence
6,10
11 5 12 4 1 7 9 3 8 2
c
10
c
5
c
11
c
4
c
12
c
6
c
9
c
3
c
8
c
2
c
1
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
83
+ u
82
+ ··· + u
2
− 1i
* 1 irreducible components of dim
C
= 0, with total 83 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
83
+ u
82
+ · · · + u
2
− 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
5
=
−u
u
3
+ u
a
12
=
u
2
+ 1
−u
4
− 2u
2
a
4
=
−u
3
− 2u
u
3
+ u
a
1
=
u
10
+ 5u
8
+ 8u
6
+ 3u
4
− u
2
+ 1
−u
10
− 4u
8
− 5u
6
− 2u
4
− u
2
a
7
=
−u
21
− 10u
19
+ ··· + 2u
3
− u
u
21
+ 9u
19
+ 33u
17
+ 62u
15
+ 62u
13
+ 33u
11
+ 13u
9
+ 6u
7
+ u
5
+ u
3
+ u
a
9
=
−u
6
− 3u
4
− 2u
2
+ 1
u
8
+ 4u
6
+ 4u
4
a
3
=
−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
8
=
u
50
+ 23u
48
+ ··· − u
2
+ 1
−u
50
− 22u
48
+ ··· + 4u
4
− u
2
a
2
=
−u
46
− 21u
44
+ ··· − 2u
2
+ 1
u
48
+ 22u
46
+ ··· − 2u
6
− 2u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
82
− 4u
81
+ ··· − 4u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
83
+ 29u
82
+ ··· + 2u + 1
c
2
, c
7
u
83
+ u
82
+ ··· + 2u + 1
c
3
, c
6
u
83
− u
82
+ ··· − 134u + 61
c
4
u
83
+ u
82
+ ··· + 12u + 1
c
5
, c
10
, c
11
u
83
− u
82
+ ··· − u
2
+ 1
c
9
u
83
+ 17u
82
+ ··· − 49616u − 2993
c
12
u
83
− 7u
82
+ ··· + 24u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
83
+ 51y
82
+ ··· − 14y −1
c
2
, c
7
y
83
− 29y
82
+ ··· + 2y −1
c
3
, c
6
y
83
− 57y
82
+ ··· + 104454y −3721
c
4
y
83
+ 7y
82
+ ··· − 46y −1
c
5
, c
10
, c
11
y
83
+ 75y
82
+ ··· + 2y −1
c
9
y
83
+ 31y
82
+ ··· − 117757622y −8958049
c
12
y
83
− y
82
+ ··· − 70y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.043610 + 0.954497I
2.99428 − 2.75779I 0
u = −0.043610 − 0.954497I
2.99428 + 2.75779I 0
u = −0.193895 + 1.128830I
−0.07783 − 3.45046I 0
u = −0.193895 − 1.128830I
−0.07783 + 3.45046I 0
u = −0.101245 + 1.152230I
−1.54161 − 1.68012I 0
u = −0.101245 − 1.152230I
−1.54161 + 1.68012I 0
u = 0.211269 + 1.138100I
−1.18955 + 8.94241I 0
u = 0.211269 − 1.138100I
−1.18955 − 8.94241I 0
u = 0.186175 + 1.186390I
−5.77198 + 3.02870I 0
u = 0.186175 − 1.186390I
−5.77198 − 3.02870I 0
u = −0.704891 + 0.311857I
−0.79242 − 12.21670I −2.18841 + 10.17372I
u = −0.704891 − 0.311857I
−0.79242 + 12.21670I −2.18841 − 10.17372I
u = 0.699597 + 0.306759I
0.47850 + 6.65142I −0.11746 − 5.64209I
u = 0.699597 − 0.306759I
0.47850 − 6.65142I −0.11746 + 5.64209I
u = −0.689405 + 0.322663I
−5.51074 − 5.83032I −7.31545 + 6.21495I
u = −0.689405 − 0.322663I
−5.51074 + 5.83032I −7.31545 − 6.21495I
u = −0.664164 + 0.333637I
−2.13352 + 0.66471I −4.32398 + 0.73800I
u = −0.664164 − 0.333637I
−2.13352 − 0.66471I −4.32398 − 0.73800I
u = 0.666137 + 0.310929I
−0.61066 + 4.17003I −1.12157 − 6.41756I
u = 0.666137 − 0.310929I
−0.61066 − 4.17003I −1.12157 + 6.41756I
u = −0.413044 + 0.606395I
−1.96609 + 8.30515I −4.80450 − 4.74190I
u = −0.413044 − 0.606395I
−1.96609 − 8.30515I −4.80450 + 4.74190I
u = 0.681707 + 0.228443I
4.87892 + 6.05893I 3.69719 − 7.82984I
u = 0.681707 − 0.228443I
4.87892 − 6.05893I 3.69719 + 7.82984I
u = 0.396025 + 0.595654I
−0.70685 − 2.80704I −2.83084 + 0.14074I
u = 0.396025 − 0.595654I
−0.70685 + 2.80704I −2.83084 − 0.14074I
u = −0.433749 + 0.565710I
−6.52578 + 1.97002I −9.89118 − 0.17014I
u = −0.433749 − 0.565710I
−6.52578 − 1.97002I −9.89118 + 0.17014I
u = −0.676333 + 0.213106I
5.07043 − 0.51123I 4.53334 + 1.71722I
u = −0.676333 − 0.213106I
5.07043 + 0.51123I 4.53334 − 1.71722I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.056683 + 1.299530I
−2.45039 − 2.35052I 0
u = 0.056683 − 1.299530I
−2.45039 + 2.35052I 0
u = −0.459986 + 0.517245I
−2.93903 − 4.43801I −6.35807 + 5.78841I
u = −0.459986 − 0.517245I
−2.93903 + 4.43801I −6.35807 − 5.78841I
u = 0.206486 + 1.294640I
−2.19216 − 2.49780I 0
u = 0.206486 − 1.294640I
−2.19216 + 2.49780I 0
u = 0.065792 + 0.683224I
3.01063 − 2.72363I 0.33673 + 3.01262I
u = 0.065792 − 0.683224I
3.01063 + 2.72363I 0.33673 − 3.01262I
u = 0.663935 + 0.070069I
1.99980 − 5.64967I 1.93456 + 4.39907I
u = 0.663935 − 0.070069I
1.99980 + 5.64967I 1.93456 − 4.39907I
u = 0.599228 + 0.293132I
−0.52508 + 3.63472I −4.33135 − 8.21660I
u = 0.599228 − 0.293132I
−0.52508 − 3.63472I −4.33135 + 8.21660I
u = −0.215631 + 1.323780I
−1.38918 − 2.84888I 0
u = −0.215631 − 1.323780I
−1.38918 + 2.84888I 0
u = −0.650050 + 0.090053I
3.00127 + 0.24831I 4.10024 + 0.88196I
u = −0.650050 − 0.090053I
3.00127 − 0.24831I 4.10024 − 0.88196I
u = 0.418598 + 0.502791I
−1.54362 − 0.53691I −4.16267 − 0.20150I
u = 0.418598 − 0.502791I
−1.54362 + 0.53691I −4.16267 + 0.20150I
u = 0.629102
−2.23149 −3.30240
u = −0.578536 + 0.182974I
1.16698 − 0.86834I 4.20454 + 1.66227I
u = −0.578536 − 0.182974I
1.16698 + 0.86834I 4.20454 − 1.66227I
u = −0.224381 + 1.380400I
−3.84517 − 3.80291I 0
u = −0.224381 − 1.380400I
−3.84517 + 3.80291I 0
u = −0.263144 + 1.381250I
0.00387 − 3.92061I 0
u = −0.263144 − 1.381250I
0.00387 + 3.92061I 0
u = 0.185687 + 1.397190I
−6.66224 + 1.71449I 0
u = 0.185687 − 1.397190I
−6.66224 − 1.71449I 0
u = 0.266672 + 1.388180I
−0.26381 + 9.50415I 0
u = 0.266672 − 1.388180I
−0.26381 − 9.50415I 0
u = 0.23377 + 1.40944I
−5.96149 + 6.69826I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.23377 − 1.40944I
−5.96149 − 6.69826I 0
u = 0.15542 + 1.43741I
−7.65214 + 1.56539I 0
u = 0.15542 − 1.43741I
−7.65214 − 1.56539I 0
u = 0.25949 + 1.42349I
−6.16028 + 7.55512I 0
u = 0.25949 − 1.42349I
−6.16028 − 7.55512I 0
u = 0.13211 + 1.44166I
−7.06020 − 0.99574I 0
u = 0.13211 − 1.44166I
−7.06020 + 0.99574I 0
u = 0.27263 + 1.42481I
−5.06046 + 10.19410I 0
u = 0.27263 − 1.42481I
−5.06046 − 10.19410I 0
u = −0.27438 + 1.42745I
−6.3577 − 15.7841I 0
u = −0.27438 − 1.42745I
−6.3577 + 15.7841I 0
u = −0.25586 + 1.43089I
−7.78361 − 2.69789I 0
u = −0.25586 − 1.43089I
−7.78361 + 2.69789I 0
u = −0.13037 + 1.44798I
−8.40998 + 6.46616I 0
u = −0.13037 − 1.44798I
−8.40998 − 6.46616I 0
u = −0.26681 + 1.43012I
−11.1229 − 9.3181I 0
u = −0.26681 − 1.43012I
−11.1229 + 9.3181I 0
u = −0.15977 + 1.44638I
−9.16030 − 6.66044I 0
u = −0.15977 − 1.44638I
−9.16030 + 6.66044I 0
u = −0.14440 + 1.44851I
−12.87500 − 0.05403I 0
u = −0.14440 − 1.44851I
−12.87500 + 0.05403I 0
u = 0.371683 + 0.367425I
−1.215020 − 0.522353I −7.30431 + 0.66479I
u = 0.371683 − 0.367425I
−1.215020 + 0.522353I −7.30431 − 0.66479I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
u
83
+ 29u
82
+ ··· + 2u + 1
c
2
, c
7
u
83
+ u
82
+ ··· + 2u + 1
c
3
, c
6
u
83
− u
82
+ ··· − 134u + 61
c
4
u
83
+ u
82
+ ··· + 12u + 1
c
5
, c
10
, c
11
u
83
− u
82
+ ··· − u
2
+ 1
c
9
u
83
+ 17u
82
+ ··· − 49616u − 2993
c
12
u
83
− 7u
82
+ ··· + 24u − 1
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
83
+ 51y
82
+ ··· − 14y −1
c
2
, c
7
y
83
− 29y
82
+ ··· + 2y −1
c
3
, c
6
y
83
− 57y
82
+ ··· + 104454y −3721
c
4
y
83
+ 7y
82
+ ··· − 46y −1
c
5
, c
10
, c
11
y
83
+ 75y
82
+ ··· + 2y −1
c
9
y
83
+ 31y
82
+ ··· − 117757622y −8958049
c
12
y
83
− y
82
+ ··· − 70y −1
9
