12a
0497
(K12a
0497
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 10 2 1 12 11 5 4 6
Solving Sequence
3,7
2 1 8 4 6 12 9 5 11 10
c
2
c
1
c
7
c
3
c
6
c
12
c
8
c
4
c
11
c
10
c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
104
− u
103
+ ··· + 2u
3
+ 1i
* 1 irreducible components of dim
C
= 0, with total 104 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
104
− u
103
+ · · · + 2u
3
+ 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
8
=
u
5
− 2u
3
+ u
u
5
− u
3
+ u
a
4
=
−u
10
+ 3u
8
− 4u
6
+ 3u
4
− u
2
+ 1
−u
10
+ 2u
8
− 3u
6
+ 2u
4
− u
2
a
6
=
u
−u
3
+ u
a
12
=
u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
9
=
u
19
− 4u
17
+ 8u
15
− 8u
13
+ 3u
11
+ 2u
9
− 2u
7
+ 2u
5
− 3u
3
+ 2u
−u
21
+ 5u
19
− 13u
17
+ 20u
15
− 20u
13
+ 13u
11
− 7u
9
+ 4u
7
− u
5
− u
3
+ u
a
5
=
u
50
− 11u
48
+ ··· + u
2
+ 1
−u
52
+ 12u
50
+ ··· − 8u
6
+ u
4
a
11
=
−u
28
+ 7u
26
+ ··· + u
2
+ 1
−u
28
+ 6u
26
+ ··· + 8u
6
− 3u
4
a
10
=
u
77
− 18u
75
+ ··· − 4u
3
+ u
u
77
− 17u
75
+ ··· − u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
102
− 92u
100
+ ··· − 4u
2
− 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
104
+ 47u
103
+ ··· + 2u
2
+ 1
c
2
, c
6
u
104
− u
103
+ ··· + 2u
3
+ 1
c
3
, c
12
u
104
+ u
103
+ ··· − 22u + 1
c
4
u
104
− u
103
+ ··· − 4786u + 1237
c
5
, c
10
u
104
+ u
103
+ ··· + 2u + 1
c
7
u
104
− 3u
103
+ ··· − 8u + 3
c
8
u
104
+ 13u
103
+ ··· + 20u + 1
c
9
u
104
+ 49u
103
+ ··· + 2u
2
+ 1
c
11
u
104
+ 5u
103
+ ··· + 17926u + 3477
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
104
+ 21y
103
+ ··· + 4y + 1
c
2
, c
6
y
104
− 47y
103
+ ··· + 2y
2
+ 1
c
3
, c
12
y
104
− 79y
103
+ ··· + 112y + 1
c
4
y
104
− 23y
103
+ ··· − 66086992y + 1530169
c
5
, c
10
y
104
+ 49y
103
+ ··· + 2y
2
+ 1
c
7
y
104
+ 5y
103
+ ··· + 800y + 9
c
8
y
104
+ y
103
+ ··· + 284y + 1
c
9
y
104
+ 13y
103
+ ··· + 4y + 1
c
11
y
104
+ 29y
103
+ ··· + 539591540y + 12089529
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.859307 + 0.524203I
−0.01758 + 7.72337I 0
u = −0.859307 − 0.524203I
−0.01758 − 7.72337I 0
u = 0.836775 + 0.503199I
1.90773 − 2.97029I 0
u = 0.836775 − 0.503199I
1.90773 + 2.97029I 0
u = −1.011650 + 0.233039I
−2.04169 + 0.66017I 0
u = −1.011650 − 0.233039I
−2.04169 − 0.66017I 0
u = −0.980187 + 0.397197I
−1.88622 + 1.31284I 0
u = −0.980187 − 0.397197I
−1.88622 − 1.31284I 0
u = −1.056710 + 0.066632I
0.57803 + 2.08421I 0
u = −1.056710 − 0.066632I
0.57803 − 2.08421I 0
u = −0.958501 + 0.452296I
−1.91153 + 1.29780I 0
u = −0.958501 − 0.452296I
−1.91153 − 1.29780I 0
u = 1.070350 + 0.091384I
1.69880 + 2.66563I 0
u = 1.070350 − 0.091384I
1.69880 − 2.66563I 0
u = 1.055850 + 0.204960I
−5.41329 + 2.54049I 0
u = 1.055850 − 0.204960I
−5.41329 − 2.54049I 0
u = 0.542072 + 0.741306I
3.99783 − 9.10436I 0
u = 0.542072 − 0.741306I
3.99783 + 9.10436I 0
u = 1.051860 + 0.253380I
−4.49361 − 4.87932I 0
u = 1.051860 − 0.253380I
−4.49361 + 4.87932I 0
u = −0.534590 + 0.741284I
6.16977 + 4.04816I 0
u = −0.534590 − 0.741284I
6.16977 − 4.04816I 0
u = −0.515131 + 0.748064I
7.20284 + 1.69792I 0
u = −0.515131 − 0.748064I
7.20284 − 1.69792I 0
u = −1.083390 + 0.136794I
−4.04015 − 2.23636I 0
u = −1.083390 − 0.136794I
−4.04015 + 2.23636I 0
u = 0.504216 + 0.753178I
5.99912 + 3.19718I 0
u = 0.504216 − 0.753178I
5.99912 − 3.19718I 0
u = 1.092950 + 0.116654I
0.50313 + 4.81762I 0
u = 1.092950 − 0.116654I
0.50313 − 4.81762I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.756728 + 0.484409I
2.14268 − 1.17121I 6.64343 + 0.I
u = 0.756728 − 0.484409I
2.14268 + 1.17121I 6.64343 + 0.I
u = 0.531824 + 0.723039I
1.51039 − 1.63841I 0
u = 0.531824 − 0.723039I
1.51039 + 1.63841I 0
u = 0.453000 + 0.771117I
5.72060 − 0.33111I 5.65604 + 0.I
u = 0.453000 − 0.771117I
5.72060 + 0.33111I 5.65604 + 0.I
u = −0.442763 + 0.774845I
6.80677 − 4.55207I 7.37432 + 3.79202I
u = −0.442763 − 0.774845I
6.80677 + 4.55207I 7.37432 − 3.79202I
u = −1.101690 + 0.121004I
−1.74425 − 9.83174I 0
u = −1.101690 − 0.121004I
−1.74425 + 9.83174I 0
u = 0.422973 + 0.784494I
3.34574 + 11.96320I 0. − 7.58874I
u = 0.422973 − 0.784494I
3.34574 − 11.96320I 0. + 7.58874I
u = −0.427276 + 0.781006I
5.58256 − 6.89102I 5.88164 + 3.70083I
u = −0.427276 − 0.781006I
5.58256 + 6.89102I 5.88164 − 3.70083I
u = 0.420575 + 0.770410I
0.90649 + 4.32693I 0. − 2.33566I
u = 0.420575 − 0.770410I
0.90649 − 4.32693I 0. + 2.33566I
u = −0.705886 + 0.507842I
0.40911 − 3.44910I 3.11069 + 2.13802I
u = −0.705886 − 0.507842I
0.40911 + 3.44910I 3.11069 − 2.13802I
u = −1.077900 + 0.384069I
−3.24714 + 0.72316I 0
u = −1.077900 − 0.384069I
−3.24714 − 0.72316I 0
u = 1.091470 + 0.378875I
−5.64601 + 3.93267I 0
u = 1.091470 − 0.378875I
−5.64601 − 3.93267I 0
u = 1.057270 + 0.468756I
−1.30857 − 5.15318I 0
u = 1.057270 − 0.468756I
−1.30857 + 5.15318I 0
u = 1.091190 + 0.402366I
−7.16519 − 3.66403I 0
u = 1.091190 − 0.402366I
−7.16519 + 3.66403I 0
u = 0.442649 + 0.704496I
2.18390 + 1.10352I 3.36438 − 0.54429I
u = 0.442649 − 0.704496I
2.18390 − 1.10352I 3.36438 + 0.54429I
u = −0.406121 + 0.717438I
−0.98090 − 4.64543I −1.49398 + 4.59581I
u = −0.406121 − 0.717438I
−0.98090 + 4.64543I −1.49398 − 4.59581I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.096760 + 0.443551I
−6.88645 + 3.66322I 0
u = −1.096760 − 0.443551I
−6.88645 − 3.66322I 0
u = 1.092910 + 0.459875I
−2.73025 − 6.49785I 0
u = 1.092910 − 0.459875I
−2.73025 + 6.49785I 0
u = −1.102030 + 0.460728I
−5.09595 + 11.30370I 0
u = −1.102030 − 0.460728I
−5.09595 − 11.30370I 0
u = 1.033640 + 0.601494I
0.01999 − 3.42754I 0
u = 1.033640 − 0.601494I
0.01999 + 3.42754I 0
u = 1.031380 + 0.616617I
2.54297 + 3.93822I 0
u = 1.031380 − 0.616617I
2.54297 − 3.93822I 0
u = −1.036210 + 0.614543I
4.67843 + 1.11092I 0
u = −1.036210 − 0.614543I
4.67843 − 1.11092I 0
u = −1.076910 + 0.561271I
−2.47407 + 2.03216I 0
u = −1.076910 − 0.561271I
−2.47407 − 2.03216I 0
u = −1.049530 + 0.613467I
5.61409 + 3.47527I 0
u = −1.049530 − 0.613467I
5.61409 − 3.47527I 0
u = 1.056730 + 0.613529I
4.35675 − 8.38369I 0
u = 1.056730 − 0.613529I
4.35675 + 8.38369I 0
u = 1.076960 + 0.578529I
0.31558 − 6.04373I 0
u = 1.076960 − 0.578529I
0.31558 + 6.04373I 0
u = −1.090550 + 0.576963I
−2.98339 + 9.60531I 0
u = −1.090550 − 0.576963I
−2.98339 − 9.60531I 0
u = 1.086520 + 0.607111I
3.83813 − 4.87610I 0
u = 1.086520 − 0.607111I
3.83813 + 4.87610I 0
u = −0.425267 + 0.621881I
−0.56836 + 2.70224I 0.03525 − 3.31047I
u = −0.425267 − 0.621881I
−0.56836 − 2.70224I 0.03525 + 3.31047I
u = −1.092040 + 0.605858I
4.87795 + 9.76344I 0
u = −1.092040 − 0.605858I
4.87795 − 9.76344I 0
u = 1.099510 + 0.597884I
−1.10494 − 9.49521I 0
u = 1.099510 − 0.597884I
−1.10494 + 9.49521I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.100100 + 0.603734I
3.58412 + 12.10850I 0
u = −1.100100 − 0.603734I
3.58412 − 12.10850I 0
u = 1.102800 + 0.603758I
1.3260 − 17.1890I 0
u = 1.102800 − 0.603758I
1.3260 + 17.1890I 0
u = −0.440195 + 0.550648I
−0.56785 + 2.71251I 0.81371 − 3.53130I
u = −0.440195 − 0.550648I
−0.56785 − 2.71251I 0.81371 + 3.53130I
u = −0.115185 + 0.609334I
−2.40566 − 7.26290I −1.85956 + 7.00955I
u = −0.115185 − 0.609334I
−2.40566 + 7.26290I −1.85956 − 7.00955I
u = 0.122607 + 0.579644I
−0.12195 + 2.52084I 1.47418 − 3.47002I
u = 0.122607 − 0.579644I
−0.12195 − 2.52084I 1.47418 + 3.47002I
u = −0.062282 + 0.583449I
−4.12580 + 0.18635I −5.37095 + 0.17680I
u = −0.062282 − 0.583449I
−4.12580 − 0.18635I −5.37095 − 0.17680I
u = 0.223352 + 0.497108I
0.88054 + 1.24792I 3.91671 − 4.24844I
u = 0.223352 − 0.497108I
0.88054 − 1.24792I 3.91671 + 4.24844I
8
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
104
+ 47u
103
+ ··· + 2u
2
+ 1
c
2
, c
6
u
104
− u
103
+ ··· + 2u
3
+ 1
c
3
, c
12
u
104
+ u
103
+ ··· − 22u + 1
c
4
u
104
− u
103
+ ··· − 4786u + 1237
c
5
, c
10
u
104
+ u
103
+ ··· + 2u + 1
c
7
u
104
− 3u
103
+ ··· − 8u + 3
c
8
u
104
+ 13u
103
+ ··· + 20u + 1
c
9
u
104
+ 49u
103
+ ··· + 2u
2
+ 1
c
11
u
104
+ 5u
103
+ ··· + 17926u + 3477
9
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
104
+ 21y
103
+ ··· + 4y + 1
c
2
, c
6
y
104
− 47y
103
+ ··· + 2y
2
+ 1
c
3
, c
12
y
104
− 79y
103
+ ··· + 112y + 1
c
4
y
104
− 23y
103
+ ··· − 66086992y + 1530169
c
5
, c
10
y
104
+ 49y
103
+ ··· + 2y
2
+ 1
c
7
y
104
+ 5y
103
+ ··· + 800y + 9
c
8
y
104
+ y
103
+ ··· + 284y + 1
c
9
y
104
+ 13y
103
+ ··· + 4y + 1
c
11
y
104
+ 29y
103
+ ··· + 539591540y + 12089529
10
