12a
0583
(K12a
0583
)
A knot diagram
1
Linearized knot diagam
3 7 9 10 11 8 2 1 12 5 4 6
Solving Sequence
3,7
2 8 1 9 4 6 12 10 11 5
c
2
c
7
c
1
c
8
c
3
c
6
c
12
c
9
c
11
c
5
c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
80
− u
79
+ ··· + 2u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 80 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
80
− u
79
+ · · · + 2u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
8
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
9
=
u
7
+ 2u
5
+ 2u
3
+ 2u
u
7
+ u
5
+ 2u
3
+ u
a
4
=
−u
14
− 3u
12
− 6u
10
− 9u
8
− 8u
6
− 6u
4
− 2u
2
+ 1
−u
14
− 2u
12
− 5u
10
− 6u
8
− 6u
6
− 4u
4
− u
2
a
6
=
u
3
u
5
+ u
3
+ u
a
12
=
u
10
+ u
8
+ 2u
6
+ u
4
+ u
2
+ 1
u
12
+ 2u
10
+ 4u
8
+ 4u
6
+ 3u
4
+ 2u
2
a
10
=
−u
29
− 4u
27
+ ··· + 2u
3
+ 3u
−u
31
− 5u
29
+ ··· + 4u
3
+ u
a
11
=
u
40
+ 7u
38
+ ··· + 4u
2
+ 1
u
40
+ 6u
38
+ ··· − 12u
6
+ 2u
2
a
5
=
−u
74
− 11u
72
+ ··· + u
2
+ 1
−u
76
− 12u
74
+ ··· + 18u
6
+ 5u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
78
+ 4u
77
+ ··· + 8u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
80
+ 25u
79
+ ··· + 4u + 1
c
2
, c
7
u
80
+ u
79
+ ··· + 2u
2
+ 1
c
3
, c
12
u
80
+ u
79
+ ··· − 172u + 40
c
4
, c
5
, c
10
u
80
− u
79
+ ··· + 2u + 1
c
8
u
80
− 5u
79
+ ··· − 932u + 57
c
9
u
80
+ 19u
79
+ ··· + 1544u + 89
c
11
u
80
+ 3u
79
+ ··· + 14u + 3
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
80
+ 61y
79
+ ··· + 24y + 1
c
2
, c
7
y
80
+ 25y
79
+ ··· + 4y + 1
c
3
, c
12
y
80
− 63y
79
+ ··· + 27216y + 1600
c
4
, c
5
, c
10
y
80
− 71y
79
+ ··· + 4y + 1
c
8
y
80
− 19y
79
+ ··· − 264424y + 3249
c
9
y
80
+ 9y
79
+ ··· + 393576y + 7921
c
11
y
80
+ 5y
79
+ ··· − 52y + 9
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.619966 + 0.786914I
0.42644 − 1.54033I 0
u = −0.619966 − 0.786914I
0.42644 + 1.54033I 0
u = −0.229389 + 0.976414I
−0.61767 − 2.77149I 0
u = −0.229389 − 0.976414I
−0.61767 + 2.77149I 0
u = −0.203923 + 0.991830I
−0.77157 − 2.75902I 0
u = −0.203923 − 0.991830I
−0.77157 + 2.75902I 0
u = −0.309223 + 0.937662I
−3.45303 + 4.19727I 0
u = −0.309223 − 0.937662I
−3.45303 − 4.19727I 0
u = 0.518377 + 0.839755I
−5.13729 + 3.43589I 0
u = 0.518377 − 0.839755I
−5.13729 − 3.43589I 0
u = −0.024413 + 0.986356I
−3.66960 − 1.60184I −7.19925 + 4.73035I
u = −0.024413 − 0.986356I
−3.66960 + 1.60184I −7.19925 − 4.73035I
u = 0.148549 + 1.004380I
−6.95009 + 1.80190I 0
u = 0.148549 − 1.004380I
−6.95009 − 1.80190I 0
u = 0.273076 + 0.944130I
1.59921 − 0.69313I 0
u = 0.273076 − 0.944130I
1.59921 + 0.69313I 0
u = 0.029820 + 1.016980I
−9.23696 + 4.28967I 0
u = 0.029820 − 1.016980I
−9.23696 − 4.28967I 0
u = 0.662709 + 0.705824I
1.21175 − 1.58323I 0. + 4.26377I
u = 0.662709 − 0.705824I
1.21175 + 1.58323I 0. − 4.26377I
u = 0.202557 + 1.021710I
0.97049 + 6.47019I 0
u = 0.202557 − 1.021710I
0.97049 − 6.47019I 0
u = −0.197204 + 1.033250I
−4.29004 − 10.10410I 0
u = −0.197204 − 1.033250I
−4.29004 + 10.10410I 0
u = −0.664562 + 0.656622I
−4.15092 + 4.60431I −2.70077 − 3.70353I
u = −0.664562 − 0.656622I
−4.15092 − 4.60431I −2.70077 + 3.70353I
u = −0.800857 + 0.723425I
−0.65569 + 1.27499I 0
u = −0.800857 − 0.723425I
−0.65569 − 1.27499I 0
u = 0.833959 + 0.720054I
2.54380 − 9.63751I 0
u = 0.833959 − 0.720054I
2.54380 + 9.63751I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.831932 + 0.726163I
7.79063 + 5.89158I 0
u = −0.831932 − 0.726163I
7.79063 − 5.89158I 0
u = 0.825177 + 0.735546I
5.94352 − 1.97384I 0
u = 0.825177 − 0.735546I
5.94352 + 1.97384I 0
u = −0.738819 + 0.827281I
0.331327 + 0.184079I 0
u = −0.738819 − 0.827281I
0.331327 − 0.184079I 0
u = 0.824599 + 0.748438I
6.16085 − 1.74955I 0
u = 0.824599 − 0.748438I
6.16085 + 1.74955I 0
u = −0.823667 + 0.762018I
8.44386 − 2.05213I 0
u = −0.823667 − 0.762018I
8.44386 + 2.05213I 0
u = 0.822681 + 0.770940I
3.46646 + 5.77538I 0
u = 0.822681 − 0.770940I
3.46646 − 5.77538I 0
u = 0.723307 + 0.867234I
4.04288 + 2.75909I 0
u = 0.723307 − 0.867234I
4.04288 − 2.75909I 0
u = 0.625784 + 0.954049I
−5.78541 + 1.18269I 0
u = 0.625784 − 0.954049I
−5.78541 − 1.18269I 0
u = −0.651819 + 0.939019I
−0.08169 − 3.46733I 0
u = −0.651819 − 0.939019I
−0.08169 + 3.46733I 0
u = −0.729625 + 0.901949I
0.10678 − 5.76811I 0
u = −0.729625 − 0.901949I
0.10678 + 5.76811I 0
u = 0.669067 + 0.963826I
0.45244 + 6.78522I 0
u = 0.669067 − 0.963826I
0.45244 − 6.78522I 0
u = −0.662943 + 0.978808I
−5.07006 − 9.78770I 0
u = −0.662943 − 0.978808I
−5.07006 + 9.78770I 0
u = −0.729433 + 0.993592I
−1.47902 − 7.03962I 0
u = −0.729433 − 0.993592I
−1.47902 + 7.03962I 0
u = 0.758648 + 0.973630I
2.84191 + 0.14624I 0
u = 0.758648 − 0.973630I
2.84191 − 0.14624I 0
u = −0.755419 + 0.979729I
7.77358 − 3.86199I 0
u = −0.755419 − 0.979729I
7.77358 + 3.86199I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.750624 + 0.988208I
5.42406 + 7.65060I 0
u = 0.750624 − 0.988208I
5.42406 − 7.65060I 0
u = 0.745337 + 0.995580I
5.14520 + 7.85865I 0
u = 0.745337 − 0.995580I
5.14520 − 7.85865I 0
u = −0.745312 + 1.003050I
6.94092 − 11.79480I 0
u = −0.745312 − 1.003050I
6.94092 + 11.79480I 0
u = 0.743866 + 1.006870I
1.6640 + 15.5411I 0
u = 0.743866 − 1.006870I
1.6640 − 15.5411I 0
u = 0.451632 + 0.486887I
−4.91838 + 3.38985I −3.46005 − 4.67060I
u = 0.451632 − 0.486887I
−4.91838 − 3.38985I −3.46005 + 4.67060I
u = −0.649486 + 0.072886I
−0.73064 − 7.38585I 2.01990 + 5.41683I
u = −0.649486 − 0.072886I
−0.73064 + 7.38585I 2.01990 − 5.41683I
u = 0.642091 + 0.053310I
4.41670 + 3.73992I 6.95982 − 4.49240I
u = 0.642091 − 0.053310I
4.41670 − 3.73992I 6.95982 + 4.49240I
u = −0.625192 + 0.014679I
2.42454 − 0.05216I 4.20411 − 0.59319I
u = −0.625192 − 0.014679I
2.42454 + 0.05216I 4.20411 + 0.59319I
u = 0.517369 + 0.128509I
−3.48911 − 0.30076I −0.040470 − 1.348912I
u = 0.517369 − 0.128509I
−3.48911 + 0.30076I −0.040470 + 1.348912I
u = −0.276045 + 0.350553I
0.105034 − 0.970178I 2.01489 + 6.99046I
u = −0.276045 − 0.350553I
0.105034 + 0.970178I 2.01489 − 6.99046I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
80
+ 25u
79
+ ··· + 4u + 1
c
2
, c
7
u
80
+ u
79
+ ··· + 2u
2
+ 1
c
3
, c
12
u
80
+ u
79
+ ··· − 172u + 40
c
4
, c
5
, c
10
u
80
− u
79
+ ··· + 2u + 1
c
8
u
80
− 5u
79
+ ··· − 932u + 57
c
9
u
80
+ 19u
79
+ ··· + 1544u + 89
c
11
u
80
+ 3u
79
+ ··· + 14u + 3
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
80
+ 61y
79
+ ··· + 24y + 1
c
2
, c
7
y
80
+ 25y
79
+ ··· + 4y + 1
c
3
, c
12
y
80
− 63y
79
+ ··· + 27216y + 1600
c
4
, c
5
, c
10
y
80
− 71y
79
+ ··· + 4y + 1
c
8
y
80
− 19y
79
+ ··· − 264424y + 3249
c
9
y
80
+ 9y
79
+ ··· + 393576y + 7921
c
11
y
80
+ 5y
79
+ ··· − 52y + 9
9
