12a
0406
(K12a
0406
)
A knot diagram
1
Linearized knot diagam
3 6 9 11 7 2 1 5 12 4 10 8
Solving Sequence
2,7
6 3 1 8 5 9 4 12 10 11
c
6
c
2
c
1
c
7
c
5
c
8
c
3
c
12
c
9
c
11
c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
89
+ u
88
+ ··· + u − 1i
* 1 irreducible components of dim
C
= 0, with total 89 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
89
+ u
88
+ · · · + 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
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
2
+ 1
u
2
a
9
=
u
14
+ 3u
12
+ 6u
10
+ 7u
8
+ 6u
6
+ 4u
4
+ 2u
2
+ 1
u
14
+ 2u
12
+ 3u
10
+ 2u
8
− u
2
a
4
=
−u
31
− 6u
29
+ ··· − 18u
5
− 6u
3
−u
31
− 5u
29
+ ··· + 2u
3
+ u
a
12
=
u
13
+ 2u
11
+ 3u
9
+ 2u
7
− u
u
15
+ 3u
13
+ 6u
11
+ 7u
9
+ 6u
7
+ 4u
5
+ 2u
3
+ u
a
10
=
u
42
+ 7u
40
+ ··· + u
2
+ 1
u
44
+ 8u
42
+ ··· + 22u
6
+ 5u
4
a
11
=
u
71
+ 12u
69
+ ··· + 16u
5
+ 4u
3
u
73
+ 13u
71
+ ··· + 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
88
− 60u
86
+ ··· + 16u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
89
+ 31u
88
+ ··· − 3u − 1
c
2
, c
6
u
89
− u
88
+ ··· + u + 1
c
3
u
89
+ u
88
+ ··· + 361u + 97
c
4
, c
10
u
89
− u
88
+ ··· + u + 1
c
7
, c
12
u
89
+ 5u
88
+ ··· + 107u + 21
c
8
u
89
− 7u
88
+ ··· − 1205u − 391
c
9
, c
11
u
89
+ 29u
88
+ ··· − 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
89
+ 55y
88
+ ··· + 5y −1
c
2
, c
6
y
89
+ 31y
88
+ ··· − 3y −1
c
3
y
89
− 9y
88
+ ··· + 469821y −9409
c
4
, c
10
y
89
− 29y
88
+ ··· − 3y −1
c
7
, c
12
y
89
+ 59y
88
+ ··· − 9131y −441
c
8
y
89
+ 11y
88
+ ··· − 5202795y −152881
c
9
, c
11
y
89
+ 63y
88
+ ··· − 27y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.792424 + 0.618504I
3.11119 − 5.13284I 0
u = 0.792424 − 0.618504I
3.11119 + 5.13284I 0
u = −0.796751 + 0.614079I
2.10885 + 10.87920I 0
u = −0.796751 − 0.614079I
2.10885 − 10.87920I 0
u = 0.756551 + 0.674024I
5.26973 − 2.66595I 0
u = 0.756551 − 0.674024I
5.26973 + 2.66595I 0
u = −0.781291 + 0.601828I
−3.26113 + 5.11902I 0
u = −0.781291 − 0.601828I
−3.26113 − 5.11902I 0
u = −0.749471 + 0.687801I
4.91888 − 3.02362I 0
u = −0.749471 − 0.687801I
4.91888 + 3.02362I 0
u = 0.762514 + 0.617485I
0.72677 − 2.95488I 0
u = 0.762514 − 0.617485I
0.72677 + 2.95488I 0
u = −0.050173 + 0.978604I
−0.29363 − 2.69848I 0
u = −0.050173 − 0.978604I
−0.29363 + 2.69848I 0
u = 0.414241 + 0.879359I
0.79840 + 7.49051I 0
u = 0.414241 − 0.879359I
0.79840 − 7.49051I 0
u = −0.448726 + 0.856142I
1.61410 − 2.05998I 0
u = −0.448726 − 0.856142I
1.61410 + 2.05998I 0
u = −0.746043 + 0.583768I
−1.104240 − 0.816505I 0
u = −0.746043 − 0.583768I
−1.104240 + 0.816505I 0
u = −0.705718 + 0.816241I
1.374950 − 0.274630I 0
u = −0.705718 − 0.816241I
1.374950 + 0.274630I 0
u = −0.037143 + 1.080270I
−5.00271 − 2.21550I 0
u = −0.037143 − 1.080270I
−5.00271 + 2.21550I 0
u = −0.063504 + 1.094470I
−2.92880 − 4.38942I 0
u = −0.063504 − 1.094470I
−2.92880 + 4.38942I 0
u = 0.018621 + 1.097080I
−6.71736 − 1.83677I 0
u = 0.018621 − 1.097080I
−6.71736 + 1.83677I 0
u = 0.045471 + 1.100660I
−9.16961 + 4.22423I 0
u = 0.045471 − 1.100660I
−9.16961 − 4.22423I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.063947 + 1.101120I
−3.96933 + 10.08100I 0
u = 0.063947 − 1.101120I
−3.96933 − 10.08100I 0
u = 0.111277 + 0.878977I
−0.48030 − 2.60995I −8.16580 + 1.81655I
u = 0.111277 − 0.878977I
−0.48030 + 2.60995I −8.16580 − 1.81655I
u = −0.748159 + 0.826966I
6.86792 + 4.32397I 0
u = −0.748159 − 0.826966I
6.86792 − 4.32397I 0
u = 0.715743 + 0.859066I
4.12520 + 2.73162I 0
u = 0.715743 − 0.859066I
4.12520 − 2.73162I 0
u = 0.701524 + 0.532948I
−1.45390 − 3.14036I −5.81541 + 3.08693I
u = 0.701524 − 0.532948I
−1.45390 + 3.14036I −5.81541 − 3.08693I
u = 0.745460 + 0.835125I
7.56666 + 1.42671I 0
u = 0.745460 − 0.835125I
7.56666 − 1.42671I 0
u = 0.313983 + 0.821757I
−3.73770 + 2.25778I −12.76156 − 5.27279I
u = 0.313983 − 0.821757I
−3.73770 − 2.25778I −12.76156 + 5.27279I
u = −0.702092 + 0.892182I
1.14647 − 5.11858I 0
u = −0.702092 − 0.892182I
1.14647 + 5.11858I 0
u = 0.735138 + 0.888062I
7.40603 + 4.18505I 0
u = 0.735138 − 0.888062I
7.40603 − 4.18505I 0
u = −0.734636 + 0.895406I
6.66040 − 9.94218I 0
u = −0.734636 − 0.895406I
6.66040 + 9.94218I 0
u = −0.611338 + 0.569358I
−0.124299 − 0.982347I −2.27042 + 3.59861I
u = −0.611338 − 0.569358I
−0.124299 + 0.982347I −2.27042 − 3.59861I
u = −0.599043 + 1.012220I
0.31919 − 2.05341I 0
u = −0.599043 − 1.012220I
0.31919 + 2.05341I 0
u = 0.596824 + 1.020580I
−0.71708 − 3.53466I 0
u = 0.596824 − 1.020580I
−0.71708 + 3.53466I 0
u = 0.662757 + 0.464863I
−4.15479 + 2.64865I −8.87639 − 4.03321I
u = 0.662757 − 0.464863I
−4.15479 − 2.64865I −8.87639 + 4.03321I
u = −0.632747 + 1.010330I
−1.35976 − 4.01784I 0
u = −0.632747 − 1.010330I
−1.35976 + 4.01784I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.616311 + 1.024920I
−5.65284 + 2.29612I 0
u = 0.616311 − 1.024920I
−5.65284 − 2.29612I 0
u = −0.687197 + 0.991834I
4.00117 − 2.45258I 0
u = −0.687197 − 0.991834I
4.00117 + 2.45258I 0
u = 0.638227 + 1.029020I
−2.85651 + 8.30192I 0
u = 0.638227 − 1.029020I
−2.85651 − 8.30192I 0
u = 0.688393 + 1.000560I
4.28705 + 8.16569I 0
u = 0.688393 − 1.000560I
4.28705 − 8.16569I 0
u = −0.664209 + 1.031080I
−2.41122 − 4.56435I 0
u = −0.664209 − 1.031080I
−2.41122 + 4.56435I 0
u = 0.657312 + 0.403482I
0.89298 + 8.30474I −2.77230 − 7.50293I
u = 0.657312 − 0.403482I
0.89298 − 8.30474I −2.77230 + 7.50293I
u = 0.677609 + 1.026170I
−0.48705 + 8.43111I 0
u = 0.677609 − 1.026170I
−0.48705 − 8.43111I 0
u = −0.679374 + 1.036700I
−4.55418 − 10.64520I 0
u = −0.679374 − 1.036700I
−4.55418 + 10.64520I 0
u = 0.688505 + 1.034580I
1.86598 + 10.72270I 0
u = 0.688505 − 1.034580I
1.86598 − 10.72270I 0
u = −0.688639 + 1.037620I
0.8409 − 16.4799I 0
u = −0.688639 − 1.037620I
0.8409 + 16.4799I 0
u = −0.635260 + 0.400865I
1.86099 − 2.66579I −0.88903 + 2.73641I
u = −0.635260 − 0.400865I
1.86099 + 2.66579I −0.88903 − 2.73641I
u = −0.349167 + 0.527838I
−0.135235 − 1.066210I −2.23468 + 5.96441I
u = −0.349167 − 0.527838I
−0.135235 + 1.066210I −2.23468 − 5.96441I
u = −0.501948 + 0.197273I
3.26226 − 1.15588I 2.07588 + 2.90357I
u = −0.501948 − 0.197273I
3.26226 + 1.15588I 2.07588 − 2.90357I
u = 0.507837 + 0.153612I
2.69964 − 4.37412I 0.81673 + 3.12761I
u = 0.507837 − 0.153612I
2.69964 + 4.37412I 0.81673 − 3.12761I
u = 0.403915
−1.63407 −4.55070
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
89
+ 31u
88
+ ··· − 3u − 1
c
2
, c
6
u
89
− u
88
+ ··· + u + 1
c
3
u
89
+ u
88
+ ··· + 361u + 97
c
4
, c
10
u
89
− u
88
+ ··· + u + 1
c
7
, c
12
u
89
+ 5u
88
+ ··· + 107u + 21
c
8
u
89
− 7u
88
+ ··· − 1205u − 391
c
9
, c
11
u
89
+ 29u
88
+ ··· − 3u + 1
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
89
+ 55y
88
+ ··· + 5y −1
c
2
, c
6
y
89
+ 31y
88
+ ··· − 3y −1
c
3
y
89
− 9y
88
+ ··· + 469821y −9409
c
4
, c
10
y
89
− 29y
88
+ ··· − 3y −1
c
7
, c
12
y
89
+ 59y
88
+ ··· − 9131y −441
c
8
y
89
+ 11y
88
+ ··· − 5202795y −152881
c
9
, c
11
y
89
+ 63y
88
+ ··· − 27y −1
9
