12a
0147
(K12a
0147
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 10 11 12 1 4 6 8 7
Solving Sequence
1,7
12 8
4,9
10 3 2 11 6 5
c
12
c
7
c
8
c
9
c
3
c
1
c
11
c
6
c
5
c
2
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
58
+ u
57
+ ··· + b − u, 2u
57
− u
56
+ ··· + a − 1, u
60
− 2u
59
+ ··· − 2u + 1i
I
u
2
= hb − 1, −u
4
− u
3
− 2u
2
+ a − u − 1, u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 66 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
58
+ u
57
+ · · · + b − u, 2u
57
− u
56
+ · · · + a − 1, u
60
− 2u
59
+ · · · − 2u + 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
12
=
1
u
2
a
8
=
u
u
3
+ u
a
4
=
−2u
57
+ u
56
+ ··· − 5u + 1
−u
58
− u
57
+ ··· + 4u
2
+ u
a
9
=
u
3
+ 2u
u
3
+ u
a
10
=
−u
8
− 3u
6
− 3u
4
+ 1
−u
10
− 4u
8
− 5u
6
+ 3u
2
a
3
=
−u
55
+ u
54
+ ··· + 13u
2
− 5u
−u
57
+ u
56
+ ··· − 22u
3
+ 5u
2
a
2
=
u
57
− u
56
+ ··· − 10u
2
+ 4u
u
57
− u
56
+ ··· + 14u
3
− 5u
2
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
5
=
u
11
+ 4u
9
+ 6u
7
+ 2u
5
− 3u
3
− 2u
u
13
+ 5u
11
+ 9u
9
+ 4u
7
− 6u
5
− 5u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
59
+ 8u
58
+ ··· + 16u + 11
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
60
+ 25u
59
+ ··· + 71u + 1
c
2
, c
4
u
60
− 7u
59
+ ··· − 15u + 1
c
3
, c
9
u
60
− u
59
+ ··· − 128u + 64
c
5
, c
6
, c
8
c
10
u
60
+ 2u
59
+ ··· − 22u + 17
c
7
, c
11
, c
12
u
60
− 2u
59
+ ··· − 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
60
+ 27y
59
+ ··· − 5339y + 1
c
2
, c
4
y
60
− 25y
59
+ ··· − 71y + 1
c
3
, c
9
y
60
− 39y
59
+ ··· − 102400y + 4096
c
5
, c
6
, c
8
c
10
y
60
− 74y
59
+ ··· − 246y + 289
c
7
, c
11
, c
12
y
60
+ 46y
59
+ ··· + 2y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.291512 + 1.030160I
a = −0.678030 − 1.056140I
b = −1.19725 + 0.90363I
2.03627 + 3.48281I 9.26462 + 0.I
u = −0.291512 − 1.030160I
a = −0.678030 + 1.056140I
b = −1.19725 − 0.90363I
2.03627 − 3.48281I 9.26462 + 0.I
u = 0.924382 + 0.020442I
a = 4.05935 − 0.66619I
b = 3.19998 − 0.28395I
15.6684 + 2.9598I 14.3979 − 0.9035I
u = 0.924382 − 0.020442I
a = 4.05935 + 0.66619I
b = 3.19998 + 0.28395I
15.6684 − 2.9598I 14.3979 + 0.9035I
u = 0.920041 + 0.033760I
a = −3.85415 + 1.05460I
b = −3.05121 + 0.44044I
13.7623 + 9.2779I 12.25398 − 5.25271I
u = 0.920041 − 0.033760I
a = −3.85415 − 1.05460I
b = −3.05121 − 0.44044I
13.7623 − 9.2779I 12.25398 + 5.25271I
u = −0.911537 + 0.010474I
a = 0.074147 + 0.576052I
b = 0.121976 + 0.842888I
9.99754 − 2.62685I 11.37857 + 2.57042I
u = −0.911537 − 0.010474I
a = 0.074147 − 0.576052I
b = 0.121976 − 0.842888I
9.99754 + 2.62685I 11.37857 − 2.57042I
u = 0.907065
a = −5.12768
b = −3.74684
8.33706 11.8870
u = −0.858590
a = 0.363466
b = 0.491382
6.74177 17.3790
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.312735 + 1.108170I
a = 0.561203 + 1.060260I
b = 1.21319 − 0.89450I
3.00527 − 2.16368I 0
u = −0.312735 − 1.108170I
a = 0.561203 − 1.060260I
b = 1.21319 + 0.89450I
3.00527 + 2.16368I 0
u = 0.220037 + 1.166580I
a = −0.541278 − 0.506954I
b = −0.442672 − 0.001765I
−2.04443 + 1.13435I 0
u = 0.220037 − 1.166580I
a = −0.541278 + 0.506954I
b = −0.442672 + 0.001765I
−2.04443 − 1.13435I 0
u = 0.090975 + 1.210730I
a = −0.625680 − 0.018522I
b = 0.008321 + 0.346144I
−2.94977 + 1.52826I 0
u = 0.090975 − 1.210730I
a = −0.625680 + 0.018522I
b = 0.008321 − 0.346144I
−2.94977 − 1.52826I 0
u = −0.216557 + 1.227250I
a = −0.06688 − 1.83452I
b = −1.97312 + 0.77412I
−3.87712 − 2.82894I 0
u = −0.216557 − 1.227250I
a = −0.06688 + 1.83452I
b = −1.97312 − 0.77412I
−3.87712 + 2.82894I 0
u = −0.023050 + 1.250010I
a = 1.380020 − 0.264318I
b = −0.591773 − 0.904308I
−5.85350 − 1.02296I 0
u = −0.023050 − 1.250010I
a = 1.380020 + 0.264318I
b = −0.591773 + 0.904308I
−5.85350 + 1.02296I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.245047 + 1.253190I
a = 0.378482 + 0.886324I
b = 0.132951 + 0.216928I
−2.88526 + 5.03495I 0
u = 0.245047 − 1.253190I
a = 0.378482 − 0.886324I
b = 0.132951 − 0.216928I
−2.88526 − 5.03495I 0
u = −0.705473 + 0.105742I
a = 1.36818 + 0.60284I
b = 1.53947 + 0.34903I
5.97344 − 1.58067I 14.4844 + 1.7262I
u = −0.705473 − 0.105742I
a = 1.36818 − 0.60284I
b = 1.53947 − 0.34903I
5.97344 + 1.58067I 14.4844 − 1.7262I
u = −0.683970 + 0.169452I
a = −1.37278 − 0.90433I
b = −1.63862 − 0.45396I
4.53909 − 7.15924I 11.78808 + 7.26929I
u = −0.683970 − 0.169452I
a = −1.37278 + 0.90433I
b = −1.63862 + 0.45396I
4.53909 + 7.15924I 11.78808 − 7.26929I
u = −0.289347 + 1.277000I
a = −0.288688 + 1.121530I
b = 1.51609 − 0.18929I
1.70407 − 5.14058I 0
u = −0.289347 − 1.277000I
a = −0.288688 − 1.121530I
b = 1.51609 + 0.18929I
1.70407 + 5.14058I 0
u = 0.132541 + 1.308630I
a = −0.406370 + 0.704082I
b = 0.249931 − 0.025514I
−3.38321 + 0.85618I 0
u = 0.132541 − 1.308630I
a = −0.406370 − 0.704082I
b = 0.249931 + 0.025514I
−3.38321 − 0.85618I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.066974 + 1.325380I
a = 0.781022 − 0.695467I
b = −0.543698 − 0.075581I
−4.16051 + 5.05095I 0
u = 0.066974 − 1.325380I
a = 0.781022 + 0.695467I
b = −0.543698 + 0.075581I
−4.16051 − 5.05095I 0
u = −0.396765 + 1.275800I
a = −0.075936 + 0.314839I
b = 0.490833 − 0.033606I
2.77814 − 4.50220I 0
u = −0.396765 − 1.275800I
a = −0.075936 − 0.314839I
b = 0.490833 + 0.033606I
2.77814 + 4.50220I 0
u = −0.266120 + 1.310510I
a = 0.553874 − 1.188430I
b = −1.70796 + 0.00761I
−0.07047 − 10.54190I 0
u = −0.266120 − 1.310510I
a = 0.553874 + 1.188430I
b = −1.70796 − 0.00761I
−0.07047 + 10.54190I 0
u = 0.457433 + 1.260060I
a = −1.82540 + 1.52099I
b = −2.98099 − 0.61431I
9.96888 − 4.36737I 0
u = 0.457433 − 1.260060I
a = −1.82540 − 1.52099I
b = −2.98099 + 0.61431I
9.96888 + 4.36737I 0
u = −0.442079 + 1.277110I
a = 0.504030 + 0.136393I
b = −0.009416 − 0.838158I
6.06778 − 2.20599I 0
u = −0.442079 − 1.277110I
a = 0.504030 − 0.136393I
b = −0.009416 + 0.838158I
6.06778 + 2.20599I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.456253 + 1.272990I
a = 1.76917 − 1.83592I
b = 3.14034 + 0.47569I
11.78740 + 1.96281I 0
u = 0.456253 − 1.272990I
a = 1.76917 + 1.83592I
b = 3.14034 − 0.47569I
11.78740 − 1.96281I 0
u = 0.435543 + 1.284440I
a = −2.03302 + 2.66752I
b = −3.71170 − 0.21616I
4.34700 + 4.79676I 0
u = 0.435543 − 1.284440I
a = −2.03302 − 2.66752I
b = −3.71170 + 0.21616I
4.34700 − 4.79676I 0
u = −0.436271 + 1.293570I
a = −0.519420 − 0.001879I
b = 0.243847 + 0.801514I
5.94185 − 7.44193I 0
u = −0.436271 − 1.293570I
a = −0.519420 + 0.001879I
b = 0.243847 − 0.801514I
5.94185 + 7.44193I 0
u = 0.442698 + 1.304280I
a = 1.24864 − 2.54832I
b = 3.18374 − 0.09677I
11.54400 + 7.84056I 0
u = 0.442698 − 1.304280I
a = 1.24864 + 2.54832I
b = 3.18374 + 0.09677I
11.54400 − 7.84056I 0
u = 0.616209 + 0.070001I
a = −0.315993 + 1.163010I
b = −0.151276 + 0.030346I
1.15428 + 1.92974I 10.88557 − 4.32279I
u = 0.616209 − 0.070001I
a = −0.315993 − 1.163010I
b = −0.151276 − 0.030346I
1.15428 − 1.92974I 10.88557 + 4.32279I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.435774 + 1.312250I
a = −1.01023 + 2.65881I
b = −3.05202 + 0.27246I
9.5655 + 14.1217I 0
u = 0.435774 − 1.312250I
a = −1.01023 − 2.65881I
b = −3.05202 − 0.27246I
9.5655 − 14.1217I 0
u = 0.329295 + 0.475961I
a = 0.395337 − 0.738913I
b = −0.440113 + 0.509380I
1.24419 + 3.93574I 8.26947 − 6.96230I
u = 0.329295 − 0.475961I
a = 0.395337 + 0.738913I
b = −0.440113 − 0.509380I
1.24419 − 3.93574I 8.26947 + 6.96230I
u = −0.566627
a = −2.54741
b = −2.01582
−0.173331 14.7800
u = 0.421793 + 0.356280I
a = −0.581552 + 0.715018I
b = 0.190880 − 0.469674I
1.63592 − 0.97554I 10.14221 − 1.13061I
u = 0.421793 − 0.356280I
a = −0.581552 − 0.715018I
b = 0.190880 + 0.469674I
1.63592 + 0.97554I 10.14221 + 1.13061I
u = 0.342205
a = −0.672021
b = 0.116519
0.576782 17.2090
u = −0.131606 + 0.232247I
a = 0.11377 − 2.33220I
b = −0.662340 − 0.292492I
−1.60725 − 0.57664I −2.01562 + 2.57957I
u = −0.131606 − 0.232247I
a = 0.11377 + 2.33220I
b = −0.662340 + 0.292492I
−1.60725 + 0.57664I −2.01562 − 2.57957I
10
II.
I
u
2
= hb − 1, −u
4
− u
3
− 2u
2
+ a − u − 1, u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
12
=
1
u
2
a
8
=
u
u
3
+ u
a
4
=
u
4
+ u
3
+ 2u
2
+ u + 1
1
a
9
=
u
3
+ 2u
u
3
+ u
a
10
=
u
3
+ 2u
u
3
+ u
a
3
=
u
4
+ u
3
+ 2u
2
+ u + 1
1
a
2
=
u
4
+ u
3
+ 2u
2
+ u + 2
1
a
11
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
−u
5
− 2u
3
− u
−u
5
− u
4
− 2u
3
− u
2
− u + 1
a
5
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
4
+ 2u
3
+ 5u
2
+ 2u + 3
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
9
u
6
c
4
(u + 1)
6
c
5
, c
6
, c
8
u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1
c
7
u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1
c
10
u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1
c
11
, c
12
u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
9
y
6
c
5
, c
6
, c
8
c
10
y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1
c
7
, c
11
, c
12
y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.873214
a = 1.56737
b = 1.00000
6.01515 5.47870
u = 0.138835 + 1.234450I
a = −0.356069 − 0.921195I
b = 1.00000
−4.60518 + 1.97241I 0.92955 − 2.53106I
u = 0.138835 − 1.234450I
a = −0.356069 + 0.921195I
b = 1.00000
−4.60518 − 1.97241I 0.92955 + 2.53106I
u = −0.408802 + 1.276380I
a = 0.645284 + 0.801205I
b = 1.00000
2.05064 − 4.59213I 1.87701 + 3.61028I
u = −0.408802 − 1.276380I
a = 0.645284 − 0.801205I
b = 1.00000
2.05064 + 4.59213I 1.87701 − 3.61028I
u = 0.413150
a = 1.85419
b = 1.00000
−0.906083 4.90820
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
60
+ 25u
59
+ ··· + 71u + 1)
c
2
((u − 1)
6
)(u
60
− 7u
59
+ ··· − 15u + 1)
c
3
, c
9
u
6
(u
60
− u
59
+ ··· − 128u + 64)
c
4
((u + 1)
6
)(u
60
− 7u
59
+ ··· − 15u + 1)
c
5
, c
6
, c
8
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)(u
60
+ 2u
59
+ ··· − 22u + 17)
c
7
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)(u
60
− 2u
59
+ ··· − 2u + 1)
c
10
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)(u
60
+ 2u
59
+ ··· − 22u + 17)
c
11
, c
12
(u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1)(u
60
− 2u
59
+ ··· − 2u + 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
6
)(y
60
+ 27y
59
+ ··· − 5339y + 1)
c
2
, c
4
((y −1)
6
)(y
60
− 25y
59
+ ··· − 71y + 1)
c
3
, c
9
y
6
(y
60
− 39y
59
+ ··· − 102400y + 4096)
c
5
, c
6
, c
8
c
10
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
· (y
60
− 74y
59
+ ··· − 246y + 289)
c
7
, c
11
, c
12
(y
6
+ 5y
5
+ ··· − 5y + 1)(y
60
+ 46y
59
+ ··· + 2y + 1)
16
