12a
0879
(K12a
0879
)
A knot diagram
1
Linearized knot diagam
4 6 7 10 2 3 11 12 1 5 9 8
Solving Sequence
2,5
6 3
7,10
11 8 4 1 9 12
c
5
c
2
c
6
c
10
c
7
c
4
c
1
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−27u
65
− 62u
64
+ ··· + 2b − 19, 65u
65
+ 146u
64
+ ··· + 4a + 79, u
66
+ 4u
65
+ ··· − 7u + 1i
I
u
2
= hb, a
3
− a
2
u + a
2
+ 2u − 3, u
2
− u − 1i
* 2 irreducible components of dim
C
= 0, with total 72 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
= h−27u
65
− 62u
64
+ · · · + 2b − 19, 65u
65
+ 146u
64
+ · · · + 4a +
79, u
66
+ 4u
65
+ · · · − 7u + 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u
2
a
3
=
−u
−u
3
+ u
a
7
=
−u
2
+ 1
−u
4
+ 2u
2
a
10
=
−16.2500u
65
− 36.5000u
64
+ ··· + 117.250u − 19.7500
27
2
u
65
+ 31u
64
+ ··· −
137
2
u +
19
2
a
11
=
−2.75000u
65
− 5.50000u
64
+ ··· + 48.7500u − 10.2500
27
2
u
65
+ 31u
64
+ ··· −
137
2
u +
19
2
a
8
=
−
1
4
u
64
−
3
4
u
63
+ ··· +
3
2
u +
9
4
−u
9
+ 5u
7
− 7u
5
+ 2u
3
− u
a
4
=
u
3
− 2u
u
5
− 3u
3
+ u
a
1
=
u
7
− 4u
5
+ 4u
3
u
9
− 5u
7
+ 7u
5
− 2u
3
+ u
a
9
=
−12.5000u
65
− 27.2500u
64
+ ··· + 97.5000u − 17.2500
21
4
u
65
+
49
4
u
64
+ ··· −
113
4
u + 4
a
12
=
−3u
65
−
19
4
u
64
+ ··· + 27u −
19
4
1
4
u
65
+
1
2
u
64
+ ··· −
3
4
u +
1
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −23u
65
− 59u
64
+ ··· +
175
2
u +
5
2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
66
− 16u
65
+ ··· − 7063u − 529
c
2
, c
3
, c
5
c
6
u
66
+ 4u
65
+ ··· − 7u + 1
c
4
, c
10
u
66
− u
65
+ ··· − 32u − 64
c
7
, c
9
u
66
− 3u
65
+ ··· + 394u − 241
c
8
, c
11
, c
12
u
66
+ 3u
65
+ ··· − 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
66
+ 8y
65
+ ··· − 58875795y + 279841
c
2
, c
3
, c
5
c
6
y
66
− 76y
65
+ ··· − 39y + 1
c
4
, c
10
y
66
− 35y
65
+ ··· − 87040y + 4096
c
7
, c
9
y
66
− 45y
65
+ ··· + 1824338y + 58081
c
8
, c
11
, c
12
y
66
+ 55y
65
+ ··· + 26y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.072920 + 0.173234I
a = 0.033699 − 0.206753I
b = −1.156190 + 0.223934I
−1.68039 − 4.13387I 0
u = −1.072920 − 0.173234I
a = 0.033699 + 0.206753I
b = −1.156190 − 0.223934I
−1.68039 + 4.13387I 0
u = 0.690848 + 0.580355I
a = 1.60685 + 1.18393I
b = −1.265350 + 0.605450I
1.32088 − 11.43940I 0
u = 0.690848 − 0.580355I
a = 1.60685 − 1.18393I
b = −1.265350 − 0.605450I
1.32088 + 11.43940I 0
u = 0.664269 + 0.585797I
a = −1.63457 − 1.15491I
b = 1.281820 − 0.540344I
5.90981 − 7.14877I 0
u = 0.664269 − 0.585797I
a = −1.63457 + 1.15491I
b = 1.281820 + 0.540344I
5.90981 + 7.14877I 0
u = 0.625394 + 0.587261I
a = 1.67658 + 1.11501I
b = −1.286450 + 0.445199I
2.78876 − 2.77757I 0
u = 0.625394 − 0.587261I
a = 1.67658 − 1.11501I
b = −1.286450 − 0.445199I
2.78876 + 2.77757I 0
u = −0.749842 + 0.310450I
a = 0.324495 + 0.129177I
b = 0.649778 − 0.650531I
−5.73446 + 0.49899I −5.69937 − 1.38908I
u = −0.749842 − 0.310450I
a = 0.324495 − 0.129177I
b = 0.649778 + 0.650531I
−5.73446 − 0.49899I −5.69937 + 1.38908I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.189200 + 0.068111I
a = −0.238134 + 0.114543I
b = 1.228180 − 0.049346I
2.35220 − 0.00558I 0
u = −1.189200 − 0.068111I
a = −0.238134 − 0.114543I
b = 1.228180 + 0.049346I
2.35220 + 0.00558I 0
u = 0.646920 + 0.426476I
a = −1.85311 − 1.39072I
b = 0.922593 − 0.479193I
−4.87688 − 4.92488I −2.91516 + 7.92049I
u = 0.646920 − 0.426476I
a = −1.85311 + 1.39072I
b = 0.922593 + 0.479193I
−4.87688 + 4.92488I −2.91516 − 7.92049I
u = 0.325420 + 0.652249I
a = −1.70719 − 0.69127I
b = 1.302590 + 0.277842I
3.67408 − 1.40819I 4.92934 + 2.83994I
u = 0.325420 − 0.652249I
a = −1.70719 + 0.69127I
b = 1.302590 − 0.277842I
3.67408 + 1.40819I 4.92934 − 2.83994I
u = 0.547891 + 0.477188I
a = 1.92682 + 1.12711I
b = −1.034770 + 0.276618I
1.07485 − 3.31172I 3.02602 + 8.16126I
u = 0.547891 − 0.477188I
a = 1.92682 − 1.12711I
b = −1.034770 − 0.276618I
1.07485 + 3.31172I 3.02602 − 8.16126I
u = −0.550846 + 0.473180I
a = −0.638662 − 0.120591I
b = −0.283002 + 1.026680I
−1.79557 + 5.51844I −0.23058 − 6.89017I
u = −0.550846 − 0.473180I
a = −0.638662 + 0.120591I
b = −0.283002 − 1.026680I
−1.79557 − 5.51844I −0.23058 + 6.89017I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.281335 + 0.666408I
a = 1.67352 + 0.63814I
b = −1.291680 − 0.386170I
7.04097 + 2.92886I 8.20980 − 1.22760I
u = 0.281335 − 0.666408I
a = 1.67352 − 0.63814I
b = −1.291680 + 0.386170I
7.04097 − 2.92886I 8.20980 + 1.22760I
u = 0.246514 + 0.675439I
a = −1.64567 − 0.59911I
b = 1.274070 + 0.469465I
2.63500 + 7.21380I 3.80665 − 3.88169I
u = 0.246514 − 0.675439I
a = −1.64567 + 0.59911I
b = 1.274070 − 0.469465I
2.63500 − 7.21380I 3.80665 + 3.88169I
u = −1.318540 + 0.118766I
a = 0.453383 − 0.293355I
b = −1.314510 − 0.011883I
−1.46349 + 4.26617I 0
u = −1.318540 − 0.118766I
a = 0.453383 + 0.293355I
b = −1.314510 + 0.011883I
−1.46349 − 4.26617I 0
u = −0.488537 + 0.457113I
a = 0.700481 + 0.055283I
b = 0.160120 − 0.986891I
2.36817 + 1.61935I 5.06499 − 4.29154I
u = −0.488537 − 0.457113I
a = 0.700481 − 0.055283I
b = 0.160120 + 0.986891I
2.36817 − 1.61935I 5.06499 + 4.29154I
u = −0.604078 + 0.148414I
a = −0.253436 + 0.106782I
b = −0.286923 + 0.422139I
−1.106760 + 0.360302I −7.12806 − 1.59413I
u = −0.604078 − 0.148414I
a = −0.253436 − 0.106782I
b = −0.286923 − 0.422139I
−1.106760 − 0.360302I −7.12806 + 1.59413I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.403566 + 0.462584I
a = −0.820575 − 0.001706I
b = 0.001443 + 0.972652I
−1.36002 − 2.20380I 1.274205 − 0.508380I
u = −0.403566 − 0.462584I
a = −0.820575 + 0.001706I
b = 0.001443 − 0.972652I
−1.36002 + 2.20380I 1.274205 + 0.508380I
u = 0.407492 + 0.444561I
a = −2.10136 − 0.83022I
b = 0.941571 − 0.012463I
1.50011 + 0.02255I 5.79860 + 0.11054I
u = 0.407492 − 0.444561I
a = −2.10136 + 0.83022I
b = 0.941571 + 0.012463I
1.50011 − 0.02255I 5.79860 − 0.11054I
u = 0.446019 + 0.205803I
a = 3.01031 + 1.00239I
b = −0.585824 + 0.096244I
−3.60533 + 2.43505I 4.47869 + 3.50639I
u = 0.446019 − 0.205803I
a = 3.01031 − 1.00239I
b = −0.585824 − 0.096244I
−3.60533 − 2.43505I 4.47869 − 3.50639I
u = 1.51687 + 0.09420I
a = 0.265118 + 0.603915I
b = 0.284104 + 1.091710I
−7.76260 + 0.42615I 0
u = 1.51687 − 0.09420I
a = 0.265118 − 0.603915I
b = 0.284104 − 1.091710I
−7.76260 − 0.42615I 0
u = −1.52878 + 0.09849I
a = 1.127160 − 0.797641I
b = −1.075640 − 0.324127I
−5.04567 + 1.71176I 0
u = −1.52878 − 0.09849I
a = 1.127160 + 0.797641I
b = −1.075640 + 0.324127I
−5.04567 − 1.71176I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.53900 + 0.11695I
a = −0.336179 − 0.567584I
b = −0.393546 − 1.106990I
−4.45170 − 3.60064I 0
u = 1.53900 − 0.11695I
a = −0.336179 + 0.567584I
b = −0.393546 + 1.106990I
−4.45170 + 3.60064I 0
u = −1.54855 + 0.07058I
a = −1.41831 + 0.83959I
b = 0.944998 + 0.301189I
−10.50730 − 1.36159I 0
u = −1.54855 − 0.07058I
a = −1.41831 − 0.83959I
b = 0.944998 − 0.301189I
−10.50730 + 1.36159I 0
u = −1.55067 + 0.13221I
a = −0.959087 + 0.994864I
b = 1.134420 + 0.460428I
−5.97241 + 5.48876I 0
u = −1.55067 − 0.13221I
a = −0.959087 − 0.994864I
b = 1.134420 − 0.460428I
−5.97241 − 5.48876I 0
u = 1.55509 + 0.13012I
a = 0.379992 + 0.543053I
b = 0.471872 + 1.119230I
−8.88354 − 7.66796I 0
u = 1.55509 − 0.13012I
a = 0.379992 − 0.543053I
b = 0.471872 − 1.119230I
−8.88354 + 7.66796I 0
u = 0.061635 + 0.421413I
a = 1.80766 + 0.02094I
b = −0.645194 − 0.497522I
−3.43044 + 2.02248I 1.43635 − 3.15758I
u = 0.061635 − 0.421413I
a = 1.80766 − 0.02094I
b = −0.645194 + 0.497522I
−3.43044 − 2.02248I 1.43635 + 3.15758I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.57094 + 0.17640I
a = −0.738128 + 1.094960I
b = 1.267420 + 0.596203I
−4.54503 + 5.58353I 0
u = −1.57094 − 0.17640I
a = −0.738128 − 1.094960I
b = 1.267420 − 0.596203I
−4.54503 − 5.58353I 0
u = 1.58225 + 0.03832I
a = 0.163322 + 0.361601I
b = 0.266777 + 0.702013I
−8.64237 − 1.04768I 0
u = 1.58225 − 0.03832I
a = 0.163322 − 0.361601I
b = 0.266777 − 0.702013I
−8.64237 + 1.04768I 0
u = −1.58571 + 0.12589I
a = 0.99022 − 1.21656I
b = −1.044450 − 0.580460I
−12.4486 + 6.9737I 0
u = −1.58571 − 0.12589I
a = 0.99022 + 1.21656I
b = −1.044450 + 0.580460I
−12.4486 − 6.9737I 0
u = −1.58854 + 0.17927I
a = 0.712511 − 1.165440I
b = −1.26100 − 0.66919I
−1.64539 + 9.99256I 0
u = −1.58854 − 0.17927I
a = 0.712511 + 1.165440I
b = −1.26100 + 0.66919I
−1.64539 − 9.99256I 0
u = −1.59986 + 0.17767I
a = −0.704976 + 1.212660I
b = 1.24315 + 0.71519I
−6.3848 + 14.2753I 0
u = −1.59986 − 0.17767I
a = −0.704976 − 1.212660I
b = 1.24315 − 0.71519I
−6.3848 − 14.2753I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.61738 + 0.07768I
a = −0.344588 − 0.328731I
b = −0.607410 − 0.737385I
−13.86580 − 1.91791I 0
u = 1.61738 − 0.07768I
a = −0.344588 + 0.328731I
b = −0.607410 + 0.737385I
−13.86580 + 1.91791I 0
u = 1.66435
a = −0.362345
b = −0.777375
−7.02502 0
u = 1.66975 + 0.02246I
a = 0.391254 + 0.078239I
b = 0.840309 + 0.197273I
−11.05450 + 3.59857I 0
u = 1.66975 − 0.02246I
a = 0.391254 − 0.078239I
b = 0.840309 − 0.197273I
−11.05450 − 3.59857I 0
u = 0.188647
a = −3.33648
b = 0.410787
0.829449 12.8870
11
II. I
u
2
= hb, a
3
− a
2
u + a
2
+ 2u − 3, u
2
− u − 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
6
=
1
u + 1
a
3
=
−u
−u − 1
a
7
=
−u
−u
a
10
=
a
0
a
11
=
a
0
a
8
=
−a
2
u − u
−u
a
4
=
1
0
a
1
=
u
u
a
9
=
au + 2a
au + a
a
12
=
−3a
2
u − a
2
+ a + 2u − 1
−2a
2
u − a
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −a
2
− 2au + a − u − 3
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
(u
2
+ u − 1)
3
c
4
, c
10
u
6
c
5
, c
6
(u
2
− u − 1)
3
c
7
, c
9
(u
3
− u
2
+ 1)
2
c
8
(u
3
+ u
2
+ 2u + 1)
2
c
11
, c
12
(u
3
− u
2
+ 2u − 1)
2
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
, c
6
(y
2
− 3y + 1)
3
c
4
, c
10
y
6
c
7
, c
9
(y
3
− y
2
+ 2y −1)
2
c
8
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = 1.22142
b = 0
0.126494 −1.14270
u = −0.618034
a = −1.41973 + 1.20521I
b = 0
−4.01109 − 2.82812I −6.11966 + 6.11708I
u = −0.618034
a = −1.41973 − 1.20521I
b = 0
−4.01109 + 2.82812I −6.11966 − 6.11708I
u = 1.61803
a = 0.542287 + 0.460350I
b = 0
−11.90680 + 2.82812I −5.91278 − 1.52866I
u = 1.61803
a = 0.542287 − 0.460350I
b = 0
−11.90680 − 2.82812I −5.91278 + 1.52866I
u = 1.61803
a = −0.466540
b = 0
−7.76919 −3.79250
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
+ u − 1)
3
)(u
66
− 16u
65
+ ··· − 7063u − 529)
c
2
, c
3
((u
2
+ u − 1)
3
)(u
66
+ 4u
65
+ ··· − 7u + 1)
c
4
, c
10
u
6
(u
66
− u
65
+ ··· − 32u − 64)
c
5
, c
6
((u
2
− u − 1)
3
)(u
66
+ 4u
65
+ ··· − 7u + 1)
c
7
, c
9
((u
3
− u
2
+ 1)
2
)(u
66
− 3u
65
+ ··· + 394u − 241)
c
8
((u
3
+ u
2
+ 2u + 1)
2
)(u
66
+ 3u
65
+ ··· − 2u − 1)
c
11
, c
12
((u
3
− u
2
+ 2u − 1)
2
)(u
66
+ 3u
65
+ ··· − 2u − 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
− 3y + 1)
3
)(y
66
+ 8y
65
+ ··· − 5.88758 × 10
7
y + 279841)
c
2
, c
3
, c
5
c
6
((y
2
− 3y + 1)
3
)(y
66
− 76y
65
+ ··· − 39y + 1)
c
4
, c
10
y
6
(y
66
− 35y
65
+ ··· − 87040y + 4096)
c
7
, c
9
((y
3
− y
2
+ 2y −1)
2
)(y
66
− 45y
65
+ ··· + 1824338y + 58081)
c
8
, c
11
, c
12
((y
3
+ 3y
2
+ 2y −1)
2
)(y
66
+ 55y
65
+ ··· + 26y + 1)
17
