12a
1064
(K12a
1064
)
A knot diagram
1
Linearized knot diagam
4 7 9 1 2 10 11 12 6 3 8 5
Solving Sequence
5,12
1 4 2
6,9
3 8 11 7 10
c
12
c
4
c
1
c
5
c
3
c
8
c
11
c
7
c
10
c
2
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.52109 × 10
85
u
82
+ 8.64634 × 10
85
u
81
+ ··· + 1.02529 × 10
87
b + 1.52237 × 10
87
,
− 1.47090 × 10
87
u
82
− 1.63708 × 10
87
u
81
+ ··· + 1.02529 × 10
87
a − 7.79066 × 10
86
, u
83
+ u
82
+ ··· − 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 83 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−2.52×10
85
u
82
+8.65×10
85
u
81
+· · ·+1.03×10
87
b+1.52×10
87
, −1.47×
10
87
u
82
−1.64×10
87
u
81
+· · ·+1.03×10
87
a−7.79×10
86
, u
83
+u
82
+· · ·−2u−1i
(i) Arc colorings
a
5
=
0
u
a
12
=
1
0
a
1
=
1
u
2
a
4
=
u
u
3
+ u
a
2
=
u
2
+ 1
u
4
+ 2u
2
a
6
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
9
=
1.43461u
82
+ 1.59669u
81
+ ··· − 48.1974u + 0.759849
0.0245891u
82
− 0.0843305u
81
+ ··· − 0.539171u − 1.48482
a
3
=
−3.85435u
82
− 3.70576u
81
+ ··· + 12.1010u − 10.3867
−0.109874u
82
− 0.158192u
81
+ ··· + 6.49193u + 1.37180
a
8
=
1.45920u
82
+ 1.51236u
81
+ ··· − 48.7366u − 0.724973
0.0245891u
82
− 0.0843305u
81
+ ··· − 0.539171u − 1.48482
a
11
=
1.57618u
82
+ 0.907236u
81
+ ··· − 69.1885u − 0.00842359
−0.0277634u
82
− 0.0657480u
81
+ ··· − 1.84911u − 2.19386
a
7
=
−1.40639u
82
− 1.36785u
81
+ ··· + 42.0418u − 2.35067
0.0598792u
82
− 0.104829u
81
+ ··· + 2.65151u + 1.36301
a
10
=
1.48382u
82
+ 1.56199u
81
+ ··· − 47.0880u + 0.730578
0.0160101u
82
− 0.00198206u
81
+ ··· − 1.69531u − 1.51353
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3.75821u
82
+ 4.13643u
81
+ ··· − 2.88911u − 1.93224
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
83
− u
82
+ ··· − 2u + 1
c
2
u
83
− 3u
82
+ ··· − 8u − 97
c
3
u
83
− u
82
+ ··· − 29240u − 5563
c
5
u
83
+ u
82
+ ··· + 9630u + 2689
c
6
, c
9
u
83
− u
82
+ ··· − 7u
2
+ 1
c
7
, c
8
, c
11
u
83
+ 7u
82
+ ··· + 7u
2
− 1
c
10
u
83
+ 3u
82
+ ··· − 4u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
83
+ 71y
82
+ ··· − 102y −1
c
2
y
83
− 513y
82
+ ··· + 637742y −9409
c
3
y
83
− 533y
82
+ ··· + 2125110634y −30946969
c
5
y
83
− 29y
82
+ ··· − 827229158y −7230721
c
6
, c
9
y
83
− 53y
82
+ ··· + 14y −1
c
7
, c
8
, c
11
y
83
− 85y
82
+ ··· + 14y −1
c
10
y
83
+ 7y
82
+ ··· + 66y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.904665 + 0.431308I
a = 0.444111 − 0.833130I
b = 1.48483 + 0.03450I
−6.93263 − 2.69856I 0
u = 0.904665 − 0.431308I
a = 0.444111 + 0.833130I
b = 1.48483 − 0.03450I
−6.93263 + 2.69856I 0
u = −0.523171 + 0.935123I
a = 0.078517 − 0.193819I
b = −1.53601 − 0.20823I
−4.33446 − 7.80527I 0
u = −0.523171 − 0.935123I
a = 0.078517 + 0.193819I
b = −1.53601 + 0.20823I
−4.33446 + 7.80527I 0
u = 0.926387 + 0.043053I
a = −1.253500 + 0.168894I
b = −1.47810 − 0.00383I
−7.59406 − 0.00917I −13.41457 + 0.I
u = 0.926387 − 0.043053I
a = −1.253500 − 0.168894I
b = −1.47810 + 0.00383I
−7.59406 + 0.00917I −13.41457 + 0.I
u = −0.387244 + 0.823860I
a = −0.565051 − 0.405945I
b = 0.547345 + 0.608594I
2.54832 − 4.77196I 0. + 4.88934I
u = −0.387244 − 0.823860I
a = −0.565051 + 0.405945I
b = 0.547345 − 0.608594I
2.54832 + 4.77196I 0. − 4.88934I
u = −0.371273 + 1.048980I
a = −0.208988 + 0.342891I
b = 1.56520 + 0.18830I
−7.61151 − 2.62136I 0
u = −0.371273 − 1.048980I
a = −0.208988 − 0.342891I
b = 1.56520 − 0.18830I
−7.61151 + 2.62136I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.849324 + 0.250360I
a = −1.03559 − 1.28238I
b = −1.55846 + 0.25137I
−6.4541 + 12.6262I −7.38891 − 7.59104I
u = −0.849324 − 0.250360I
a = −1.03559 + 1.28238I
b = −1.55846 − 0.25137I
−6.4541 − 12.6262I −7.38891 + 7.59104I
u = 0.349735 + 1.067780I
a = −0.248736 − 0.432337I
b = 0.508066 + 0.276673I
1.92187 − 4.22604I 0
u = 0.349735 − 1.067780I
a = −0.248736 + 0.432337I
b = 0.508066 − 0.276673I
1.92187 + 4.22604I 0
u = −0.801322 + 0.161892I
a = 1.19606 + 1.08916I
b = 1.57257 − 0.25982I
−10.32350 + 6.88913I −11.30755 − 5.10720I
u = −0.801322 − 0.161892I
a = 1.19606 − 1.08916I
b = 1.57257 + 0.25982I
−10.32350 − 6.88913I −11.30755 + 5.10720I
u = 0.527206 + 0.622474I
a = −0.213152 − 0.852381I
b = 1.47354 + 0.06068I
−6.26479 − 2.24210I −10.47377 + 2.86125I
u = 0.527206 − 0.622474I
a = −0.213152 + 0.852381I
b = 1.47354 − 0.06068I
−6.26479 + 2.24210I −10.47377 − 2.86125I
u = 0.811237
a = 0.122702
b = 0.422769
−1.35401 −13.8280
u = −0.768502 + 0.243547I
a = 0.659044 + 0.689542I
b = 0.601985 − 0.744053I
0.63414 + 8.95004I −4.61101 − 8.69193I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.768502 − 0.243547I
a = 0.659044 − 0.689542I
b = 0.601985 + 0.744053I
0.63414 − 8.95004I −4.61101 + 8.69193I
u = 0.609295 + 1.049720I
a = −0.073062 + 0.756246I
b = −1.48758 − 0.06918I
−4.55776 − 5.42713I 0
u = 0.609295 − 1.049720I
a = −0.073062 − 0.756246I
b = −1.48758 + 0.06918I
−4.55776 + 5.42713I 0
u = 0.699140 + 0.354524I
a = 0.157935 + 0.565146I
b = −0.436838 − 0.172780I
−0.61000 − 2.03869I −10.08458 + 9.40265I
u = 0.699140 − 0.354524I
a = 0.157935 − 0.565146I
b = −0.436838 + 0.172780I
−0.61000 + 2.03869I −10.08458 − 9.40265I
u = −0.193772 + 1.213450I
a = 1.038160 + 0.359525I
b = −0.911881 − 0.647788I
0.236787 + 0.202779I 0
u = −0.193772 − 1.213450I
a = 1.038160 − 0.359525I
b = −0.911881 + 0.647788I
0.236787 − 0.202779I 0
u = −0.110659 + 1.233990I
a = 0.64968 + 1.57490I
b = 0.062828 − 0.831522I
3.83261 − 1.11879I 0
u = −0.110659 − 1.233990I
a = 0.64968 − 1.57490I
b = 0.062828 + 0.831522I
3.83261 + 1.11879I 0
u = 0.027460 + 1.239750I
a = 1.23418 − 1.00702I
b = −1.077100 + 0.037871I
0.784753 + 0.015689I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.027460 − 1.239750I
a = 1.23418 + 1.00702I
b = −1.077100 − 0.037871I
0.784753 − 0.015689I 0
u = 0.162835 + 1.275350I
a = 0.33304 + 1.70965I
b = −0.007261 − 0.443486I
3.90089 − 2.03788I 0
u = 0.162835 − 1.275350I
a = 0.33304 − 1.70965I
b = −0.007261 + 0.443486I
3.90089 + 2.03788I 0
u = −0.235341 + 1.264360I
a = 0.743300 − 0.777633I
b = −1.74342 − 0.20507I
−1.71143 + 2.17576I 0
u = −0.235341 − 1.264360I
a = 0.743300 + 0.777633I
b = −1.74342 + 0.20507I
−1.71143 − 2.17576I 0
u = −0.679568 + 0.099033I
a = −0.715170 − 0.353529I
b = −0.663430 + 0.819395I
−3.02457 + 2.97739I −11.4522 − 8.4957I
u = −0.679568 − 0.099033I
a = −0.715170 + 0.353529I
b = −0.663430 − 0.819395I
−3.02457 − 2.97739I −11.4522 + 8.4957I
u = −0.660019 + 0.182223I
a = 0.061412 − 0.133999I
b = 0.437248 + 0.838716I
1.14107 + 3.77675I −4.42430 − 6.83951I
u = −0.660019 − 0.182223I
a = 0.061412 + 0.133999I
b = 0.437248 − 0.838716I
1.14107 − 3.77675I −4.42430 + 6.83951I
u = −0.261761 + 1.299130I
a = 0.45969 − 2.13143I
b = −1.59789 + 0.43691I
−1.29190 + 4.37029I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.261761 − 1.299130I
a = 0.45969 + 2.13143I
b = −1.59789 − 0.43691I
−1.29190 − 4.37029I 0
u = 0.219448 + 1.308160I
a = 2.73510 − 11.43200I
b = 1.41994 + 0.01827I
−0.27613 − 2.86489I 0
u = 0.219448 − 1.308160I
a = 2.73510 + 11.43200I
b = 1.41994 − 0.01827I
−0.27613 + 2.86489I 0
u = 0.259628 + 1.304990I
a = 0.360641 − 0.794383I
b = 0.334600 + 0.235718I
2.59124 − 3.33493I 0
u = 0.259628 − 1.304990I
a = 0.360641 + 0.794383I
b = 0.334600 − 0.235718I
2.59124 + 3.33493I 0
u = 0.665599
a = 0.644909
b = 0.324269
−1.54000 −7.43950
u = −0.658981 + 0.038729I
a = −1.62674 − 0.57595I
b = −1.64085 + 0.31051I
−5.47873 + 1.02972I −17.8027 − 5.9458I
u = −0.658981 − 0.038729I
a = −1.62674 + 0.57595I
b = −1.64085 − 0.31051I
−5.47873 − 1.02972I −17.8027 + 5.9458I
u = −0.276913 + 1.324360I
a = −0.40863 − 1.80806I
b = −0.573341 + 0.956974I
1.44716 + 6.45467I 0
u = −0.276913 − 1.324360I
a = −0.40863 + 1.80806I
b = −0.573341 − 0.956974I
1.44716 − 6.45467I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.364043 + 1.314560I
a = −0.16640 + 1.51924I
b = −1.46030 − 0.07333I
−3.32542 − 4.47511I 0
u = 0.364043 − 1.314560I
a = −0.16640 − 1.51924I
b = −1.46030 + 0.07333I
−3.32542 + 4.47511I 0
u = 0.227692 + 1.349670I
a = −0.67339 − 1.41304I
b = −0.310421 + 0.278426I
5.03483 − 3.41427I 0
u = 0.227692 − 1.349670I
a = −0.67339 + 1.41304I
b = −0.310421 − 0.278426I
5.03483 + 3.41427I 0
u = −0.272805 + 1.364300I
a = −0.911810 − 0.993141I
b = 0.551748 + 0.917797I
6.03553 + 7.19350I 0
u = −0.272805 − 1.364300I
a = −0.911810 + 0.993141I
b = 0.551748 − 0.917797I
6.03553 − 7.19350I 0
u = −0.092196 + 1.389330I
a = −0.06722 + 1.61828I
b = 0.803073 − 0.549130I
8.45681 + 0.24363I 0
u = −0.092196 − 1.389330I
a = −0.06722 − 1.61828I
b = 0.803073 + 0.549130I
8.45681 − 0.24363I 0
u = 0.101162 + 1.394370I
a = −1.84470 − 0.66191I
b = 1.340300 + 0.132764I
0.07406 − 4.01812I 0
u = 0.101162 − 1.394370I
a = −1.84470 + 0.66191I
b = 1.340300 − 0.132764I
0.07406 + 4.01812I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.337682 + 1.362540I
a = −0.37629 + 2.05946I
b = 1.56580 − 0.31162I
−5.51432 + 10.99590I 0
u = −0.337682 − 1.362540I
a = −0.37629 − 2.05946I
b = 1.56580 + 0.31162I
−5.51432 − 10.99590I 0
u = 0.574728 + 0.106362I
a = −0.33938 − 2.36609I
b = −0.116893 + 0.292931I
0.395479 − 0.483381I 4.40966 − 13.36233I
u = 0.574728 − 0.106362I
a = −0.33938 + 2.36609I
b = −0.116893 − 0.292931I
0.395479 + 0.483381I 4.40966 + 13.36233I
u = 0.575433
a = 27.0401
b = 1.42241
−4.41961 257.880
u = −0.31415 + 1.39980I
a = 0.30356 + 1.69619I
b = 0.589076 − 0.824484I
5.85194 + 12.87300I 0
u = −0.31415 − 1.39980I
a = 0.30356 − 1.69619I
b = 0.589076 + 0.824484I
5.85194 − 12.87300I 0
u = −0.35115 + 1.41539I
a = 0.36276 − 2.03460I
b = −1.56117 + 0.28469I
−1.1644 + 16.9553I 0
u = −0.35115 − 1.41539I
a = 0.36276 + 2.03460I
b = −1.56117 − 0.28469I
−1.1644 − 16.9553I 0
u = 0.30034 + 1.43004I
a = 0.126466 + 0.985341I
b = −0.369330 − 0.393419I
5.05592 − 5.76330I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.30034 − 1.43004I
a = 0.126466 − 0.985341I
b = −0.369330 + 0.393419I
5.05592 + 5.76330I 0
u = −0.02030 + 1.47331I
a = −0.512899 − 1.238070I
b = 0.295028 + 0.672756I
9.93674 − 3.97534I 0
u = −0.02030 − 1.47331I
a = −0.512899 + 1.238070I
b = 0.295028 − 0.672756I
9.93674 + 3.97534I 0
u = −0.199566 + 0.452923I
a = 1.24239 + 1.62287I
b = 0.461828 − 0.484933I
2.79973 − 0.93314I 1.18279 − 2.17360I
u = −0.199566 − 0.452923I
a = 1.24239 − 1.62287I
b = 0.461828 + 0.484933I
2.79973 + 0.93314I 1.18279 + 2.17360I
u = 0.39359 + 1.47783I
a = −0.439946 − 1.227010I
b = 1.46110 + 0.10369I
−0.91436 − 7.48576I 0
u = 0.39359 − 1.47783I
a = −0.439946 + 1.227010I
b = 1.46110 − 0.10369I
−0.91436 + 7.48576I 0
u = 0.04543 + 1.54868I
a = 1.134650 + 0.625371I
b = −1.41362 − 0.19449I
4.49350 − 7.02190I 0
u = 0.04543 − 1.54868I
a = 1.134650 − 0.625371I
b = −1.41362 + 0.19449I
4.49350 + 7.02190I 0
u = 0.158913 + 0.328968I
a = 0.938978 + 0.786692I
b = −0.332746 − 0.347602I
−0.233005 − 0.980237I −4.40622 + 6.53050I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.158913 − 0.328968I
a = 0.938978 − 0.786692I
b = −0.332746 + 0.347602I
−0.233005 + 0.980237I −4.40622 − 6.53050I
u = −0.012139 + 0.141810I
a = 2.01713 − 6.48316I
b = −1.384180 − 0.065251I
−3.17129 − 0.11870I −1.99127 − 1.49453I
u = −0.012139 − 0.141810I
a = 2.01713 + 6.48316I
b = −1.384180 + 0.065251I
−3.17129 + 0.11870I −1.99127 + 1.49453I
13
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
12
u
83
− u
82
+ ··· − 2u + 1
c
2
u
83
− 3u
82
+ ··· − 8u − 97
c
3
u
83
− u
82
+ ··· − 29240u − 5563
c
5
u
83
+ u
82
+ ··· + 9630u + 2689
c
6
, c
9
u
83
− u
82
+ ··· − 7u
2
+ 1
c
7
, c
8
, c
11
u
83
+ 7u
82
+ ··· + 7u
2
− 1
c
10
u
83
+ 3u
82
+ ··· − 4u − 1
14
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
12
y
83
+ 71y
82
+ ··· − 102y −1
c
2
y
83
− 513y
82
+ ··· + 637742y −9409
c
3
y
83
− 533y
82
+ ··· + 2125110634y −30946969
c
5
y
83
− 29y
82
+ ··· − 827229158y −7230721
c
6
, c
9
y
83
− 53y
82
+ ··· + 14y −1
c
7
, c
8
, c
11
y
83
− 85y
82
+ ··· + 14y −1
c
10
y
83
+ 7y
82
+ ··· + 66y −1
15
