12n
0009
(K12n
0009
)
A knot diagram
1
Linearized knot diagam
3 5 6 7 2 11 4 6 12 7 9 10
Solving Sequence
6,11 4,7
5 8 9 12 3 2 1 10
c
6
c
4
c
7
c
8
c
11
c
3
c
2
c
1
c
10
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2.21642 × 10
44
u
44
− 9.65342 × 10
44
u
43
+ ··· + 5.80500 × 10
44
b + 4.56035 × 10
43
,
− 9.69683 × 10
44
u
44
+ 2.59441 × 10
45
u
43
+ ··· + 5.80500 × 10
44
a − 1.42142 × 10
45
, u
45
− 3u
44
+ ··· − 2u + 1i
I
u
2
= h−u
2
a + b, u
4
a + u
4
+ u
2
a + u
3
+ a
2
− au + 3u
2
+ u + 2, u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 55 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
= h2.22×10
44
u
44
−9.65×10
44
u
43
+· · ·+5.80×10
44
b+4.56×10
43
, −9.70×
10
44
u
44
+2.59×10
45
u
43
+· · ·+5.80×10
44
a−1.42×10
45
, u
45
−3u
44
+· · ·−2u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
4
=
1.67043u
44
− 4.46927u
43
+ ··· + 1.43251u + 2.44861
−0.381812u
44
+ 1.66295u
43
+ ··· − 2.28564u − 0.0785591
a
7
=
1
u
2
a
5
=
1.52725u
44
− 3.73078u
43
+ ··· − 0.266722u + 2.91206
−0.353492u
44
+ 1.38147u
43
+ ··· − 1.52456u − 0.387507
a
8
=
0.180463u
44
− 0.229067u
43
+ ··· − 0.106601u − 0.509733
0.932433u
44
− 3.31426u
43
+ ··· + 3.71638u − 1.49789
a
9
=
1.11290u
44
− 3.54332u
43
+ ··· + 3.60978u − 2.00762
0.932433u
44
− 3.31426u
43
+ ··· + 3.71638u − 1.49789
a
12
=
0.107422u
44
− 0.715021u
43
+ ··· + 1.62877u + 0.305097
0.795848u
44
− 2.98218u
43
+ ··· + 4.34562u − 1.30977
a
3
=
1.28862u
44
− 2.80632u
43
+ ··· − 0.853129u + 2.37005
−0.381812u
44
+ 1.66295u
43
+ ··· − 2.28564u − 0.0785591
a
2
=
0.248367u
44
− 0.966971u
43
+ ··· + 5.08102u + 1.34780
−0.418841u
44
+ 1.39898u
43
+ ··· − 1.39587u + 0.364330
a
1
=
0.180463u
44
− 0.229067u
43
+ ··· − 0.106601u − 0.509733
−0.611791u
44
+ 2.34940u
43
+ ··· − 3.27220u + 1.18556
a
10
=
u
u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6.45073u
44
− 19.7307u
43
+ ··· + 14.2789u − 6.88518
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
45
+ 28u
44
+ ··· + 13u − 1
c
2
, c
5
u
45
+ 6u
44
+ ··· + u − 1
c
3
u
45
− 6u
44
+ ··· + 11u − 1
c
4
, c
7
u
45
+ 3u
44
+ ··· − 2048u + 1024
c
6
, c
10
u
45
+ 3u
44
+ ··· − 2u − 1
c
8
u
45
+ 9u
44
+ ··· − 305892u + 52489
c
9
, c
11
, c
12
u
45
+ 3u
44
+ ··· + 8u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
45
− 16y
44
+ ··· + 2813y −1
c
2
, c
5
y
45
+ 28y
44
+ ··· + 13y −1
c
3
y
45
− 60y
44
+ ··· + 13y −1
c
4
, c
7
y
45
+ 55y
44
+ ··· − 12582912y −1048576
c
6
, c
10
y
45
+ 9y
44
+ ··· − 8y −1
c
8
y
45
+ 37y
44
+ ··· − 75656299984y −2755095121
c
9
, c
11
, c
12
y
45
− 35y
44
+ ··· − 8y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.996119 + 0.282709I
a = 0.110387 + 0.980594I
b = 0.080579 + 0.175761I
1.42637 − 0.55806I 2.83426 − 0.60220I
u = −0.996119 − 0.282709I
a = 0.110387 − 0.980594I
b = 0.080579 − 0.175761I
1.42637 + 0.55806I 2.83426 + 0.60220I
u = 0.783242 + 0.506620I
a = −0.030126 − 0.893560I
b = −0.396180 + 0.324015I
−3.24493 − 1.98845I −2.05742 + 2.49039I
u = 0.783242 − 0.506620I
a = −0.030126 + 0.893560I
b = −0.396180 − 0.324015I
−3.24493 + 1.98845I −2.05742 − 2.49039I
u = −0.647911 + 0.616131I
a = 0.277858 + 0.505783I
b = −1.283800 − 0.505811I
−0.49292 + 5.46151I 3.53146 − 8.21286I
u = −0.647911 − 0.616131I
a = 0.277858 − 0.505783I
b = −1.283800 + 0.505811I
−0.49292 − 5.46151I 3.53146 + 8.21286I
u = 0.415458 + 1.074940I
a = −0.242176 + 0.556359I
b = 0.272242 + 0.056149I
−1.16555 − 2.65109I 0.66724 + 3.06904I
u = 0.415458 − 1.074940I
a = −0.242176 − 0.556359I
b = 0.272242 − 0.056149I
−1.16555 + 2.65109I 0.66724 − 3.06904I
u = −0.300364 + 0.770681I
a = 0.78986 − 1.26679I
b = −0.252806 − 0.197943I
0.37099 − 1.66366I 5.28694 + 1.76198I
u = −0.300364 − 0.770681I
a = 0.78986 + 1.26679I
b = −0.252806 + 0.197943I
0.37099 + 1.66366I 5.28694 − 1.76198I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.349037 + 1.204480I
a = 0.230921 − 0.225780I
b = −0.048432 + 0.642308I
6.11434 + 3.25836I 9.12554 − 6.20048I
u = −0.349037 − 1.204480I
a = 0.230921 + 0.225780I
b = −0.048432 − 0.642308I
6.11434 − 3.25836I 9.12554 + 6.20048I
u = 0.224318 + 0.711056I
a = 0.683426 + 0.176982I
b = −0.044045 − 0.249882I
0.376942 − 1.142080I 4.49943 + 6.11117I
u = 0.224318 − 0.711056I
a = 0.683426 − 0.176982I
b = −0.044045 + 0.249882I
0.376942 + 1.142080I 4.49943 − 6.11117I
u = −0.084183 + 0.723735I
a = −0.081939 − 0.906872I
b = 1.06476 + 1.42506I
4.88394 + 1.66123I 14.9262 − 3.5385I
u = −0.084183 − 0.723735I
a = −0.081939 + 0.906872I
b = 1.06476 − 1.42506I
4.88394 − 1.66123I 14.9262 + 3.5385I
u = 0.315867 + 0.654924I
a = 0.133646 + 1.369790I
b = −1.28532 − 1.81254I
3.26588 − 4.39540I 10.11446 + 8.40755I
u = 0.315867 − 0.654924I
a = 0.133646 − 1.369790I
b = −1.28532 + 1.81254I
3.26588 + 4.39540I 10.11446 − 8.40755I
u = 0.928999 + 0.912938I
a = 1.01128 + 1.05587I
b = −1.83892 + 0.11929I
−3.43407 + 1.56417I 0
u = 0.928999 − 0.912938I
a = 1.01128 − 1.05587I
b = −1.83892 − 0.11929I
−3.43407 − 1.56417I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.004980 + 0.829128I
a = −0.550201 − 1.282520I
b = 1.72749 + 0.74464I
−8.38531 − 3.39936I 0
u = 1.004980 − 0.829128I
a = −0.550201 + 1.282520I
b = 1.72749 − 0.74464I
−8.38531 + 3.39936I 0
u = −0.918792 + 0.952300I
a = 0.87791 − 1.25175I
b = −2.04722 + 0.30573I
−7.36187 + 3.39187I 0
u = −0.918792 − 0.952300I
a = 0.87791 + 1.25175I
b = −2.04722 − 0.30573I
−7.36187 − 3.39187I 0
u = 0.908778 + 0.983223I
a = 0.68380 + 1.36694I
b = −2.05663 − 0.74421I
−3.22324 − 8.34361I 0
u = 0.908778 − 0.983223I
a = 0.68380 − 1.36694I
b = −2.05663 + 0.74421I
−3.22324 + 8.34361I 0
u = −1.045050 + 0.865904I
a = −0.726480 + 1.134250I
b = 1.94070 − 0.29376I
−11.88600 − 1.79976I 0
u = −1.045050 − 0.865904I
a = −0.726480 − 1.134250I
b = 1.94070 + 0.29376I
−11.88600 + 1.79976I 0
u = 0.871713 + 1.077210I
a = −1.17410 − 0.85705I
b = 1.83482 − 0.04447I
−7.57148 − 3.49814I 0
u = 0.871713 − 1.077210I
a = −1.17410 + 0.85705I
b = 1.83482 + 0.04447I
−7.57148 + 3.49814I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.086870 + 0.893598I
a = −0.799128 − 0.940104I
b = 1.90700 − 0.12468I
−7.31081 + 6.80058I 0
u = 1.086870 − 0.893598I
a = −0.799128 + 0.940104I
b = 1.90700 + 0.12468I
−7.31081 − 6.80058I 0
u = −0.510690 + 1.315230I
a = −0.303054 − 0.084448I
b = 0.565338 − 0.295471I
4.91496 + 6.28302I 0
u = −0.510690 − 1.315230I
a = −0.303054 + 0.084448I
b = 0.565338 + 0.295471I
4.91496 − 6.28302I 0
u = −0.915870 + 1.077500I
a = −1.01938 + 1.15677I
b = 2.08407 − 0.22155I
−11.1799 + 8.9578I 0
u = −0.915870 − 1.077500I
a = −1.01938 − 1.15677I
b = 2.08407 + 0.22155I
−11.1799 − 8.9578I 0
u = −0.039688 + 0.578919I
a = 1.94846 + 0.78209I
b = −0.187471 − 0.759973I
0.66871 − 1.39964I 7.21689 + 5.45878I
u = −0.039688 − 0.578919I
a = 1.94846 − 0.78209I
b = −0.187471 + 0.759973I
0.66871 + 1.39964I 7.21689 − 5.45878I
u = −0.571271
a = 1.59952
b = 0.143336
2.17682 3.08930
u = 0.94832 + 1.08708I
a = −0.78152 − 1.29730I
b = 2.14143 + 0.52643I
−6.6450 − 14.1896I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.94832 − 1.08708I
a = −0.78152 + 1.29730I
b = 2.14143 − 0.52643I
−6.6450 + 14.1896I 0
u = −0.323389 + 0.438179I
a = −1.32309 − 1.43900I
b = −0.774207 + 0.940763I
−0.07007 + 2.75890I 1.271024 − 0.509737I
u = −0.323389 − 0.438179I
a = −1.32309 + 1.43900I
b = −0.774207 − 0.940763I
−0.07007 − 2.75890I 1.271024 + 0.509737I
u = 0.428186 + 0.132966I
a = 1.98389 + 7.20476I
b = −0.475066 + 0.996976I
1.97991 + 2.18754I −20.6628 + 4.9777I
u = 0.428186 − 0.132966I
a = 1.98389 − 7.20476I
b = −0.475066 − 0.996976I
1.97991 − 2.18754I −20.6628 − 4.9777I
9
II. I
u
2
=
h−u
2
a+b, u
4
a+u
4
+u
2
a+u
3
+a
2
−au+3u
2
+u+2, u
5
+u
4
+2u
3
+u
2
+u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
4
=
a
u
2
a
a
7
=
1
u
2
a
5
=
a
u
2
a
a
8
=
1
u
2
a
9
=
u
2
+ 1
u
2
a
12
=
−u
4
− u
2
− 1
−u
4
− u
3
− u
2
− 1
a
3
=
u
2
a + a
u
2
a
a
2
=
u
4
+ u
2
a + u
2
+ a − u
u
2
a + 1
a
1
=
−1
0
a
10
=
u
u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
4
a − u
3
a + u
4
− 3u
2
a + 5u
3
− au + 7u
2
− a + 5u + 8
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
5
c
2
(u
2
+ u + 1)
5
c
4
, c
7
u
10
c
6
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
c
8
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
c
9
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
c
10
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
c
11
, c
12
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
5
c
4
, c
7
y
10
c
6
, c
10
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
c
8
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
c
9
, c
11
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339110 + 0.822375I
a = 1.219640 − 0.330957I
b = −0.500000 + 0.866025I
0.329100 + 0.499304I 2.59686 + 1.45733I
u = 0.339110 + 0.822375I
a = −0.323203 + 1.221720I
b = −0.500000 − 0.866025I
0.32910 − 3.56046I 6.44749 + 8.37485I
u = 0.339110 − 0.822375I
a = 1.219640 + 0.330957I
b = −0.500000 − 0.866025I
0.329100 − 0.499304I 2.59686 − 1.45733I
u = 0.339110 − 0.822375I
a = −0.323203 − 1.221720I
b = −0.500000 + 0.866025I
0.32910 + 3.56046I 6.44749 − 8.37485I
u = −0.766826
a = −0.85031 + 1.47278I
b = −0.500000 + 0.866025I
2.40108 + 2.02988I 7.10008 − 1.25892I
u = −0.766826
a = −0.85031 − 1.47278I
b = −0.500000 − 0.866025I
2.40108 − 2.02988I 7.10008 + 1.25892I
u = −0.455697 + 1.200150I
a = 0.575710 + 0.191698I
b = −0.500000 − 0.866025I
5.87256 + 2.37095I 6.27578 + 1.37298I
u = −0.455697 + 1.200150I
a = −0.121840 − 0.594429I
b = −0.500000 + 0.866025I
5.87256 + 6.43072I 11.57979 − 6.03904I
u = −0.455697 − 1.200150I
a = 0.575710 − 0.191698I
b = −0.500000 + 0.866025I
5.87256 − 2.37095I 6.27578 − 1.37298I
u = −0.455697 − 1.200150I
a = −0.121840 + 0.594429I
b = −0.500000 − 0.866025I
5.87256 − 6.43072I 11.57979 + 6.03904I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
5
)(u
45
+ 28u
44
+ ··· + 13u − 1)
c
2
((u
2
+ u + 1)
5
)(u
45
+ 6u
44
+ ··· + u − 1)
c
3
((u
2
− u + 1)
5
)(u
45
− 6u
44
+ ··· + 11u − 1)
c
4
, c
7
u
10
(u
45
+ 3u
44
+ ··· − 2048u + 1024)
c
5
((u
2
− u + 1)
5
)(u
45
+ 6u
44
+ ··· + u − 1)
c
6
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
)(u
45
+ 3u
44
+ ··· − 2u − 1)
c
8
((u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
)(u
45
+ 9u
44
+ ··· − 305892u + 52489)
c
9
((u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
)(u
45
+ 3u
44
+ ··· + 8u − 1)
c
10
((u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
)(u
45
+ 3u
44
+ ··· − 2u − 1)
c
11
, c
12
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
)(u
45
+ 3u
44
+ ··· + 8u − 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
5
)(y
45
− 16y
44
+ ··· + 2813y −1)
c
2
, c
5
((y
2
+ y + 1)
5
)(y
45
+ 28y
44
+ ··· + 13y −1)
c
3
((y
2
+ y + 1)
5
)(y
45
− 60y
44
+ ··· + 13y −1)
c
4
, c
7
y
10
(y
45
+ 55y
44
+ ··· − 1.25829 × 10
7
y −1048576)
c
6
, c
10
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
)(y
45
+ 9y
44
+ ··· − 8y −1)
c
8
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
· (y
45
+ 37y
44
+ ··· − 75656299984y −2755095121)
c
9
, c
11
, c
12
((y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
)(y
45
− 35y
44
+ ··· − 8y −1)
15
