12n
0024
(K12n
0024
)
A knot diagram
1
Linearized knot diagam
3 5 6 7 2 10 5 12 11 6 8 9
Solving Sequence
2,6
5 3
1,11
10 7 8 4 9 12
c
5
c
2
c
1
c
10
c
6
c
7
c
4
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−987290740395u
33
− 5379029654817u
32
+ ··· + 837919692176b − 653062691196,
− 1563526467031u
33
− 8197997634981u
32
+ ··· + 837919692176a + 1275617520034,
u
34
+ 6u
33
+ ··· + 5u + 1i
I
u
2
= h−a
3
− 3au + b + 3a + 1, a
5
+ a
4
u − 2a
4
+ 2a
3
u − 3a
3
− 5a
2
u + 2a
2
− 2au + 4a + u, u
2
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 44 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−9.87×10
11
u
33
−5.38×10
12
u
32
+· · ·+8.38×10
11
b−6.53×10
11
, −1.56×
10
12
u
33
−8.20×10
12
u
32
+· · ·+8.38×10
11
a+1.28×10
12
, u
34
+6u
33
+· · ·+5u+1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
11
=
1.86596u
33
+ 9.78375u
32
+ ··· + 1.06021u − 1.52236
1.17826u
33
+ 6.41951u
32
+ ··· + 5.45973u + 0.779386
a
10
=
0.687698u
33
+ 3.36425u
32
+ ··· − 4.39952u − 2.30175
1.17826u
33
+ 6.41951u
32
+ ··· + 5.45973u + 0.779386
a
7
=
−1.28785u
33
− 8.52538u
32
+ ··· − 21.2336u − 4.29654
0.361519u
33
+ 2.60589u
32
+ ··· + 0.591225u − 0.926328
a
8
=
−1.37658u
33
− 9.45845u
32
+ ··· − 25.9217u − 6.02116
1.27771u
33
+ 6.49148u
32
+ ··· + 2.68331u − 0.525657
a
4
=
−u
3
u
3
+ u
a
9
=
0.00960441u
33
− 1.00925u
32
+ ··· − 18.8321u − 4.39435
0.833123u
33
+ 4.09945u
32
+ ··· − 0.950070u − 1.07697
a
12
=
−0.818376u
33
− 6.54935u
32
+ ··· − 31.6588u − 7.66755
1.56035u
33
+ 7.49904u
32
+ ··· + 0.0306098u − 1.66930
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
1379117222209
837919692176
u
33
+
1029169729969
119702813168
u
32
+ ··· +
2734506517567
837919692176
u −
434006716289
104739961522
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
34
+ 6u
33
+ ··· + 17u + 1
c
2
, c
5
u
34
+ 6u
33
+ ··· + 5u + 1
c
3
u
34
− 6u
33
+ ··· + 10043u + 23377
c
4
, c
7
u
34
+ 3u
33
+ ··· + 4096u + 1024
c
6
, c
10
u
34
− 3u
33
+ ··· − 2u + 1
c
8
, c
11
, c
12
u
34
− 3u
33
+ ··· − 2u + 1
c
9
u
34
+ 3u
33
+ ··· − 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
34
+ 50y
33
+ ··· + 17y + 1
c
2
, c
5
y
34
+ 6y
33
+ ··· + 17y + 1
c
3
y
34
+ 94y
33
+ ··· + 17344598433y + 546484129
c
4
, c
7
y
34
− 55y
33
+ ··· − 6291456y + 1048576
c
6
, c
10
y
34
+ 3y
33
+ ··· − 2y + 1
c
8
, c
11
, c
12
y
34
− 25y
33
+ ··· − 2y + 1
c
9
y
34
+ 59y
33
+ ··· + 6y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.460595 + 0.926013I
a = 1.65664 + 1.65921I
b = 0.408796 − 0.306002I
−1.92220 + 2.39604I 9.18658 + 7.54131I
u = 0.460595 − 0.926013I
a = 1.65664 − 1.65921I
b = 0.408796 + 0.306002I
−1.92220 − 2.39604I 9.18658 − 7.54131I
u = 0.916388 + 0.231859I
a = 0.575411 + 0.072095I
b = 0.740585 + 0.042237I
1.77655 + 0.14759I 6.63914 + 0.92800I
u = 0.916388 − 0.231859I
a = 0.575411 − 0.072095I
b = 0.740585 − 0.042237I
1.77655 − 0.14759I 6.63914 − 0.92800I
u = −0.139053 + 0.917478I
a = 0.883284 + 0.335732I
b = −0.309625 − 1.098890I
−6.97147 + 2.86372I −9.65845 − 4.16249I
u = −0.139053 − 0.917478I
a = 0.883284 − 0.335732I
b = −0.309625 + 1.098890I
−6.97147 − 2.86372I −9.65845 + 4.16249I
u = 0.615154 + 0.975680I
a = −0.929833 + 0.597421I
b = −0.525453 − 0.313759I
0.54741 + 2.67952I 3.39595 − 1.50494I
u = 0.615154 − 0.975680I
a = −0.929833 − 0.597421I
b = −0.525453 + 0.313759I
0.54741 − 2.67952I 3.39595 + 1.50494I
u = 0.429644 + 0.715588I
a = −0.53311 − 2.00244I
b = 0.036081 + 0.595902I
−1.17601 + 1.39012I −7.01664 − 5.97525I
u = 0.429644 − 0.715588I
a = −0.53311 + 2.00244I
b = 0.036081 − 0.595902I
−1.17601 − 1.39012I −7.01664 + 5.97525I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.523759 + 0.558320I
a = −1.97777 − 0.12112I
b = −0.563128 + 1.220590I
−5.45470 − 5.60091I −2.61064 + 1.17728I
u = −0.523759 − 0.558320I
a = −1.97777 + 0.12112I
b = −0.563128 − 1.220590I
−5.45470 + 5.60091I −2.61064 − 1.17728I
u = 0.976795 + 0.800627I
a = −0.742471 + 0.095802I
b = −0.726847 − 0.193549I
1.16029 + 3.25320I 4.65048 − 6.79539I
u = 0.976795 − 0.800627I
a = −0.742471 − 0.095802I
b = −0.726847 + 0.193549I
1.16029 − 3.25320I 4.65048 + 6.79539I
u = −1.089890 + 0.830630I
a = 0.725849 + 0.611806I
b = 1.11344 + 0.97215I
9.51601 + 5.95991I 0.51921 − 2.93310I
u = −1.089890 − 0.830630I
a = 0.725849 − 0.611806I
b = 1.11344 − 0.97215I
9.51601 − 5.95991I 0.51921 + 2.93310I
u = −0.982318 + 0.958357I
a = 1.53840 + 0.41969I
b = 1.00540 − 1.12383I
8.99044 − 1.80322I 0. + 1.42178I
u = −0.982318 − 0.958357I
a = 1.53840 − 0.41969I
b = 1.00540 + 1.12383I
8.99044 + 1.80322I 0. − 1.42178I
u = 0.502370 + 1.284930I
a = 0.386591 − 0.485376I
b = 0.637032 + 0.537211I
−1.85905 + 5.40081I −1.55683 − 8.82721I
u = 0.502370 − 1.284930I
a = 0.386591 + 0.485376I
b = 0.637032 − 0.537211I
−1.85905 − 5.40081I −1.55683 + 8.82721I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.957231 + 0.999067I
a = 0.518277 + 0.648716I
b = 1.11992 + 1.01734I
8.85325 − 5.31381I 0. + 2.92536I
u = −0.957231 − 0.999067I
a = 0.518277 − 0.648716I
b = 1.11992 − 1.01734I
8.85325 + 5.31381I 0. − 2.92536I
u = −1.046170 + 0.937050I
a = −0.620076 − 0.611485I
b = −1.11562 − 0.99302I
13.38330 + 0.23885I 2.96282 + 0.I
u = −1.046170 − 0.937050I
a = −0.620076 + 0.611485I
b = −1.11562 + 0.99302I
13.38330 − 0.23885I 2.96282 + 0.I
u = 0.198700 + 0.560261I
a = −1.17033 − 1.74922I
b = 0.007937 + 0.744382I
−1.29654 + 1.36041I −5.30238 − 4.63375I
u = 0.198700 − 0.560261I
a = −1.17033 + 1.74922I
b = 0.007937 − 0.744382I
−1.29654 − 1.36041I −5.30238 + 4.63375I
u = −0.96143 + 1.05476I
a = −1.50621 − 0.49472I
b = −1.02274 + 1.10646I
12.9727 − 7.5739I 2.34047 + 4.26054I
u = −0.96143 − 1.05476I
a = −1.50621 + 0.49472I
b = −1.02274 − 1.10646I
12.9727 + 7.5739I 2.34047 − 4.26054I
u = −0.90074 + 1.11269I
a = 1.50810 + 0.56457I
b = 1.04148 − 1.09306I
8.5560 − 13.1935I 0. + 6.90026I
u = −0.90074 − 1.11269I
a = 1.50810 − 0.56457I
b = 1.04148 + 1.09306I
8.5560 + 13.1935I 0. − 6.90026I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.373509 + 0.310679I
a = 2.41143 + 0.07043I
b = 0.482363 − 0.901628I
−0.05073 − 2.05660I 0.17254 + 2.58405I
u = −0.373509 − 0.310679I
a = 2.41143 − 0.07043I
b = 0.482363 + 0.901628I
−0.05073 + 2.05660I 0.17254 − 2.58405I
u = −0.125550 + 0.377744I
a = −1.22419 − 1.84916I
b = −0.829608 − 0.231361I
−2.61203 − 0.40815I −2.95865 − 1.32770I
u = −0.125550 − 0.377744I
a = −1.22419 + 1.84916I
b = −0.829608 + 0.231361I
−2.61203 + 0.40815I −2.95865 + 1.32770I
8
II. I
u
2
= h−a
3
− 3au + b + 3a + 1, a
4
u + 2a
3
u + · · · + 2a
2
+ 4a, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u − 1
a
3
=
u
u − 1
a
1
=
−1
0
a
11
=
a
a
3
+ 3au − 3a − 1
a
10
=
−a
3
− 3au + 4a + 1
a
3
+ 3au − 3a − 1
a
7
=
a
4
u − a
4
− 3a
2
u − au + a − u + 1
−a
4
u + 3a
2
+ au + u
a
8
=
a
4
u − a
4
− 3a
2
u − au + a − u + 1
−a
4
u + 3a
2
+ au + u
a
4
=
1
u − 1
a
9
=
a
4
u + a
4
+ a
3
u − 2a
3
+ 2a
2
u − 5a
2
− 6au + 2a − u + 2
2a
4
u − a
4
− a
3
u − 3a
2
u − 2a
2
− 2au + 3a + u
a
12
=
a
4
u − a
4
+ a
3
− 3a
2
u + au − a − u
−a
4
u + a
3
u + 3a
2
+ au − 2a
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6a
4
u − 6a
4
− 3a
3
u − 2a
3
− 19a
2
u + 5a
2
− 11au + 17a + 4u + 2
9
(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
+ u
4
− 2u
3
− u
2
+ u − 1)
2
c
9
(u
5
− 3u
4
+ 4u
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
10
(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
, c
11
, c
12
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
c
9
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.535003 − 0.266485I
b = 0.455697 − 1.200150I
−5.87256 − 2.37095I −1.90884 + 0.95814I
u = 0.500000 + 0.866025I
a = −1.31030 + 0.92177I
b = −0.339110 − 0.822375I
−0.32910 + 3.56046I −2.43337 − 7.40396I
u = 0.500000 + 0.866025I
a = 1.54372 − 0.52281I
b = 0.455697 + 1.200150I
−5.87256 + 6.43072I −7.21285 − 8.37016I
u = 0.500000 + 0.866025I
a = 0.114093 − 0.334410I
b = −0.339110 + 0.822375I
−0.329100 + 0.499304I 1.41726 + 0.48644I
u = 0.500000 + 0.866025I
a = 1.68749 − 0.66409I
b = 0.766826
−2.40108 + 2.02988I 0.137791 − 1.258916I
u = 0.500000 − 0.866025I
a = −0.535003 + 0.266485I
b = 0.455697 + 1.200150I
−5.87256 + 2.37095I −1.90884 − 0.95814I
u = 0.500000 − 0.866025I
a = −1.31030 − 0.92177I
b = −0.339110 + 0.822375I
−0.32910 − 3.56046I −2.43337 + 7.40396I
u = 0.500000 − 0.866025I
a = 1.54372 + 0.52281I
b = 0.455697 − 1.200150I
−5.87256 − 6.43072I −7.21285 + 8.37016I
u = 0.500000 − 0.866025I
a = 0.114093 + 0.334410I
b = −0.339110 − 0.822375I
−0.329100 − 0.499304I 1.41726 − 0.48644I
u = 0.500000 − 0.866025I
a = 1.68749 + 0.66409I
b = 0.766826
−2.40108 − 2.02988I 0.137791 + 1.258916I
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
5
)(u
34
+ 6u
33
+ ··· + 17u + 1)
c
2
((u
2
+ u + 1)
5
)(u
34
+ 6u
33
+ ··· + 5u + 1)
c
3
((u
2
− u + 1)
5
)(u
34
− 6u
33
+ ··· + 10043u + 23377)
c
4
, c
7
u
10
(u
34
+ 3u
33
+ ··· + 4096u + 1024)
c
5
((u
2
− u + 1)
5
)(u
34
+ 6u
33
+ ··· + 5u + 1)
c
6
((u
5
− u
4
+ 2u
3
− u
2
+ u − 1)
2
)(u
34
− 3u
33
+ ··· − 2u + 1)
c
8
((u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
2
)(u
34
− 3u
33
+ ··· − 2u + 1)
c
9
((u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)
2
)(u
34
+ 3u
33
+ ··· − 2u + 1)
c
10
((u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
2
)(u
34
− 3u
33
+ ··· − 2u + 1)
c
11
, c
12
((u
5
− u
4
− 2u
3
+ u
2
+ u + 1)
2
)(u
34
− 3u
33
+ ··· − 2u + 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
5
)(y
34
+ 50y
33
+ ··· + 17y + 1)
c
2
, c
5
((y
2
+ y + 1)
5
)(y
34
+ 6y
33
+ ··· + 17y + 1)
c
3
((y
2
+ y + 1)
5
)(y
34
+ 94y
33
+ ··· + 1.73446 × 10
10
y + 5.46484 × 10
8
)
c
4
, c
7
y
10
(y
34
− 55y
33
+ ··· − 6291456y + 1048576)
c
6
, c
10
((y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)
2
)(y
34
+ 3y
33
+ ··· − 2y + 1)
c
8
, c
11
, c
12
((y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)
2
)(y
34
− 25y
33
+ ··· − 2y + 1)
c
9
((y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)
2
)(y
34
+ 59y
33
+ ··· + 6y + 1)
14
