12n
0344
(K12n
0344
)
A knot diagram
1
Linearized knot diagam
3 6 8 7 2 11 3 4 12 6 9 10
Solving Sequence
3,7
8 4
9,11
6 2 1 5 10 12
c
7
c
3
c
8
c
6
c
2
c
1
c
5
c
10
c
12
c
4
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.57884 × 10
37
u
43
+ 4.19415 × 10
37
u
42
+ ··· + 3.14492 × 10
36
b + 2.00463 × 10
38
,
5.51340 × 10
37
u
43
− 1.47280 × 10
38
u
42
+ ··· + 3.14492 × 10
36
a − 7.82161 × 10
38
, u
44
− 3u
43
+ ··· − 36u + 4i
I
u
2
= hau + b + 2a + 1, 2a
2
− au + 2a + 2u − 3, u
2
− 2i
I
v
1
= ha, b + v −2, v
2
− 3v + 1i
* 3 irreducible components of dim
C
= 0, with total 50 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−1.58 × 10
37
u
43
+ 4.19 × 10
37
u
42
+ · · · + 3.14 × 10
36
b + 2.00 ×
10
38
, 5.51 × 10
37
u
43
− 1.47 × 10
38
u
42
+ · · · + 3.14 × 10
36
a − 7.82 ×
10
38
, u
44
− 3u
43
+ · · · − 36u + 4i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
4
=
u
−u
3
+ u
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
11
=
−17.5312u
43
+ 46.8311u
42
+ ··· − 1316.37u + 248.706
5.02029u
43
− 13.3363u
42
+ ··· + 367.657u − 63.7420
a
6
=
3.47461u
43
− 10.7515u
42
+ ··· + 355.136u − 74.5401
−1.68885u
43
+ 5.62072u
42
+ ··· − 173.747u + 30.1506
a
2
=
−9.86564u
43
+ 26.8155u
42
+ ··· − 755.031u + 138.369
−4.70217u
43
+ 10.4432u
42
+ ··· − 226.148u + 33.6781
a
1
=
−9.86564u
43
+ 26.8155u
42
+ ··· − 755.031u + 138.369
−4.03012u
43
+ 8.38511u
42
+ ··· − 165.479u + 22.5523
a
5
=
−u
3
+ 2u
−u
3
+ u
a
10
=
−19.4067u
43
+ 52.8978u
42
+ ··· − 1495.34u + 274.133
−4.36737u
43
+ 8.86394u
42
+ ··· − 164.017u + 21.4464
a
12
=
−15.0159u
43
+ 40.6500u
42
+ ··· − 1164.20u + 225.930
5.45610u
43
− 13.6789u
42
+ ··· + 357.423u − 61.0333
(ii) Obstruction class = −1
(iii) Cusp Shapes = −58.5401u
43
+ 159.424u
42
+ ··· − 4534.07u + 846.150
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
44
+ 45u
43
+ ··· + 4203u + 81
c
2
, c
5
u
44
+ 3u
43
+ ··· + 21u − 9
c
3
, c
7
, c
8
u
44
− 3u
43
+ ··· − 36u + 4
c
4
u
44
+ 9u
43
+ ··· + 1500u − 964
c
6
, c
10
u
44
+ 2u
43
+ ··· + 10u + 1
c
9
, c
11
, c
12
u
44
+ 4u
43
+ ··· − 18u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
44
− 85y
43
+ ··· − 6110883y + 6561
c
2
, c
5
y
44
− 45y
43
+ ··· − 4203y + 81
c
3
, c
7
, c
8
y
44
− 39y
43
+ ··· − 368y + 16
c
4
y
44
+ 21y
43
+ ··· − 41187888y + 929296
c
6
, c
10
y
44
− 12y
43
+ ··· − 58y + 1
c
9
, c
11
, c
12
y
44
− 36y
43
+ ··· − 242y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.361562 + 0.932667I
a = 0.23727 − 1.40400I
b = 0.961486 − 1.024300I
−4.54866 − 9.17617I 5.81808 + 6.48451I
u = −0.361562 − 0.932667I
a = 0.23727 + 1.40400I
b = 0.961486 + 1.024300I
−4.54866 + 9.17617I 5.81808 − 6.48451I
u = 0.242419 + 0.963914I
a = 0.542404 + 0.771039I
b = 0.650253 + 0.479584I
2.03227 + 3.85207I 10.41827 − 8.61488I
u = 0.242419 − 0.963914I
a = 0.542404 − 0.771039I
b = 0.650253 − 0.479584I
2.03227 − 3.85207I 10.41827 + 8.61488I
u = −0.155342 + 0.896950I
a = −0.31935 + 1.38694I
b = −0.99704 + 1.03670I
−8.52514 − 3.75610I 2.09209 + 2.89832I
u = −0.155342 − 0.896950I
a = −0.31935 − 1.38694I
b = −0.99704 − 1.03670I
−8.52514 + 3.75610I 2.09209 − 2.89832I
u = 1.125730 + 0.043899I
a = 0.058942 + 0.745233I
b = 0.556341 + 0.553872I
1.99922 − 0.04818I 6.00000 + 0.I
u = 1.125730 − 0.043899I
a = 0.058942 − 0.745233I
b = 0.556341 − 0.553872I
1.99922 + 0.04818I 6.00000 + 0.I
u = −0.851420 + 0.746270I
a = −0.677609 − 0.190566I
b = −0.609425 − 0.874938I
−3.05540 + 3.53185I 6.00000 + 0.I
u = −0.851420 − 0.746270I
a = −0.677609 + 0.190566I
b = −0.609425 + 0.874938I
−3.05540 − 3.53185I 6.00000 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.060206 + 0.789681I
a = 0.420124 − 1.337940I
b = 1.05150 − 1.02729I
−4.31168 + 1.72166I 4.04968 − 1.22187I
u = 0.060206 − 0.789681I
a = 0.420124 + 1.337940I
b = 1.05150 + 1.02729I
−4.31168 − 1.72166I 4.04968 + 1.22187I
u = −1.104880 + 0.498321I
a = 0.424315 + 0.083138I
b = 0.625620 + 1.104260I
−5.61992 − 1.18304I 0
u = −1.104880 − 0.498321I
a = 0.424315 − 0.083138I
b = 0.625620 − 1.104260I
−5.61992 + 1.18304I 0
u = 1.22068
a = −1.07819
b = 1.88874
10.3320 0
u = 1.218830 + 0.333934I
a = 1.13833 − 0.87054I
b = −1.31850 − 0.66505I
−0.76043 + 2.33473I 0
u = 1.218830 − 0.333934I
a = 1.13833 + 0.87054I
b = −1.31850 + 0.66505I
−0.76043 − 2.33473I 0
u = −1.271900 + 0.268067I
a = −0.553133 − 1.124420I
b = 0.895901 − 0.644934I
2.75377 − 4.58010I 0
u = −1.271900 − 0.268067I
a = −0.553133 + 1.124420I
b = 0.895901 + 0.644934I
2.75377 + 4.58010I 0
u = −1.305420 + 0.064505I
a = 1.20456 + 0.91583I
b = −0.813618 + 0.359887I
5.20530 − 0.47373I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.305420 − 0.064505I
a = 1.20456 − 0.91583I
b = −0.813618 − 0.359887I
5.20530 + 0.47373I 0
u = 1.310900 + 0.166284I
a = −0.028578 + 0.886239I
b = −0.526233 + 0.907268I
5.87917 + 2.87968I 0
u = 1.310900 − 0.166284I
a = −0.028578 − 0.886239I
b = −0.526233 − 0.907268I
5.87917 − 2.87968I 0
u = −1.310400 + 0.345353I
a = −0.233101 − 0.138958I
b = −0.79762 − 1.32164I
−0.02123 − 5.81626I 0
u = −1.310400 − 0.345353I
a = −0.233101 + 0.138958I
b = −0.79762 + 1.32164I
−0.02123 + 5.81626I 0
u = −1.39785
a = 8.91764
b = −0.188474
4.90257 0
u = −0.006322 + 0.581193I
a = −0.89655 − 1.33079I
b = −0.503249 − 0.484782I
−1.17226 + 1.37524I 0.82630 − 4.37313I
u = −0.006322 − 0.581193I
a = −0.89655 + 1.33079I
b = −0.503249 + 0.484782I
−1.17226 − 1.37524I 0.82630 + 4.37313I
u = 1.37514 + 0.39616I
a = −0.881677 + 1.000200I
b = 1.24438 + 0.87011I
−3.70647 + 8.39508I 0
u = 1.37514 − 0.39616I
a = −0.881677 − 1.000200I
b = 1.24438 − 0.87011I
−3.70647 − 8.39508I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.33260 + 0.53021I
a = −0.126765 − 0.487206I
b = −0.626528 − 0.301390I
5.26881 + 2.02524I 0
u = 1.33260 − 0.53021I
a = −0.126765 + 0.487206I
b = −0.626528 + 0.301390I
5.26881 − 2.02524I 0
u = 1.45079
a = 0.972042
b = −0.251576
3.37301 0
u = −1.45928
a = −0.521642
b = 1.51795
13.6404 0
u = −1.41359 + 0.38694I
a = 0.320048 + 0.993129I
b = −0.997773 + 0.724464I
7.26218 − 8.61162I 0
u = −1.41359 − 0.38694I
a = 0.320048 − 0.993129I
b = −0.997773 − 0.724464I
7.26218 + 8.61162I 0
u = 1.48503 + 0.37724I
a = 0.730260 − 1.019420I
b = −1.20624 − 0.98697I
1.34332 + 13.91980I 0
u = 1.48503 − 0.37724I
a = 0.730260 + 1.019420I
b = −1.20624 + 0.98697I
1.34332 − 13.91980I 0
u = −0.115716 + 0.402697I
a = −0.38670 + 2.62883I
b = 0.377022 + 0.479190I
1.42746 − 0.71018I 6.25077 − 1.25816I
u = −0.115716 − 0.402697I
a = −0.38670 − 2.62883I
b = 0.377022 − 0.479190I
1.42746 + 0.71018I 6.25077 + 1.25816I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.339286
a = −1.00783
b = −1.53932
7.49147 26.0080
u = 0.302786
a = −0.689575
b = 0.583905
0.759214 14.0520
u = 0.266557
a = 9.48986
b = −0.525421
−0.455563 39.4620
u = 1.76844
a = −0.0279231
b = 0.581616
6.40427 0
9
II. I
u
2
= hau + b + 2a + 1, 2a
2
− au + 2a + 2u − 3, u
2
− 2i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−2
a
4
=
u
−u
a
9
=
−1
0
a
11
=
a
−au − 2a − 1
a
6
=
1
2
u
au + 2a + 2
a
2
=
1
2
u
au + 2a + u + 2
a
1
=
1
2
u
au + 2a + 2
a
5
=
0
−u
a
10
=
au + 2a +
1
2
u
au + 2a + 2
a
12
=
−au − a − 1
−au − 2a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)
4
c
2
(u + 1)
4
c
3
, c
4
, c
7
c
8
(u
2
− 2)
2
c
6
, c
11
, c
12
(u
2
+ u − 1)
2
c
9
, c
10
(u
2
− u − 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
4
, c
7
c
8
(y −2)
4
c
6
, c
9
, c
10
c
11
, c
12
(y
2
− 3y + 1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.41421
a = −0.473911
b = 0.618034
4.27683 12.0000
u = 1.41421
a = 0.181018
b = −1.61803
12.1725 12.0000
u = −1.41421
a = 1.05505
b = −1.61803
12.1725 12.0000
u = −1.41421
a = −2.76216
b = 0.618034
4.27683 12.0000
13
III. I
v
1
= ha, b + v − 2, v
2
− 3v + 1i
(i) Arc colorings
a
3
=
v
0
a
7
=
1
0
a
8
=
1
0
a
4
=
v
0
a
9
=
1
0
a
11
=
0
−v + 2
a
6
=
1
−v + 3
a
2
=
v − 1
v − 3
a
1
=
−1
v − 3
a
5
=
v
0
a
10
=
v − 2
v − 3
a
12
=
−v + 2
−v + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
4
, c
7
c
8
u
2
c
5
(u + 1)
2
c
6
, c
9
u
2
− u − 1
c
10
, c
11
, c
12
u
2
+ u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y − 1)
2
c
3
, c
4
, c
7
c
8
y
2
c
6
, c
9
, c
10
c
11
, c
12
y
2
− 3y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.381966
a = 0
b = 1.61803
7.23771 −6.00000
v = 2.61803
a = 0
b = −0.618034
−0.657974 −6.00000
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
44
+ 45u
43
+ ··· + 4203u + 81)
c
2
((u − 1)
2
)(u + 1)
4
(u
44
+ 3u
43
+ ··· + 21u − 9)
c
3
, c
7
, c
8
u
2
(u
2
− 2)
2
(u
44
− 3u
43
+ ··· − 36u + 4)
c
4
u
2
(u
2
− 2)
2
(u
44
+ 9u
43
+ ··· + 1500u − 964)
c
5
((u − 1)
4
)(u + 1)
2
(u
44
+ 3u
43
+ ··· + 21u − 9)
c
6
(u
2
− u − 1)(u
2
+ u − 1)
2
(u
44
+ 2u
43
+ ··· + 10u + 1)
c
9
((u
2
− u − 1)
3
)(u
44
+ 4u
43
+ ··· − 18u + 1)
c
10
((u
2
− u − 1)
2
)(u
2
+ u − 1)(u
44
+ 2u
43
+ ··· + 10u + 1)
c
11
, c
12
((u
2
+ u − 1)
3
)(u
44
+ 4u
43
+ ··· − 18u + 1)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
6
)(y
44
− 85y
43
+ ··· − 6110883y + 6561)
c
2
, c
5
((y − 1)
6
)(y
44
− 45y
43
+ ··· − 4203y + 81)
c
3
, c
7
, c
8
y
2
(y − 2)
4
(y
44
− 39y
43
+ ··· − 368y + 16)
c
4
y
2
(y − 2)
4
(y
44
+ 21y
43
+ ··· − 4.11879 × 10
7
y + 929296)
c
6
, c
10
((y
2
− 3y + 1)
3
)(y
44
− 12y
43
+ ··· − 58y + 1)
c
9
, c
11
, c
12
((y
2
− 3y + 1)
3
)(y
44
− 36y
43
+ ··· − 242y + 1)
19
