12n
0312
(K12n
0312
)
A knot diagram
1
Linearized knot diagam
3 6 7 11 8 2 12 6 7 5 10 9
Solving Sequence
2,6
3 7
4,9
10 1 8 5 12 11
c
2
c
6
c
3
c
9
c
1
c
8
c
5
c
12
c
11
c
4
, c
7
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.27353 × 10
50
u
39
+ 5.95554 × 10
50
u
38
+ ··· + 5.81254 × 10
51
b + 4.59993 × 10
51
,
7.75948 × 10
50
u
39
− 3.86755 × 10
51
u
38
+ ··· + 5.81254 × 10
51
a − 9.39756 × 10
51
, u
40
− 2u
39
+ ··· + 7u + 1i
I
u
2
= h2u
14
− u
13
+ 8u
12
− 5u
11
+ 19u
10
− 13u
9
+ 27u
8
− 16u
7
+ 28u
6
− 9u
5
+ 20u
4
+ u
3
+ 10u
2
+ b + 2u + 2,
u
15
− 2u
14
+ ··· + a − 2, u
16
− u
15
+ ··· − u + 1i
* 2 irreducible components of dim
C
= 0, with total 56 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−5.27×10
50
u
39
+5.96×10
50
u
38
+· · ·+5.81×10
51
b+4.60×10
51
, 7.76×
10
50
u
39
−3.87×10
51
u
38
+· · ·+5.81×10
51
a−9.40×10
51
, u
40
−2u
39
+· · ·+7u+1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
9
=
−0.133496u
39
+ 0.665380u
38
+ ··· + 15.0043u + 1.61677
0.0907267u
39
− 0.102460u
38
+ ··· + 0.430261u − 0.791380
a
10
=
−0.224885u
39
+ 0.863520u
38
+ ··· + 12.9927u + 1.29738
−0.000662998u
39
+ 0.0956792u
38
+ ··· − 1.58129u − 1.11078
a
1
=
u
2
+ 1
−u
4
a
8
=
−0.133496u
39
+ 0.665380u
38
+ ··· + 15.0043u + 1.61677
−0.100609u
39
+ 0.340183u
38
+ ··· − 2.22497u − 1.18977
a
5
=
1.39954u
39
− 3.02014u
38
+ ··· + 26.1706u + 4.28089
0.281992u
39
− 0.623894u
38
+ ··· + 2.36583u + 0.204479
a
12
=
−0.0433203u
39
+ 0.378199u
38
+ ··· + 15.8786u + 2.05202
0.483864u
39
− 1.27646u
38
+ ··· − 0.426089u − 1.03092
a
11
=
−2.08778u
39
+ 5.36211u
38
+ ··· − 10.8586u − 2.03985
−0.147373u
39
+ 0.395336u
38
+ ··· − 2.10105u − 0.958378
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4.30999u
39
− 10.1429u
38
+ ··· + 42.2706u + 1.05077
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
40
+ 6u
39
+ ··· + 23u + 1
c
2
, c
6
u
40
− 2u
39
+ ··· + 7u + 1
c
3
u
40
+ 5u
39
+ ··· + 5688833u + 456713
c
4
, c
10
u
40
+ 13u
38
+ ··· − 4u + 7
c
5
, c
8
u
40
+ u
39
+ ··· + 4497u + 361
c
7
u
40
+ 3u
39
+ ··· − 4u + 1
c
9
u
40
− 5u
39
+ ··· − 361724u + 608312
c
11
u
40
− 26u
39
+ ··· − 362u + 49
c
12
u
40
− u
39
+ ··· − 3750504u + 772753
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
40
+ 66y
39
+ ··· − 193y + 1
c
2
, c
6
y
40
+ 6y
39
+ ··· + 23y + 1
c
3
y
40
+ 123y
39
+ ··· + 6314489480935y + 208586764369
c
4
, c
10
y
40
+ 26y
39
+ ··· + 362y + 49
c
5
, c
8
y
40
− 59y
39
+ ··· + 134503y + 130321
c
7
y
40
− y
39
+ ··· + 8y + 1
c
9
y
40
+ 53y
39
+ ··· + 1499383242864y + 370043489344
c
11
y
40
− 18y
39
+ ··· − 40394y + 2401
c
12
y
40
+ 77y
39
+ ··· − 906264208390y + 597147199009
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.262608 + 0.958166I
a = −0.189880 + 0.941685I
b = 0.00591 + 1.77956I
−0.43866 + 2.24384I −3.81906 − 5.12194I
u = 0.262608 − 0.958166I
a = −0.189880 − 0.941685I
b = 0.00591 − 1.77956I
−0.43866 − 2.24384I −3.81906 + 5.12194I
u = 0.926209 + 0.156398I
a = 0.217139 + 0.674278I
b = 0.392314 − 0.960986I
2.50089 + 2.28563I 2.12764 − 2.97233I
u = 0.926209 − 0.156398I
a = 0.217139 − 0.674278I
b = 0.392314 + 0.960986I
2.50089 − 2.28563I 2.12764 + 2.97233I
u = −0.415141 + 0.823170I
a = −0.510209 − 1.251400I
b = 0.404330 − 0.813064I
4.59855 + 0.55508I 3.65213 + 0.54524I
u = −0.415141 − 0.823170I
a = −0.510209 + 1.251400I
b = 0.404330 + 0.813064I
4.59855 − 0.55508I 3.65213 − 0.54524I
u = −0.709121 + 0.812210I
a = 0.656724 + 0.475234I
b = 0.73014 + 1.50996I
4.83926 − 5.18733I 5.25176 + 6.54277I
u = −0.709121 − 0.812210I
a = 0.656724 − 0.475234I
b = 0.73014 − 1.50996I
4.83926 + 5.18733I 5.25176 − 6.54277I
u = 0.319846 + 1.045980I
a = 0.260908 + 0.248366I
b = −0.336124 − 0.552993I
−1.70481 + 5.48650I −4.87092 − 6.70893I
u = 0.319846 − 1.045980I
a = 0.260908 − 0.248366I
b = −0.336124 + 0.552993I
−1.70481 − 5.48650I −4.87092 + 6.70893I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.751933 + 0.494508I
a = 1.392250 + 0.221845I
b = 0.514073 − 0.795694I
1.51098 + 1.78901I 0.82025 − 3.56687I
u = 0.751933 − 0.494508I
a = 1.392250 − 0.221845I
b = 0.514073 + 0.795694I
1.51098 − 1.78901I 0.82025 + 3.56687I
u = −0.297122 + 0.826943I
a = −0.493050 + 0.530886I
b = −0.409100 − 0.824445I
−2.88688 − 1.42829I −8.07911 − 0.82991I
u = −0.297122 − 0.826943I
a = −0.493050 − 0.530886I
b = −0.409100 + 0.824445I
−2.88688 + 1.42829I −8.07911 + 0.82991I
u = 0.294371 + 0.826929I
a = 0.378431 + 0.565801I
b = 0.768928 + 0.890271I
−0.24576 + 1.84711I −2.38841 − 3.47069I
u = 0.294371 − 0.826929I
a = 0.378431 − 0.565801I
b = 0.768928 − 0.890271I
−0.24576 − 1.84711I −2.38841 + 3.47069I
u = −1.054610 + 0.435101I
a = −1.58864 + 0.59883I
b = −0.25725 − 1.66736I
4.29616 − 5.85650I 5.18701 + 8.29672I
u = −1.054610 − 0.435101I
a = −1.58864 − 0.59883I
b = −0.25725 + 1.66736I
4.29616 + 5.85650I 5.18701 − 8.29672I
u = 0.454261 + 1.183960I
a = 0.032608 + 0.790796I
b = 0.87425 + 1.29247I
−0.78848 + 2.37152I −2.00000 + 0.I
u = 0.454261 − 1.183960I
a = 0.032608 − 0.790796I
b = 0.87425 − 1.29247I
−0.78848 − 2.37152I −2.00000 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.12042 + 0.91969I
a = −1.129020 + 0.673147I
b = −0.30929 + 1.59265I
16.0958 + 2.3517I 0
u = 1.12042 − 0.91969I
a = −1.129020 − 0.673147I
b = −0.30929 − 1.59265I
16.0958 − 2.3517I 0
u = −1.04883 + 1.00662I
a = −0.943173 − 0.988165I
b = 0.16566 − 1.65850I
11.50030 + 0.22277I 0
u = −1.04883 − 1.00662I
a = −0.943173 + 0.988165I
b = 0.16566 + 1.65850I
11.50030 − 0.22277I 0
u = −1.01766 + 1.04986I
a = 1.113840 + 0.762342I
b = 0.69672 + 2.05244I
11.34810 − 7.79886I 0
u = −1.01766 − 1.04986I
a = 1.113840 − 0.762342I
b = 0.69672 − 2.05244I
11.34810 + 7.79886I 0
u = −0.407119 + 0.328791I
a = 1.96312 + 0.79373I
b = 1.54195 − 0.43951I
1.42527 − 5.22858I −1.53718 + 8.98097I
u = −0.407119 − 0.328791I
a = 1.96312 − 0.79373I
b = 1.54195 + 0.43951I
1.42527 + 5.22858I −1.53718 − 8.98097I
u = −0.87350 + 1.19690I
a = −0.196741 + 0.749309I
b = −2.00712 + 0.06148I
0.46508 − 3.72342I 0
u = −0.87350 − 1.19690I
a = −0.196741 − 0.749309I
b = −2.00712 − 0.06148I
0.46508 + 3.72342I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.96551 + 1.14045I
a = 0.808271 − 0.969514I
b = 0.22694 − 1.92160I
15.3328 + 5.2849I 0
u = 0.96551 − 1.14045I
a = 0.808271 + 0.969514I
b = 0.22694 + 1.92160I
15.3328 − 5.2849I 0
u = −0.455563 + 0.075943I
a = −3.41002 + 0.16418I
b = −0.022227 − 0.704888I
4.54784 + 1.17562I 6.58243 − 1.22324I
u = −0.455563 − 0.075943I
a = −3.41002 − 0.16418I
b = −0.022227 + 0.704888I
4.54784 − 1.17562I 6.58243 + 1.22324I
u = 1.03222 + 1.17188I
a = −1.053170 + 0.792325I
b = −0.64032 + 2.51487I
15.1921 + 13.6048I 0
u = 1.03222 − 1.17188I
a = −1.053170 − 0.792325I
b = −0.64032 − 2.51487I
15.1921 − 13.6048I 0
u = 1.22561 + 0.99201I
a = 1.019900 − 0.871315I
b = −0.68980 − 1.82950I
15.9053 − 5.4238I 0
u = 1.22561 − 0.99201I
a = 1.019900 + 0.871315I
b = −0.68980 + 1.82950I
15.9053 + 5.4238I 0
u = −0.074323 + 0.230026I
a = −0.32928 + 2.47850I
b = −1.149970 − 0.375487I
−1.50780 − 0.09249I −7.98485 − 1.09942I
u = −0.074323 − 0.230026I
a = −0.32928 − 2.47850I
b = −1.149970 + 0.375487I
−1.50780 + 0.09249I −7.98485 + 1.09942I
8
II.
I
u
2
= h2u
14
− u
13
+ · · · + b + 2, u
15
− 2u
14
+ · · · + a − 2, u
16
− u
15
+ · · · − u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
4
=
u
4
+ u
2
+ 1
u
4
a
9
=
−u
15
+ 2u
14
+ ··· − 7u + 2
−2u
14
+ u
13
+ ··· − 2u − 2
a
10
=
−u
14
− 4u
12
+ ··· − 3u − 1
u
15
− 5u
14
+ ··· + 2u − 5
a
1
=
u
2
+ 1
−u
4
a
8
=
−u
15
+ 2u
14
+ ··· − 7u + 2
−3u
14
+ 2u
13
+ ··· − 15u
2
− 3
a
5
=
2u
15
− 5u
14
+ ··· + 11u − 5
−2u
15
+ 4u
14
+ ··· − 3u + 4
a
12
=
u
15
+ 4u
13
+ ··· + u + 5
u
14
+ 4u
12
+ ··· + 13u
2
+ 4
a
11
=
6u
15
− 4u
14
+ ··· + 8u + 4
5u
15
− 7u
14
+ ··· + 11u − 5
(ii) Obstruction class = 1
(iii) Cusp Shapes = −14u
15
+ 22u
14
− 69u
13
+ 102u
12
− 195u
11
+ 266u
10
− 354u
9
+
393u
8
− 428u
7
+ 384u
6
− 338u
5
+ 239u
4
− 155u
3
+ 106u
2
− 38u + 19
9
(iv) u-Polynomials at the component
10
Crossings u-Polynomials at each crossing
c
1
u
16
− 9u
15
+ ··· − 11u + 1
c
2
u
16
− u
15
+ ··· − u + 1
c
3
u
16
− 2u
15
+ ··· + u + 1
c
4
u
16
+ u
15
+ ··· + 3u
2
+ 1
c
5
u
16
− 6u
14
+ ··· + u + 1
c
6
u
16
+ u
15
+ ··· + u + 1
c
7
u
16
+ 2u
15
+ ··· + 2u + 1
c
8
u
16
− 6u
14
+ ··· − u + 1
c
9
u
16
+ 4u
15
+ ··· + 6u + 1
c
10
u
16
− u
15
+ ··· + 3u
2
+ 1
c
11
u
16
− 9u
15
+ ··· − 6u + 1
c
12
u
16
− 2u
15
+ ··· − 2u + 1
11
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
+ 5y
15
+ ··· − 5y + 1
c
2
, c
6
y
16
+ 9y
15
+ ··· + 11y + 1
c
3
y
16
− 2y
15
+ ··· + 23y + 1
c
4
, c
10
y
16
+ 9y
15
+ ··· + 6y + 1
c
5
, c
8
y
16
− 12y
15
+ ··· − 17y + 1
c
7
y
16
− 6y
15
+ ··· − 12y + 1
c
9
y
16
+ 4y
15
+ ··· − 2y + 1
c
11
y
16
+ y
15
+ ··· + 2y + 1
c
12
y
16
− 12y
15
+ ··· − 6y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.929391 + 0.578619I
a = 1.120080 + 0.128738I
b = 0.91178 − 1.33839I
3.21916 + 5.01414I 0.26989 − 5.16816I
u = 0.929391 − 0.578619I
a = 1.120080 − 0.128738I
b = 0.91178 + 1.33839I
3.21916 − 5.01414I 0.26989 + 5.16816I
u = −0.451615 + 1.007870I
a = 0.338249 + 0.437888I
b = 0.231634 − 0.176676I
−2.35639 − 2.66812I −6.05034 + 3.60958I
u = −0.451615 − 1.007870I
a = 0.338249 − 0.437888I
b = 0.231634 + 0.176676I
−2.35639 + 2.66812I −6.05034 − 3.60958I
u = 0.396309 + 1.073370I
a = −0.565280 + 0.711972I
b = −1.052300 + 0.412205I
−0.63819 + 7.12816I −3.20870 − 8.22524I
u = 0.396309 − 1.073370I
a = −0.565280 − 0.711972I
b = −1.052300 − 0.412205I
−0.63819 − 7.12816I −3.20870 + 8.22524I
u = −0.462450 + 0.682292I
a = −0.332664 − 0.550280I
b = −0.85241 − 1.25415I
−1.24504 − 1.12270I −5.33111 + 3.33125I
u = −0.462450 − 0.682292I
a = −0.332664 + 0.550280I
b = −0.85241 + 1.25415I
−1.24504 + 1.12270I −5.33111 − 3.33125I
u = 0.255308 + 0.671839I
a = −0.033499 − 1.285680I
b = 0.94036 − 1.49852I
0.99305 − 4.20394I −1.88003 + 3.39974I
u = 0.255308 − 0.671839I
a = −0.033499 + 1.285680I
b = 0.94036 + 1.49852I
0.99305 + 4.20394I −1.88003 − 3.39974I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.485789 + 1.201540I
a = −0.150894 + 1.067090I
b = 0.29348 + 1.84901I
0.487588 + 0.633074I −0.204988 − 0.217129I
u = 0.485789 − 1.201540I
a = −0.150894 − 1.067090I
b = 0.29348 − 1.84901I
0.487588 − 0.633074I −0.204988 + 0.217129I
u = 0.030701 + 0.695739I
a = −0.07548 − 2.07079I
b = 0.336792 − 0.535431I
3.73407 + 1.39379I −4.07877 − 4.94416I
u = 0.030701 − 0.695739I
a = −0.07548 + 2.07079I
b = 0.336792 + 0.535431I
3.73407 − 1.39379I −4.07877 + 4.94416I
u = −0.683433 + 1.166390I
a = −0.300514 + 0.906230I
b = −1.80932 + 0.74833I
−0.90438 − 3.31503I −5.01594 + 7.05179I
u = −0.683433 − 1.166390I
a = −0.300514 − 0.906230I
b = −1.80932 − 0.74833I
−0.90438 + 3.31503I −5.01594 − 7.05179I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
16
− 9u
15
+ ··· − 11u + 1)(u
40
+ 6u
39
+ ··· + 23u + 1)
c
2
(u
16
− u
15
+ ··· − u + 1)(u
40
− 2u
39
+ ··· + 7u + 1)
c
3
(u
16
− 2u
15
+ ··· + u + 1)(u
40
+ 5u
39
+ ··· + 5688833u + 456713)
c
4
(u
16
+ u
15
+ ··· + 3u
2
+ 1)(u
40
+ 13u
38
+ ··· − 4u + 7)
c
5
(u
16
− 6u
14
+ ··· + u + 1)(u
40
+ u
39
+ ··· + 4497u + 361)
c
6
(u
16
+ u
15
+ ··· + u + 1)(u
40
− 2u
39
+ ··· + 7u + 1)
c
7
(u
16
+ 2u
15
+ ··· + 2u + 1)(u
40
+ 3u
39
+ ··· − 4u + 1)
c
8
(u
16
− 6u
14
+ ··· − u + 1)(u
40
+ u
39
+ ··· + 4497u + 361)
c
9
(u
16
+ 4u
15
+ ··· + 6u + 1)(u
40
− 5u
39
+ ··· − 361724u + 608312)
c
10
(u
16
− u
15
+ ··· + 3u
2
+ 1)(u
40
+ 13u
38
+ ··· − 4u + 7)
c
11
(u
16
− 9u
15
+ ··· − 6u + 1)(u
40
− 26u
39
+ ··· − 362u + 49)
c
12
(u
16
− 2u
15
+ ··· − 2u + 1)(u
40
− u
39
+ ··· − 3750504u + 772753)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
16
+ 5y
15
+ ··· − 5y + 1)(y
40
+ 66y
39
+ ··· − 193y + 1)
c
2
, c
6
(y
16
+ 9y
15
+ ··· + 11y + 1)(y
40
+ 6y
39
+ ··· + 23y + 1)
c
3
(y
16
− 2y
15
+ ··· + 23y + 1)
· (y
40
+ 123y
39
+ ··· + 6314489480935y + 208586764369)
c
4
, c
10
(y
16
+ 9y
15
+ ··· + 6y + 1)(y
40
+ 26y
39
+ ··· + 362y + 49)
c
5
, c
8
(y
16
− 12y
15
+ ··· − 17y + 1)(y
40
− 59y
39
+ ··· + 134503y + 130321)
c
7
(y
16
− 6y
15
+ ··· − 12y + 1)(y
40
− y
39
+ ··· + 8y + 1)
c
9
(y
16
+ 4y
15
+ ··· − 2y + 1)
· (y
40
+ 53y
39
+ ··· + 1499383242864y + 370043489344)
c
11
(y
16
+ y
15
+ ··· + 2y + 1)(y
40
− 18y
39
+ ··· − 40394y + 2401)
c
12
(y
16
− 12y
15
+ ··· − 6y + 1)
· (y
40
+ 77y
39
+ ··· − 906264208390y + 597147199009)
17
