12n
0094
(K12n
0094
)
A knot diagram
1
Linearized knot diagam
3 5 6 2 8 3 11 5 12 7 10 9
Solving Sequence
7,10
11 8
3,12
6 4 5 2 9 1
c
10
c
7
c
11
c
6
c
3
c
5
c
2
c
9
c
12
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h237180958840u
40
+ 426640636409u
39
+ ··· + 126602287463b − 603869550171,
184156720841u
40
+ 260129939039u
39
+ ··· + 379806862389a − 927659389454,
u
41
+ 2u
40
+ ··· − 5u − 1i
I
u
2
= h−2u
4
− u
3
+ b + u − 3, a, u
5
+ u
4
− u
2
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 46 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
= h2.37 × 10
11
u
40
+ 4.27 × 10
11
u
39
+ · · · + 1.27 × 10
11
b − 6.04 × 10
11
, 1.84 ×
10
11
u
40
+2.60×10
11
u
39
+· · ·+3.80×10
11
a−9.28×10
11
, u
41
+2u
40
+· · ·−5u−1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
8
=
−u
−u
3
+ u
a
3
=
−0.484869u
40
− 0.684901u
39
+ ··· + 1.43981u + 2.44245
−1.87343u
40
− 3.36993u
39
+ ··· + 10.8768u + 4.76982
a
12
=
−u
2
+ 1
u
2
a
6
=
0.839243u
40
+ 0.839308u
39
+ ··· − 4.68096u − 0.119652
−3.44624u
40
− 3.41234u
39
+ ··· + 13.1682u + 3.81213
a
4
=
2.36382u
40
+ 2.16411u
39
+ ··· − 7.95826u + 1.01795
−5.33759u
40
− 3.95656u
39
+ ··· + 14.0481u + 5.35650
a
5
=
−0.545392u
40
− 0.945298u
39
+ ··· + 1.68058u + 1.67265
−2.45910u
40
− 2.60458u
39
+ ··· + 10.3453u + 3.00449
a
2
=
0.605914u
40
+ 0.205696u
39
+ ··· − 1.92135u + 3.09715
−4.95524u
40
− 5.16076u
39
+ ··· + 18.1862u + 6.76084
a
9
=
u
4
− u
2
+ 1
−u
4
a
1
=
−u
6
+ u
4
− 2u
2
+ 1
u
6
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
159607686408
126602287463
u
40
−
572526761426
126602287463
u
39
+ ··· +
127765468738
126602287463
u +
346980052385
126602287463
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
41
+ 44u
40
+ ··· + 2355u + 1
c
2
, c
4
u
41
− 6u
40
+ ··· + 47u − 1
c
3
, c
6
u
41
+ 7u
40
+ ··· + 64u + 32
c
5
, c
8
u
41
− 2u
40
+ ··· + u − 1
c
7
, c
10
u
41
+ 2u
40
+ ··· − 5u − 1
c
9
, c
11
, c
12
u
41
+ 12u
40
+ ··· + 9u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
41
− 88y
40
+ ··· + 5466307y −1
c
2
, c
4
y
41
− 44y
40
+ ··· + 2355y −1
c
3
, c
6
y
41
+ 33y
40
+ ··· + 49664y −1024
c
5
, c
8
y
41
+ 42y
39
+ ··· + 9y −1
c
7
, c
10
y
41
− 12y
40
+ ··· + 9y −1
c
9
, c
11
, c
12
y
41
+ 36y
40
+ ··· + 145y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.809815 + 0.656518I
a = 0.18310 + 1.61197I
b = 2.10023 − 1.97578I
−1.37603 + 0.57854I −11.62960 + 0.13351I
u = −0.809815 − 0.656518I
a = 0.18310 − 1.61197I
b = 2.10023 + 1.97578I
−1.37603 − 0.57854I −11.62960 − 0.13351I
u = 0.934060 + 0.150205I
a = −0.18148 − 1.61697I
b = 0.203825 + 1.369510I
−3.38084 − 3.41544I −14.4142 + 7.4507I
u = 0.934060 − 0.150205I
a = −0.18148 + 1.61697I
b = 0.203825 − 1.369510I
−3.38084 + 3.41544I −14.4142 − 7.4507I
u = 0.940510
a = −1.80150
b = 0.154280
−5.56664 −18.9570
u = −0.765786 + 0.781729I
a = −1.48698 + 0.38083I
b = 0.91217 + 1.53968I
2.58614 − 2.24374I −5.47598 + 3.48781I
u = −0.765786 − 0.781729I
a = −1.48698 − 0.38083I
b = 0.91217 − 1.53968I
2.58614 + 2.24374I −5.47598 − 3.48781I
u = 0.825264 + 0.768049I
a = −0.533792 − 0.264806I
b = −0.363252 − 0.579554I
2.79960 − 1.79972I −4.96538 + 4.18830I
u = 0.825264 − 0.768049I
a = −0.533792 + 0.264806I
b = −0.363252 + 0.579554I
2.79960 + 1.79972I −4.96538 − 4.18830I
u = 0.871525 + 0.715232I
a = 0.317178 − 0.359818I
b = 2.05567 + 2.91440I
0.88954 − 2.73561I 12.1135 + 7.6213I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.871525 − 0.715232I
a = 0.317178 + 0.359818I
b = 2.05567 − 2.91440I
0.88954 + 2.73561I 12.1135 − 7.6213I
u = 0.710841 + 0.488347I
a = 0.458035 − 0.499819I
b = −0.032082 + 0.328781I
1.44935 − 1.91021I −0.76032 + 4.38625I
u = 0.710841 − 0.488347I
a = 0.458035 + 0.499819I
b = −0.032082 − 0.328781I
1.44935 + 1.91021I −0.76032 − 4.38625I
u = −0.923416 + 0.674039I
a = 1.66369 + 0.14363I
b = −0.43727 − 2.53225I
−1.74586 + 4.59945I −12.56472 − 5.90817I
u = −0.923416 − 0.674039I
a = 1.66369 − 0.14363I
b = −0.43727 + 2.53225I
−1.74586 − 4.59945I −12.56472 + 5.90817I
u = 1.118030 + 0.271471I
a = −0.17044 + 1.50981I
b = −0.89384 − 1.26952I
−11.21910 − 7.94660I −13.0997 + 5.5632I
u = 1.118030 − 0.271471I
a = −0.17044 − 1.50981I
b = −0.89384 + 1.26952I
−11.21910 + 7.94660I −13.0997 − 5.5632I
u = −0.720515 + 0.902697I
a = 1.42868 − 0.16952I
b = −0.66709 − 1.95032I
−3.31648 − 7.81279I −7.43198 + 3.38635I
u = −0.720515 − 0.902697I
a = 1.42868 + 0.16952I
b = −0.66709 + 1.95032I
−3.31648 + 7.81279I −7.43198 − 3.38635I
u = −1.121650 + 0.291198I
a = 0.498876 − 1.312020I
b = −1.197720 + 0.633604I
−11.09620 − 0.45608I −13.41842 − 0.76918I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.121650 − 0.291198I
a = 0.498876 + 1.312020I
b = −1.197720 − 0.633604I
−11.09620 + 0.45608I −13.41842 + 0.76918I
u = −0.019251 + 0.828572I
a = −1.74001 + 0.53051I
b = 1.287330 − 0.377518I
−7.34491 + 4.27339I −8.31191 − 2.78880I
u = −0.019251 − 0.828572I
a = −1.74001 − 0.53051I
b = 1.287330 + 0.377518I
−7.34491 − 4.27339I −8.31191 + 2.78880I
u = 0.731013 + 0.924450I
a = 0.923425 + 0.604573I
b = −1.26483 + 1.04082I
−2.90816 − 0.63484I −9.12562 + 1.25059I
u = 0.731013 − 0.924450I
a = 0.923425 − 0.604573I
b = −1.26483 − 1.04082I
−2.90816 + 0.63484I −9.12562 − 1.25059I
u = −0.804662 + 0.114668I
a = −0.147294 + 0.641401I
b = 0.80950 − 2.46652I
−2.53010 + 0.33755I −19.6414 + 2.1587I
u = −0.804662 − 0.114668I
a = −0.147294 − 0.641401I
b = 0.80950 + 2.46652I
−2.53010 − 0.33755I −19.6414 − 2.1587I
u = 0.926559 + 0.745351I
a = 0.274837 + 0.567927I
b = −1.08422 − 1.33352I
2.48539 − 3.92858I −5.87670 + 1.12171I
u = 0.926559 − 0.745351I
a = 0.274837 − 0.567927I
b = −1.08422 + 1.33352I
2.48539 + 3.92858I −5.87670 − 1.12171I
u = −0.965249 + 0.735330I
a = 0.31200 − 1.49463I
b = −2.37280 + 1.50589I
1.97721 + 7.97688I −7.20424 − 8.75185I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.965249 − 0.735330I
a = 0.31200 + 1.49463I
b = −2.37280 − 1.50589I
1.97721 − 7.97688I −7.20424 + 8.75185I
u = −0.930134 + 0.890297I
a = −0.321692 − 0.288040I
b = −0.267302 + 0.867780I
9.70942 + 3.28933I 6.13928 − 1.45507I
u = −0.930134 − 0.890297I
a = −0.321692 + 0.288040I
b = −0.267302 − 0.867780I
9.70942 − 3.28933I 6.13928 + 1.45507I
u = −1.037090 + 0.774259I
a = −0.100822 + 1.364460I
b = 2.50179 − 1.88429I
−4.3067 + 14.0138I −8.63515 − 7.83947I
u = −1.037090 − 0.774259I
a = −0.100822 − 1.364460I
b = 2.50179 + 1.88429I
−4.3067 − 14.0138I −8.63515 + 7.83947I
u = 1.045430 + 0.785315I
a = −0.491121 − 0.952641I
b = 2.29006 + 0.47538I
−3.90534 − 5.67266I −9.98188 + 3.51111I
u = 1.045430 − 0.785315I
a = −0.491121 + 0.952641I
b = 2.29006 − 0.47538I
−3.90534 + 5.67266I −9.98188 − 3.51111I
u = −0.666990
a = 0.215563
b = 0.523845
−0.906933 −11.3940
u = −0.035730 + 0.419728I
a = 2.06556 − 0.62654I
b = −0.346501 − 0.304456I
−0.57624 + 1.50346I −4.65093 − 4.60849I
u = −0.035730 − 0.419728I
a = 2.06556 + 0.62654I
b = −0.346501 + 0.304456I
−0.57624 − 1.50346I −4.65093 + 4.60849I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.332380
a = 1.68244
b = 1.85453
−2.28489 0.221560
9
II. I
u
2
= h−2u
4
− u
3
+ b + u − 3, a, u
5
+ u
4
− u
2
+ u + 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
8
=
−u
−u
3
+ u
a
3
=
0
2u
4
+ u
3
− u + 3
a
12
=
−u
2
+ 1
u
2
a
6
=
0
u
a
4
=
0
2u
4
+ u
3
− u + 3
a
5
=
u
3
−u
4
− u
3
+ u
2
− 1
a
2
=
−u
3
3u
4
+ 2u
3
− u
2
− u + 4
a
9
=
u
4
− u
2
+ 1
−u
4
a
1
=
−u
3
u
4
+ u
3
− u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −18u
4
− 7u
3
+ 7u
2
+ 18u − 39
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
5
c
3
, c
6
u
5
c
4
(u + 1)
5
c
5
, c
9
u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1
c
7
u
5
− u
4
+ u
2
+ u − 1
c
8
, c
11
, c
12
u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1
c
10
u
5
+ u
4
− u
2
+ u + 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
6
y
5
c
5
, c
8
, c
9
c
11
, c
12
y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1
c
7
, c
10
y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.758138 + 0.584034I
a = 0
b = 0.442614 + 1.051550I
0.17487 − 2.21397I −8.20462 + 3.60694I
u = 0.758138 − 0.584034I
a = 0
b = 0.442614 − 1.051550I
0.17487 + 2.21397I −8.20462 − 3.60694I
u = −0.935538 + 0.903908I
a = 0
b = −0.304213 + 0.337334I
9.31336 + 3.33174I −14.3260 − 3.4701I
u = −0.935538 − 0.903908I
a = 0
b = −0.304213 − 0.337334I
9.31336 − 3.33174I −14.3260 + 3.4701I
u = −0.645200
a = 0
b = 3.72320
−2.52712 −48.9390
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
41
+ 44u
40
+ ··· + 2355u + 1)
c
2
((u − 1)
5
)(u
41
− 6u
40
+ ··· + 47u − 1)
c
3
, c
6
u
5
(u
41
+ 7u
40
+ ··· + 64u + 32)
c
4
((u + 1)
5
)(u
41
− 6u
40
+ ··· + 47u − 1)
c
5
(u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)(u
41
− 2u
40
+ ··· + u − 1)
c
7
(u
5
− u
4
+ u
2
+ u − 1)(u
41
+ 2u
40
+ ··· − 5u − 1)
c
8
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)(u
41
− 2u
40
+ ··· + u − 1)
c
9
(u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)(u
41
+ 12u
40
+ ··· + 9u + 1)
c
10
(u
5
+ u
4
− u
2
+ u + 1)(u
41
+ 2u
40
+ ··· − 5u − 1)
c
11
, c
12
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)(u
41
+ 12u
40
+ ··· + 9u + 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
5
)(y
41
− 88y
40
+ ··· + 5466307y −1)
c
2
, c
4
((y −1)
5
)(y
41
− 44y
40
+ ··· + 2355y −1)
c
3
, c
6
y
5
(y
41
+ 33y
40
+ ··· + 49664y −1024)
c
5
, c
8
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)(y
41
+ 42y
39
+ ··· + 9y −1)
c
7
, c
10
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)(y
41
− 12y
40
+ ··· + 9y −1)
c
9
, c
11
, c
12
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)(y
41
+ 36y
40
+ ··· + 145y −1)
15
