12n
0793
(K12n
0793
)
A knot diagram
1
Linearized knot diagam
4 6 10 8 2 11 12 4 1 3 7 8
Solving Sequence
7,11
12 8 1
3,6
2 5 10 4 9
c
11
c
7
c
12
c
6
c
2
c
5
c
10
c
3
c
8
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−9.06380 × 10
25
u
41
+ 1.37425 × 10
28
u
40
+ ··· + 2.41942 × 10
28
b − 1.11983 × 10
29
,
− 3.26749 × 10
28
u
41
− 3.64396 × 10
28
u
40
+ ··· + 2.66137 × 10
29
a + 8.28132 × 10
29
,
u
42
+ 2u
41
+ ··· − 46u + 11i
I
u
2
= hu
7
− 5u
5
+ 7u
3
+ b − 2u, u
7
− 5u
5
+ 7u
3
− u
2
+ a − 2u + 2,
u
12
+ u
11
− 8u
10
− 7u
9
+ 24u
8
+ 17u
7
− 33u
6
− 16u
5
+ 20u
4
+ 4u
3
− 4u
2
− u − 1i
* 2 irreducible components of dim
C
= 0, with total 54 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−9.06 × 10
25
u
41
+ 1.37 × 10
28
u
40
+ · · · + 2.42 × 10
28
b − 1.12 ×
10
29
, −3.27 × 10
28
u
41
− 3.64 × 10
28
u
40
+ · · · + 2.66 × 10
29
a + 8.28 ×
10
29
, u
42
+ 2u
41
+ · · · − 46u + 11i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
8
=
−u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
0.122775u
41
+ 0.136921u
40
+ ··· + 9.26541u − 3.11168
0.00374626u
41
− 0.568007u
40
+ ··· − 19.2584u + 4.62848
a
6
=
u
u
a
2
=
0.552701u
41
+ 0.271165u
40
+ ··· − 10.9013u + 2.02390
0.433672u
41
− 0.433763u
40
+ ··· − 39.4251u + 9.76406
a
5
=
1.16210u
41
+ 1.69216u
40
+ ··· + 6.54468u − 3.34003
0.919505u
41
+ 0.221580u
40
+ ··· − 40.9514u + 10.5711
a
10
=
1.17084u
41
+ 1.34160u
40
+ ··· − 4.55540u − 2.12767
1.14646u
41
+ 1.21035u
40
+ ··· − 7.23546u − 2.71408
a
4
=
0.785947u
41
+ 1.09699u
40
+ ··· + 0.412589u − 1.16966
0.634717u
41
+ 0.515957u
40
+ ··· − 23.4534u + 6.67222
a
9
=
−1.45613u
41
− 1.65616u
40
+ ··· + 6.43111u + 2.36059
−1.31980u
41
− 1.39650u
40
+ ··· + 8.42549u + 3.12293
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0586366u
41
+ 0.331503u
40
+ ··· + 5.71695u − 17.0612
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
42
− 2u
41
+ ··· − 45u − 1
c
2
, c
5
u
42
+ 3u
41
+ ··· + 3244u + 611
c
3
, c
10
u
42
+ u
41
+ ··· − 26u + 7
c
4
, c
8
u
42
− 3u
41
+ ··· + 222u + 79
c
6
, c
7
, c
11
c
12
u
42
− 2u
41
+ ··· + 46u + 11
c
9
u
42
+ u
41
+ ··· − 48u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
42
+ 34y
41
+ ··· − 3015y + 1
c
2
, c
5
y
42
− 29y
41
+ ··· − 6104784y + 373321
c
3
, c
10
y
42
+ 43y
41
+ ··· − 1208y + 49
c
4
, c
8
y
42
− 37y
41
+ ··· − 146770y + 6241
c
6
, c
7
, c
11
c
12
y
42
− 52y
41
+ ··· − 2050y + 121
c
9
y
42
+ 39y
41
+ ··· − 3522y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.221678 + 0.929619I
a = 0.236802 + 0.144006I
b = 0.200628 + 1.379120I
−0.23479 + 3.42452I −7.25006 − 2.36788I
u = 0.221678 − 0.929619I
a = 0.236802 − 0.144006I
b = 0.200628 − 1.379120I
−0.23479 − 3.42452I −7.25006 + 2.36788I
u = 0.834678 + 0.726650I
a = 0.942471 + 1.038720I
b = −0.32235 + 1.47004I
−2.09585 − 8.88492I −8.23343 + 6.33839I
u = 0.834678 − 0.726650I
a = 0.942471 − 1.038720I
b = −0.32235 − 1.47004I
−2.09585 + 8.88492I −8.23343 − 6.33839I
u = 0.839481
a = −0.147245
b = 0.446812
−1.61731 −3.83040
u = −0.649459 + 0.528735I
a = 0.425369 − 0.221209I
b = −0.883358 − 0.331381I
3.71527 + 4.57178I −4.48983 − 6.21438I
u = −0.649459 − 0.528735I
a = 0.425369 + 0.221209I
b = −0.883358 + 0.331381I
3.71527 − 4.57178I −4.48983 + 6.21438I
u = −1.205320 + 0.086480I
a = −0.45359 + 1.35560I
b = 0.093741 + 0.991733I
−4.64795 + 1.97026I −11.59090 − 3.85800I
u = −1.205320 − 0.086480I
a = −0.45359 − 1.35560I
b = 0.093741 − 0.991733I
−4.64795 − 1.97026I −11.59090 + 3.85800I
u = 0.550462 + 0.540915I
a = −1.409400 − 0.043470I
b = 0.125351 − 1.359680I
−6.87451 − 1.88626I −7.91284 + 3.72193I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.550462 − 0.540915I
a = −1.409400 + 0.043470I
b = 0.125351 + 1.359680I
−6.87451 + 1.88626I −7.91284 − 3.72193I
u = −0.560203 + 0.440638I
a = 1.43565 − 1.00821I
b = −0.04993 − 1.58808I
−7.60002 + 1.56574I −5.17924 − 4.63604I
u = −0.560203 − 0.440638I
a = 1.43565 + 1.00821I
b = −0.04993 + 1.58808I
−7.60002 − 1.56574I −5.17924 + 4.63604I
u = −0.334964 + 0.627307I
a = −0.026307 + 1.176530I
b = 0.577071 − 0.144380I
4.67940 − 0.63289I −1.299354 − 0.211342I
u = −0.334964 − 0.627307I
a = −0.026307 − 1.176530I
b = 0.577071 + 0.144380I
4.67940 + 0.63289I −1.299354 + 0.211342I
u = −1.244160 + 0.465780I
a = −0.79090 + 1.18454I
b = −0.025737 + 1.302660I
−4.81553 + 1.49702I 0
u = −1.244160 − 0.465780I
a = −0.79090 − 1.18454I
b = −0.025737 − 1.302660I
−4.81553 − 1.49702I 0
u = 0.595320 + 0.215476I
a = 0.20407 − 3.29680I
b = 0.272977 − 1.203760I
1.45303 − 2.42211I −8.67176 + 3.95905I
u = 0.595320 − 0.215476I
a = 0.20407 + 3.29680I
b = 0.272977 + 1.203760I
1.45303 + 2.42211I −8.67176 − 3.95905I
u = 1.42044 + 0.21754I
a = −0.455901 + 0.764179I
b = −0.205009 + 0.109418I
−0.93890 − 2.37365I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.42044 − 0.21754I
a = −0.455901 − 0.764179I
b = −0.205009 − 0.109418I
−0.93890 + 2.37365I 0
u = 0.509507 + 0.231007I
a = 0.734692 − 0.787767I
b = −0.636452 − 1.034150I
1.69283 + 0.80157I −9.60902 + 2.15996I
u = 0.509507 − 0.231007I
a = 0.734692 + 0.787767I
b = −0.636452 + 1.034150I
1.69283 − 0.80157I −9.60902 − 2.15996I
u = −0.506114
a = −1.86988
b = 0.407424
−2.40722 5.24600
u = −1.56067 + 0.05190I
a = 0.204618 − 1.091020I
b = 0.907751 − 0.996705I
−5.42360 + 0.16996I 0
u = −1.56067 − 0.05190I
a = 0.204618 + 1.091020I
b = 0.907751 + 0.996705I
−5.42360 − 0.16996I 0
u = 1.56797
a = 0.157767
b = −0.854086
−9.60649 0
u = −1.58059 + 0.15570I
a = 0.76812 − 1.50303I
b = −0.36026 − 1.39238I
−14.1195 + 4.4084I 0
u = −1.58059 − 0.15570I
a = 0.76812 + 1.50303I
b = −0.36026 + 1.39238I
−14.1195 − 4.4084I 0
u = 1.58699 + 0.12206I
a = −0.62381 − 2.20399I
b = 0.15580 − 1.70095I
−14.9835 − 3.5968I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.58699 − 0.12206I
a = −0.62381 + 2.20399I
b = 0.15580 + 1.70095I
−14.9835 + 3.5968I 0
u = −1.59898 + 0.06331I
a = −0.27626 − 2.55653I
b = −0.08483 − 1.42792I
−6.19779 + 3.44957I 0
u = −1.59898 − 0.06331I
a = −0.27626 + 2.55653I
b = −0.08483 + 1.42792I
−6.19779 − 3.44957I 0
u = 1.59624 + 0.14855I
a = 0.294078 − 0.648191I
b = 1.115930 − 0.471602I
−3.89460 − 7.04306I 0
u = 1.59624 − 0.14855I
a = 0.294078 + 0.648191I
b = 1.115930 + 0.471602I
−3.89460 + 7.04306I 0
u = 0.230807 + 0.288001I
a = 0.966776 + 0.311482I
b = −0.188196 + 0.489488I
−0.234295 − 0.833962I −5.60412 + 8.29990I
u = 0.230807 − 0.288001I
a = 0.966776 − 0.311482I
b = −0.188196 − 0.489488I
−0.234295 + 0.833962I −5.60412 − 8.29990I
u = −1.66654 + 0.22609I
a = −0.61931 + 1.92291I
b = 0.40841 + 1.58400I
−10.5286 + 12.5719I 0
u = −1.66654 − 0.22609I
a = −0.61931 − 1.92291I
b = 0.40841 − 1.58400I
−10.5286 − 12.5719I 0
u = −1.69539
a = −0.0379052
b = −0.681558
−10.7530 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.75180 + 0.08364I
a = 0.43693 + 1.85011I
b = −0.26084 + 1.40596I
−15.4551 − 3.4434I 0
u = 1.75180 − 0.08364I
a = 0.43693 − 1.85011I
b = −0.26084 − 1.40596I
−15.4551 + 3.4434I 0
9
II. I
u
2
=
hu
7
−5u
5
+7u
3
+b −2u, u
7
−5u
5
+7u
3
−u
2
+a −2u+2, u
12
+u
11
+· · ·−u−1i
(i) Arc colorings
a
7
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
8
=
−u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
−u
7
+ 5u
5
− 7u
3
+ u
2
+ 2u − 2
−u
7
+ 5u
5
− 7u
3
+ 2u
a
6
=
u
u
a
2
=
−u
7
+ 5u
5
− u
4
− 7u
3
+ 3u
2
+ 2u − 2
−u
7
+ 5u
5
− u
4
− 7u
3
+ 2u
2
+ 2u
a
5
=
−u
10
+ 7u
8
− u
7
− 17u
6
+ 5u
5
+ 16u
4
− 8u
3
− 4u
2
+ 5u
−u
10
+ 7u
8
− u
7
− 17u
6
+ 4u
5
+ 16u
4
− 4u
3
− 4u
2
+ u
a
10
=
−u
9
+ 7u
7
− 17u
5
+ 17u
3
− 6u
u
3
− 2u − 1
a
4
=
−u
10
+ 7u
8
− u
7
− 17u
6
+ 6u
5
+ 16u
4
− 11u
3
− 4u
2
+ 6u
−u
10
+ 7u
8
− 17u
6
+ 16u
4
− 4u
2
a
9
=
u
11
− 9u
9
+ 30u
7
− 45u
5
+ 30u
3
− 9u − 1
−u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
11
+ 6u
9
+ u
8
−10u
7
−10u
6
−u
5
+ 29u
4
+ 10u
3
−27u
2
+ u −7
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
12
− u
11
+ 3u
10
+ u
8
+ 3u
7
− 2u
6
− u
5
− u
4
− 4u
3
− u
2
+ 2u + 1
c
2
u
12
+ 2u
11
− u
10
− 4u
9
− u
8
− u
7
− 2u
6
+ 3u
5
+ u
4
+ 3u
2
− u + 1
c
3
u
12
+ 7u
10
+ 19u
8
− u
7
+ 25u
6
− 4u
5
+ 16u
4
− 5u
3
+ 3u
2
− 3u − 1
c
4
u
12
− 2u
11
− u
10
+ 4u
9
− 3u
8
+ 4u
7
− 7u
5
+ 4u
4
− 7u
3
+ 8u
2
+ 3u − 1
c
5
u
12
− 2u
11
− u
10
+ 4u
9
− u
8
+ u
7
− 2u
6
− 3u
5
+ u
4
+ 3u
2
+ u + 1
c
6
, c
7
u
12
− u
11
+ ··· + u − 1
c
8
u
12
+ 2u
11
− u
10
− 4u
9
− 3u
8
− 4u
7
+ 7u
5
+ 4u
4
+ 7u
3
+ 8u
2
− 3u − 1
c
9
u
12
+ 3u
10
− u
9
− 2u
7
− 8u
6
+ 7u
5
− 4u
4
+ 15u
3
+ 4u
2
+ u − 3
c
10
u
12
+ 7u
10
+ 19u
8
+ u
7
+ 25u
6
+ 4u
5
+ 16u
4
+ 5u
3
+ 3u
2
+ 3u − 1
c
11
, c
12
u
12
+ u
11
+ ··· − u − 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
12
+ 5y
11
+ ··· − 6y + 1
c
2
, c
5
y
12
− 6y
11
+ ··· + 5y + 1
c
3
, c
10
y
12
+ 14y
11
+ ··· − 15y + 1
c
4
, c
8
y
12
− 6y
11
+ ··· − 25y + 1
c
6
, c
7
, c
11
c
12
y
12
− 17y
11
+ ··· + 7y + 1
c
9
y
12
+ 6y
11
+ ··· − 25y + 9
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.686882 + 0.356361I
a = −1.57192 − 1.03304I
b = 0.08327 − 1.52260I
−8.42506 − 1.23513I −14.9695 + 0.5232I
u = 0.686882 − 0.356361I
a = −1.57192 + 1.03304I
b = 0.08327 + 1.52260I
−8.42506 + 1.23513I −14.9695 − 0.5232I
u = −0.697854
a = −1.27667
b = 0.236332
−2.77397 −17.7110
u = −1.350010 + 0.165727I
a = 0.122773 + 0.422338I
b = 0.327726 + 0.869804I
−1.87314 + 3.35889I −9.63200 − 3.88261I
u = −1.350010 − 0.165727I
a = 0.122773 − 0.422338I
b = 0.327726 − 0.869804I
−1.87314 − 3.35889I −9.63200 + 3.88261I
u = 1.43456 + 0.19655I
a = 0.38745 + 1.66784I
b = 0.368130 + 1.103920I
−2.74104 − 0.62345I −7.00640 − 0.32990I
u = 1.43456 − 0.19655I
a = 0.38745 − 1.66784I
b = 0.368130 − 1.103920I
−2.74104 + 0.62345I −7.00640 + 0.32990I
u = −0.076876 + 0.352057I
a = −2.49621 + 0.92625I
b = −0.378175 + 0.980375I
2.45499 − 1.46473I −3.28668 + 1.82890I
u = −0.076876 − 0.352057I
a = −2.49621 − 0.92625I
b = −0.378175 − 0.980375I
2.45499 + 1.46473I −3.28668 − 1.82890I
u = 1.67252
a = 0.219784
b = −0.577555
−11.3408 −16.0060
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.68189 + 0.10991I
a = 0.58634 − 1.91439I
b = −0.23034 − 1.54467I
−16.9020 + 3.1092I −14.7470 − 0.9268I
u = −1.68189 − 0.10991I
a = 0.58634 + 1.91439I
b = −0.23034 + 1.54467I
−16.9020 − 3.1092I −14.7470 + 0.9268I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
12
− u
11
+ 3u
10
+ u
8
+ 3u
7
− 2u
6
− u
5
− u
4
− 4u
3
− u
2
+ 2u + 1)
· (u
42
− 2u
41
+ ··· − 45u − 1)
c
2
(u
12
+ 2u
11
− u
10
− 4u
9
− u
8
− u
7
− 2u
6
+ 3u
5
+ u
4
+ 3u
2
− u + 1)
· (u
42
+ 3u
41
+ ··· + 3244u + 611)
c
3
(u
12
+ 7u
10
+ 19u
8
− u
7
+ 25u
6
− 4u
5
+ 16u
4
− 5u
3
+ 3u
2
− 3u − 1)
· (u
42
+ u
41
+ ··· − 26u + 7)
c
4
(u
12
− 2u
11
− u
10
+ 4u
9
− 3u
8
+ 4u
7
− 7u
5
+ 4u
4
− 7u
3
+ 8u
2
+ 3u − 1)
· (u
42
− 3u
41
+ ··· + 222u + 79)
c
5
(u
12
− 2u
11
− u
10
+ 4u
9
− u
8
+ u
7
− 2u
6
− 3u
5
+ u
4
+ 3u
2
+ u + 1)
· (u
42
+ 3u
41
+ ··· + 3244u + 611)
c
6
, c
7
(u
12
− u
11
+ ··· + u − 1)(u
42
− 2u
41
+ ··· + 46u + 11)
c
8
(u
12
+ 2u
11
− u
10
− 4u
9
− 3u
8
− 4u
7
+ 7u
5
+ 4u
4
+ 7u
3
+ 8u
2
− 3u − 1)
· (u
42
− 3u
41
+ ··· + 222u + 79)
c
9
(u
12
+ 3u
10
− u
9
− 2u
7
− 8u
6
+ 7u
5
− 4u
4
+ 15u
3
+ 4u
2
+ u − 3)
· (u
42
+ u
41
+ ··· − 48u + 1)
c
10
(u
12
+ 7u
10
+ 19u
8
+ u
7
+ 25u
6
+ 4u
5
+ 16u
4
+ 5u
3
+ 3u
2
+ 3u − 1)
· (u
42
+ u
41
+ ··· − 26u + 7)
c
11
, c
12
(u
12
+ u
11
+ ··· − u − 1)(u
42
− 2u
41
+ ··· + 46u + 11)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
12
+ 5y
11
+ ··· − 6y + 1)(y
42
+ 34y
41
+ ··· − 3015y + 1)
c
2
, c
5
(y
12
− 6y
11
+ ··· + 5y + 1)(y
42
− 29y
41
+ ··· − 6104784y + 373321)
c
3
, c
10
(y
12
+ 14y
11
+ ··· − 15y + 1)(y
42
+ 43y
41
+ ··· − 1208y + 49)
c
4
, c
8
(y
12
− 6y
11
+ ··· − 25y + 1)(y
42
− 37y
41
+ ··· − 146770y + 6241)
c
6
, c
7
, c
11
c
12
(y
12
− 17y
11
+ ··· + 7y + 1)(y
42
− 52y
41
+ ··· − 2050y + 121)
c
9
(y
12
+ 6y
11
+ ··· − 25y + 9)(y
42
+ 39y
41
+ ··· − 3522y + 1)
16
