12n
0164
(K12n
0164
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 9 11 10 3 1 12 7 6
Solving Sequence
6,11
7 12 1 10 8
3,9
4 5 2
c
6
c
11
c
12
c
10
c
7
c
9
c
3
c
5
c
2
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
50
− u
49
+ ··· − 4u
2
+ b, −3u
50
− 3u
49
+ ··· + a + 4, u
51
+ 2u
50
+ ··· + 6u
2
− 1i
I
u
2
= hb + 1, u
7
− 2u
5
+ u
4
+ 2u
3
− u
2
+ a + u, u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 60 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−u
50
−u
49
+· · ·−4u
2
+b, −3u
50
−3u
49
+· · ·+a+4, u
51
+2u
50
+· · ·+6u
2
−1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
12
=
u
−u
3
+ u
a
1
=
u
3
−u
3
+ u
a
10
=
−u
3
u
5
− u
3
+ u
a
8
=
u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
3
=
3u
50
+ 3u
49
+ ··· + 15u
2
− 4
u
50
+ u
49
+ ··· + 5u
3
+ 4u
2
a
9
=
−u
11
+ 2u
9
− 2u
7
− u
3
u
11
− 3u
9
+ 4u
7
− u
5
− u
3
+ u
a
4
=
5u
50
+ 5u
49
+ ··· + 22u
2
− 5
u
50
+ u
49
+ ··· + 5u
2
− u
a
5
=
−u
22
+ 5u
20
− 12u
18
+ 15u
16
− 10u
14
+ 2u
12
− u
8
+ u
6
− u
4
+ 1
u
22
− 6u
20
+ 17u
18
− 26u
16
+ 20u
14
− 13u
10
+ 10u
8
− u
6
− 2u
4
+ u
2
a
2
=
2u
50
+ 2u
49
+ ··· + u − 3
u
50
+ u
49
+ ··· + 2u
2
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −10u
50
− 13u
49
+ ··· − 22u + 5
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
51
+ 12u
50
+ ··· + 8u + 1
c
2
, c
4
u
51
− 10u
50
+ ··· − 8u + 1
c
3
, c
8
u
51
+ u
50
+ ··· + 512u + 512
c
5
u
51
− 2u
50
+ ··· + 2u + 1
c
6
, c
11
u
51
− 2u
50
+ ··· − 6u
2
+ 1
c
7
, c
12
u
51
− 6u
50
+ ··· − 64u + 5
c
9
u
51
+ 8u
50
+ ··· + 20174u − 565
c
10
u
51
− 28u
50
+ ··· + 12u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
51
+ 64y
50
+ ··· + 108y −1
c
2
, c
4
y
51
− 12y
50
+ ··· + 8y −1
c
3
, c
8
y
51
+ 57y
50
+ ··· − 4194304y −262144
c
5
y
51
− 60y
50
+ ··· + 12y −1
c
6
, c
11
y
51
− 28y
50
+ ··· + 12y −1
c
7
, c
12
y
51
+ 44y
50
+ ··· + 1176y −25
c
9
y
51
− 24y
50
+ ··· + 384067096y −319225
c
10
y
51
− 8y
50
+ ··· + 72y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.870347 + 0.438821I
a = 0.015315 + 0.902084I
b = 0.136807 − 0.606788I
−0.59383 + 3.47183I −2.57465 − 7.94209I
u = 0.870347 − 0.438821I
a = 0.015315 − 0.902084I
b = 0.136807 + 0.606788I
−0.59383 − 3.47183I −2.57465 + 7.94209I
u = 0.769432 + 0.540134I
a = −0.334413 + 0.181071I
b = 0.262412 − 0.045879I
−2.41085 + 2.18056I −0.89273 − 4.14337I
u = 0.769432 − 0.540134I
a = −0.334413 − 0.181071I
b = 0.262412 + 0.045879I
−2.41085 − 2.18056I −0.89273 + 4.14337I
u = −0.918255 + 0.555689I
a = 2.35354 − 0.32507I
b = 0.33439 + 1.82533I
4.75622 − 8.70313I −1.30654 + 7.99573I
u = −0.918255 − 0.555689I
a = 2.35354 + 0.32507I
b = 0.33439 − 1.82533I
4.75622 + 8.70313I −1.30654 − 7.99573I
u = −0.961040 + 0.526565I
a = −2.26543 + 0.37900I
b = −0.19641 − 1.57019I
5.41584 − 1.98677I 0. + 3.17688I
u = −0.961040 − 0.526565I
a = −2.26543 − 0.37900I
b = −0.19641 + 1.57019I
5.41584 + 1.98677I 0. − 3.17688I
u = −0.892007 + 0.102900I
a = −0.782404 + 0.397432I
b = −0.1264520 − 0.0345198I
1.50518 − 0.26567I 6.00026 + 0.27915I
u = −0.892007 − 0.102900I
a = −0.782404 − 0.397432I
b = −0.1264520 + 0.0345198I
1.50518 + 0.26567I 6.00026 − 0.27915I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.103930 + 0.029028I
a = 0.03014 + 2.74289I
b = 0.00205 − 1.91806I
8.92371 + 3.58327I 4.99152 − 2.55707I
u = 1.103930 − 0.029028I
a = 0.03014 − 2.74289I
b = 0.00205 + 1.91806I
8.92371 − 3.58327I 4.99152 + 2.55707I
u = −0.784529 + 0.412156I
a = 1.58952 − 1.83215I
b = 1.41941 + 0.12823I
−2.37641 − 1.79904I −1.57784 + 3.21479I
u = −0.784529 − 0.412156I
a = 1.58952 + 1.83215I
b = 1.41941 − 0.12823I
−2.37641 + 1.79904I −1.57784 − 3.21479I
u = −0.128537 + 0.840120I
a = 1.129030 + 0.709012I
b = 0.40430 − 2.07036I
8.84070 + 9.07061I −0.40037 − 4.94351I
u = −0.128537 − 0.840120I
a = 1.129030 − 0.709012I
b = 0.40430 + 2.07036I
8.84070 − 9.07061I −0.40037 + 4.94351I
u = −0.098639 + 0.843425I
a = −0.991418 − 0.802908I
b = −0.49696 + 1.82819I
9.77996 + 1.74437I 0.869817 − 0.468289I
u = −0.098639 − 0.843425I
a = −0.991418 + 0.802908I
b = −0.49696 − 1.82819I
9.77996 − 1.74437I 0.869817 + 0.468289I
u = −0.562511 + 0.604780I
a = −0.207632 − 1.106740I
b = 0.22739 − 1.74075I
3.75359 + 4.13544I −3.29521 − 2.12817I
u = −0.562511 − 0.604780I
a = −0.207632 + 1.106740I
b = 0.22739 + 1.74075I
3.75359 − 4.13544I −3.29521 + 2.12817I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.071264 + 0.783310I
a = −0.318627 − 0.574074I
b = −0.332760 + 0.593277I
2.40985 − 2.75947I 0.20281 + 3.78069I
u = 0.071264 − 0.783310I
a = −0.318627 + 0.574074I
b = −0.332760 − 0.593277I
2.40985 + 2.75947I 0.20281 − 3.78069I
u = −1.159840 + 0.371143I
a = −0.819557 + 0.084078I
b = 0.146793 − 0.318351I
3.81880 − 0.72340I 0
u = −1.159840 − 0.371143I
a = −0.819557 − 0.084078I
b = 0.146793 + 0.318351I
3.81880 + 0.72340I 0
u = −0.481732 + 0.609553I
a = −0.101202 + 0.987549I
b = −0.01229 + 1.62632I
4.06039 − 2.47774I −2.81595 + 2.59394I
u = −0.481732 − 0.609553I
a = −0.101202 − 0.987549I
b = −0.01229 − 1.62632I
4.06039 + 2.47774I −2.81595 − 2.59394I
u = 0.173693 + 0.738661I
a = −0.367593 + 0.052677I
b = 0.234475 + 0.228624I
−0.01361 − 2.88077I 0.72874 + 4.09182I
u = 0.173693 − 0.738661I
a = −0.367593 − 0.052677I
b = 0.234475 − 0.228624I
−0.01361 + 2.88077I 0.72874 − 4.09182I
u = 1.182480 + 0.442140I
a = −1.75563 − 0.72377I
b = 1.24222 + 0.73561I
3.09283 + 3.04460I 0
u = 1.182480 − 0.442140I
a = −1.75563 + 0.72377I
b = 1.24222 − 0.73561I
3.09283 − 3.04460I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.654402 + 0.333690I
a = −1.061450 − 0.491092I
b = 0.509880 + 0.457534I
−1.277320 + 0.104972I −6.49712 − 0.81478I
u = 0.654402 − 0.333690I
a = −1.061450 + 0.491092I
b = 0.509880 − 0.457534I
−1.277320 − 0.104972I −6.49712 + 0.81478I
u = 1.164800 + 0.508279I
a = −0.311275 + 0.409745I
b = 0.287422 − 0.271809I
2.86161 + 7.55446I 0
u = 1.164800 − 0.508279I
a = −0.311275 − 0.409745I
b = 0.287422 + 0.271809I
2.86161 − 7.55446I 0
u = −1.183710 + 0.466863I
a = −0.43063 − 2.86734I
b = 1.42604 + 0.63435I
2.91319 − 5.51229I 0
u = −1.183710 − 0.466863I
a = −0.43063 + 2.86734I
b = 1.42604 − 0.63435I
2.91319 + 5.51229I 0
u = −0.040008 + 0.724234I
a = 0.167745 + 1.283370I
b = 1.29438 − 0.57599I
−0.344586 + 1.125350I −2.18776 + 0.36560I
u = −0.040008 − 0.724234I
a = 0.167745 − 1.283370I
b = 1.29438 + 0.57599I
−0.344586 − 1.125350I −2.18776 − 0.36560I
u = −1.205000 + 0.421939I
a = −0.336159 + 1.363990I
b = −0.446127 − 0.523396I
6.14415 − 1.44415I 0
u = −1.205000 − 0.421939I
a = −0.336159 − 1.363990I
b = −0.446127 + 0.523396I
6.14415 + 1.44415I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.199230 + 0.483275I
a = 0.623123 + 0.813683I
b = −0.381068 − 0.691428I
5.70689 + 7.38464I 0
u = 1.199230 − 0.483275I
a = 0.623123 − 0.813683I
b = −0.381068 + 0.691428I
5.70689 − 7.38464I 0
u = 1.236290 + 0.382809I
a = −0.78559 − 2.71496I
b = 0.35139 + 2.12412I
13.00930 − 4.90240I 0
u = 1.236290 − 0.382809I
a = −0.78559 + 2.71496I
b = 0.35139 − 2.12412I
13.00930 + 4.90240I 0
u = 1.238740 + 0.402230I
a = 0.91998 + 2.41477I
b = −0.47327 − 1.91914I
13.84570 + 2.55616I 0
u = 1.238740 − 0.402230I
a = 0.91998 − 2.41477I
b = −0.47327 + 1.91914I
13.84570 − 2.55616I 0
u = −1.209920 + 0.515926I
a = 2.42150 − 2.66691I
b = 0.45186 + 2.09789I
12.0604 − 14.0151I 0
u = −1.209920 − 0.515926I
a = 2.42150 + 2.66691I
b = 0.45186 − 2.09789I
12.0604 + 14.0151I 0
u = −1.217650 + 0.504060I
a = −1.94270 + 2.65801I
b = −0.57244 − 1.82873I
13.1170 − 6.6351I 0
u = −1.217650 − 0.504060I
a = −1.94270 − 2.65801I
b = −0.57244 + 1.82873I
13.1170 + 6.6351I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.357516
a = −1.87639
b = 0.613111
−1.12692 −9.48630
10
II. I
u
2
=
hb+1, u
7
−2u
5
+u
4
+2u
3
−u
2
+a+u, u
9
−u
8
−2u
7
+3u
6
+u
5
−3u
4
+2u
3
−u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u
2
a
12
=
u
−u
3
+ u
a
1
=
u
3
−u
3
+ u
a
10
=
−u
3
u
5
− u
3
+ u
a
8
=
u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
3
=
−u
7
+ 2u
5
− u
4
− 2u
3
+ u
2
− u
−1
a
9
=
u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
4
=
−u
7
+ 2u
5
− u
4
− 2u
3
+ u
2
− u
−1
a
5
=
−u
3
u
3
− u
a
2
=
−u
7
+ 2u
5
− u
4
− u
3
+ u
2
− u
−u
3
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
8
− 6u
7
− u
6
+ 12u
5
− 5u
4
− 10u
3
+ 7u
2
− 7u − 6
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
9
c
3
, c
8
u
9
c
4
(u + 1)
9
c
5
, c
9
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
6
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
7
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
10
u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1
c
11
u
9
+ u
8
− 2u
7
− 3u
6
+ u
5
+ 3u
4
+ 2u
3
− u − 1
c
12
u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
9
c
3
, c
8
y
9
c
5
, c
9
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
6
, c
11
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
7
, c
12
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
10
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.772920 + 0.510351I
a = −0.628748 − 1.040710I
b = −1.00000
−3.42837 + 2.09337I −10.43453 − 4.18932I
u = 0.772920 − 0.510351I
a = −0.628748 + 1.040710I
b = −1.00000
−3.42837 − 2.09337I −10.43453 + 4.18932I
u = −0.825933
a = 1.66309
b = −1.00000
−0.446489 4.72420
u = −1.173910 + 0.391555I
a = 1.321020 + 0.175437I
b = −1.00000
2.72642 − 1.33617I −0.549708 + 1.017936I
u = −1.173910 − 0.391555I
a = 1.321020 − 0.175437I
b = −1.00000
2.72642 + 1.33617I −0.549708 − 1.017936I
u = 0.141484 + 0.739668I
a = 0.081981 + 0.728244I
b = −1.00000
−1.02799 − 2.45442I −6.31821 + 2.62939I
u = 0.141484 − 0.739668I
a = 0.081981 − 0.728244I
b = −1.00000
−1.02799 + 2.45442I −6.31821 − 2.62939I
u = 1.172470 + 0.500383I
a = 0.89420 − 1.47834I
b = −1.00000
1.95319 + 7.08493I −3.05967 − 5.11095I
u = 1.172470 − 0.500383I
a = 0.89420 + 1.47834I
b = −1.00000
1.95319 − 7.08493I −3.05967 + 5.11095I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
51
+ 12u
50
+ ··· + 8u + 1)
c
2
((u − 1)
9
)(u
51
− 10u
50
+ ··· − 8u + 1)
c
3
, c
8
u
9
(u
51
+ u
50
+ ··· + 512u + 512)
c
4
((u + 1)
9
)(u
51
− 10u
50
+ ··· − 8u + 1)
c
5
(u
9
− u
8
+ ··· + u + 1)(u
51
− 2u
50
+ ··· + 2u + 1)
c
6
(u
9
− u
8
+ ··· − u + 1)(u
51
− 2u
50
+ ··· − 6u
2
+ 1)
c
7
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
51
− 6u
50
+ ··· − 64u + 5)
c
9
(u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1)
· (u
51
+ 8u
50
+ ··· + 20174u − 565)
c
10
(u
9
+ 5u
8
+ 12u
7
+ 15u
6
+ 9u
5
− u
4
− 4u
3
− 2u
2
+ u + 1)
· (u
51
− 28u
50
+ ··· + 12u − 1)
c
11
(u
9
+ u
8
+ ··· − u − 1)(u
51
− 2u
50
+ ··· − 6u
2
+ 1)
c
12
(u
9
+ 3u
8
+ 8u
7
+ 13u
6
+ 17u
5
+ 17u
4
+ 12u
3
+ 6u
2
+ u − 1)
· (u
51
− 6u
50
+ ··· − 64u + 5)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
51
+ 64y
50
+ ··· + 108y −1)
c
2
, c
4
((y −1)
9
)(y
51
− 12y
50
+ ··· + 8y −1)
c
3
, c
8
y
9
(y
51
+ 57y
50
+ ··· − 4194304y −262144)
c
5
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
51
− 60y
50
+ ··· + 12y −1)
c
6
, c
11
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
51
− 28y
50
+ ··· + 12y −1)
c
7
, c
12
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
51
+ 44y
50
+ ··· + 1176y −25)
c
9
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
51
− 24y
50
+ ··· + 384067096y −319225)
c
10
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
51
− 8y
50
+ ··· + 72y −1)
16
