12n
0191
(K12n
0191
)
A knot diagram
1
Linearized knot diagam
3 5 7 2 10 11 3 12 1 6 7 9
Solving Sequence
6,10
11
3,7
8 12 5 2 1 4 9
c
10
c
6
c
7
c
11
c
5
c
2
c
1
c
4
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h2.93013 × 10
22
u
41
− 2.55618 × 10
22
u
40
+ ··· + 3.19018 × 10
22
b + 3.37541 × 10
22
,
3.37341 × 10
22
u
41
− 5.52290 × 10
22
u
40
+ ··· + 3.19018 × 10
22
a − 5.34100 × 10
22
, u
42
− 2u
41
+ ··· + 9u
2
− 1i
I
u
2
= hb − 1, −u
2
+ a − u + 1, u
3
+ u
2
− 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 45 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
=
h2.93×10
22
u
41
−2.56×10
22
u
40
+· · ·+3.19×10
22
b+3.38×10
22
, 3.37×10
22
u
41
−
5.52 × 10
22
u
40
+ · · · + 3.19 × 10
22
a − 5.34 × 10
22
, u
42
− 2u
41
+ · · · + 9u
2
− 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
3
=
−1.05743u
41
+ 1.73122u
40
+ ··· + 2.10719u + 1.67420
−0.918482u
41
+ 0.801265u
40
+ ··· − 1.32965u − 1.05806
a
7
=
−u
−u
3
+ u
a
8
=
−0.468740u
41
+ 1.75288u
40
+ ··· − 2.79645u + 2.00796
0.403032u
41
− 0.477459u
40
+ ··· − 0.178275u − 0.123472
a
12
=
−u
2
+ 1
−u
4
+ 2u
2
a
5
=
u
u
a
2
=
−0.944557u
41
+ 1.20115u
40
+ ··· + 2.24614u + 1.02215
−0.805605u
41
+ 0.271202u
40
+ ··· − 1.19070u − 1.71011
a
1
=
0.557571u
41
− 2.03034u
40
+ ··· + 3.30377u − 2.22423
0.0502449u
41
− 0.799422u
40
+ ··· + 0.797791u − 1.15514
a
4
=
−1.10864u
41
+ 1.93014u
40
+ ··· + 1.65865u + 1.89346
−0.771455u
41
+ 0.605910u
40
+ ··· − 0.932314u − 1.18080
a
9
=
−1.09560u
41
+ 2.57105u
40
+ ··· − 3.54399u + 2.46417
0.00573169u
41
+ 0.199584u
40
+ ··· − 0.855377u + 0.139917
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
14504839839598429454722
31901842262824074426539
u
41
+
28913484959271594911639
31901842262824074426539
u
40
+ ··· +
572906090932607375763123
31901842262824074426539
u −
222969079138844677276793
31901842262824074426539
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
42
+ 20u
41
+ ··· + 439u + 1
c
2
, c
4
u
42
− 4u
41
+ ··· + 31u − 1
c
3
, c
7
u
42
− 3u
41
+ ··· + 4u + 8
c
5
, c
6
, c
10
c
11
u
42
− 2u
41
+ ··· + 9u
2
− 1
c
8
, c
9
, c
12
u
42
+ 2u
41
+ ··· + 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
42
+ 8y
41
+ ··· − 130935y + 1
c
2
, c
4
y
42
− 20y
41
+ ··· − 439y + 1
c
3
, c
7
y
42
− 21y
41
+ ··· − 4304y + 64
c
5
, c
6
, c
10
c
11
y
42
− 46y
41
+ ··· − 18y + 1
c
8
, c
9
, c
12
y
42
− 34y
41
+ ··· − 18y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.622716 + 0.726936I
a = 0.249920 − 0.575224I
b = −1.08189 − 1.07126I
−1.64578 + 10.08720I −11.9616 − 7.8917I
u = −0.622716 − 0.726936I
a = 0.249920 + 0.575224I
b = −1.08189 + 1.07126I
−1.64578 − 10.08720I −11.9616 + 7.8917I
u = 0.630110 + 0.667113I
a = −0.067316 − 0.527398I
b = 1.195850 − 0.754840I
3.26280 − 5.05879I −7.66762 + 6.22497I
u = 0.630110 − 0.667113I
a = −0.067316 + 0.527398I
b = 1.195850 + 0.754840I
3.26280 + 5.05879I −7.66762 − 6.22497I
u = −0.410576 + 0.797115I
a = 0.590560 + 0.729454I
b = 0.654792 − 0.588986I
−1.01128 − 5.04828I −10.54510 + 3.70923I
u = −0.410576 − 0.797115I
a = 0.590560 − 0.729454I
b = 0.654792 + 0.588986I
−1.01128 + 5.04828I −10.54510 − 3.70923I
u = −0.613330 + 0.550269I
a = −0.152550 − 0.404189I
b = −1.211510 − 0.276966I
0.340193 − 0.146534I −9.04090 − 2.32576I
u = −0.613330 − 0.550269I
a = −0.152550 + 0.404189I
b = −1.211510 + 0.276966I
0.340193 + 0.146534I −9.04090 + 2.32576I
u = 0.384114 + 0.702008I
a = −0.371736 + 1.039810I
b = −0.789326 − 0.194769I
3.99048 + 0.46078I −5.35173 − 0.25994I
u = 0.384114 − 0.702008I
a = −0.371736 − 1.039810I
b = −0.789326 + 0.194769I
3.99048 − 0.46078I −5.35173 + 0.25994I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.418033 + 0.606743I
a = 0.084600 + 1.400980I
b = 0.934140 + 0.238589I
0.90530 + 4.12360I −8.68102 − 5.50502I
u = −0.418033 − 0.606743I
a = 0.084600 − 1.400980I
b = 0.934140 − 0.238589I
0.90530 − 4.12360I −8.68102 + 5.50502I
u = 1.36749
a = 0.995996
b = 1.03484
−6.50001 −13.6470
u = 0.505963 + 0.303182I
a = 1.89815 + 1.24925I
b = −0.202771 + 1.082850I
−4.34422 − 3.06091I −15.9828 + 7.3630I
u = 0.505963 − 0.303182I
a = 1.89815 − 1.24925I
b = −0.202771 − 1.082850I
−4.34422 + 3.06091I −15.9828 − 7.3630I
u = 1.38819 + 0.34209I
a = −0.381252 + 0.184770I
b = 0.108566 − 0.214622I
−6.74773 + 0.95826I 0
u = 1.38819 − 0.34209I
a = −0.381252 − 0.184770I
b = 0.108566 + 0.214622I
−6.74773 − 0.95826I 0
u = −1.43233
a = 10.9436
b = 11.6572
−8.26088 77.1970
u = −0.561117
a = −2.94490
b = −0.320377
−5.90144 −19.1780
u = −1.44186 + 0.20173I
a = 0.423668 + 1.035100I
b = 0.236187 + 0.379056I
−1.83573 + 2.73592I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44186 − 0.20173I
a = 0.423668 − 1.035100I
b = 0.236187 − 0.379056I
−1.83573 − 2.73592I 0
u = −1.47192
a = 1.74936
b = 2.58881
−8.07301 0
u = 1.47089 + 0.06692I
a = 0.12566 + 2.06315I
b = −0.51913 + 1.71572I
−6.78843 − 2.26447I 0
u = 1.47089 − 0.06692I
a = 0.12566 − 2.06315I
b = −0.51913 − 1.71572I
−6.78843 + 2.26447I 0
u = 1.48233 + 0.17827I
a = −0.54943 + 1.55713I
b = −0.523659 + 0.673391I
−5.29803 − 6.90242I 0
u = 1.48233 − 0.17827I
a = −0.54943 − 1.55713I
b = −0.523659 − 0.673391I
−5.29803 + 6.90242I 0
u = −1.51313 + 0.07664I
a = −0.40049 + 1.89572I
b = 0.471789 + 1.251810I
−11.04660 + 4.37109I 0
u = −1.51313 − 0.07664I
a = −0.40049 − 1.89572I
b = 0.471789 − 1.251810I
−11.04660 − 4.37109I 0
u = 1.52457
a = 0.592680
b = −0.635110
−12.8376 0
u = −0.349126 + 0.309363I
a = −1.252420 + 0.444201I
b = 0.207903 + 0.938910I
−0.798095 + 1.043220I −8.93837 − 6.28488I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.349126 − 0.309363I
a = −1.252420 − 0.444201I
b = 0.207903 − 0.938910I
−0.798095 − 1.043220I −8.93837 + 6.28488I
u = −0.464350
a = −0.268787
b = −0.520788
−0.827896 −11.7750
u = 1.57075 + 0.24415I
a = 0.42013 − 1.89705I
b = 1.31507 − 1.60521I
−8.8765 − 13.6938I 0
u = 1.57075 − 0.24415I
a = 0.42013 + 1.89705I
b = 1.31507 + 1.60521I
−8.8765 + 13.6938I 0
u = 0.175152 + 0.368374I
a = 0.719520 − 0.426879I
b = 0.25392 + 1.93248I
−3.37453 + 0.76491I −10.40964 + 7.93136I
u = 0.175152 − 0.368374I
a = 0.719520 + 0.426879I
b = 0.25392 − 1.93248I
−3.37453 − 0.76491I −10.40964 − 7.93136I
u = −1.57812 + 0.22378I
a = −0.70680 − 1.63267I
b = −1.47281 − 1.33651I
−4.07471 + 8.38744I 0
u = −1.57812 − 0.22378I
a = −0.70680 + 1.63267I
b = −1.47281 + 1.33651I
−4.07471 − 8.38744I 0
u = 1.60757 + 0.18431I
a = 0.894775 − 1.082450I
b = 1.49803 − 0.87021I
−7.24321 − 2.57720I 0
u = 1.60757 − 0.18431I
a = 0.894775 + 1.082450I
b = 1.49803 + 0.87021I
−7.24321 + 2.57720I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.321929
a = 2.42803
b = −0.909883
−2.06972 3.71630
u = −1.82062
a = −0.545929
b = −1.04503
−19.0753 0
9
II. I
u
2
= hb − 1, −u
2
+ a − u + 1, u
3
+ u
2
− 2u − 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
3
=
u
2
+ u − 1
1
a
7
=
−u
u
2
− u − 1
a
8
=
−u
u
2
− u − 1
a
12
=
−u
2
+ 1
−u
2
+ u + 1
a
5
=
u
u
a
2
=
u
2
− 1
−u + 1
a
1
=
−u
−u
a
4
=
u
2
+ u − 1
1
a
9
=
−u
2
+ 1
−u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
2
+ 4u − 24
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
7
u
3
c
4
(u + 1)
3
c
5
, c
6
, c
8
c
9
u
3
− u
2
− 2u + 1
c
10
, c
11
, c
12
u
3
+ u
2
− 2u − 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
3
c
3
, c
7
y
3
c
5
, c
6
, c
8
c
9
, c
10
, c
11
c
12
y
3
− 5y
2
+ 6y − 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.24698
a = 1.80194
b = 1.00000
−7.98968 −20.5670
u = −0.445042
a = −1.24698
b = 1.00000
−2.34991 −25.9780
u = −1.80194
a = 0.445042
b = 1.00000
−19.2692 −34.4550
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
42
+ 20u
41
+ ··· + 439u + 1)
c
2
((u − 1)
3
)(u
42
− 4u
41
+ ··· + 31u − 1)
c
3
, c
7
u
3
(u
42
− 3u
41
+ ··· + 4u + 8)
c
4
((u + 1)
3
)(u
42
− 4u
41
+ ··· + 31u − 1)
c
5
, c
6
(u
3
− u
2
− 2u + 1)(u
42
− 2u
41
+ ··· + 9u
2
− 1)
c
8
, c
9
(u
3
− u
2
− 2u + 1)(u
42
+ 2u
41
+ ··· + 4u + 1)
c
10
, c
11
(u
3
+ u
2
− 2u − 1)(u
42
− 2u
41
+ ··· + 9u
2
− 1)
c
12
(u
3
+ u
2
− 2u − 1)(u
42
+ 2u
41
+ ··· + 4u + 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
3
)(y
42
+ 8y
41
+ ··· − 130935y + 1)
c
2
, c
4
((y − 1)
3
)(y
42
− 20y
41
+ ··· − 439y + 1)
c
3
, c
7
y
3
(y
42
− 21y
41
+ ··· − 4304y + 64)
c
5
, c
6
, c
10
c
11
(y
3
− 5y
2
+ 6y − 1)(y
42
− 46y
41
+ ··· − 18y + 1)
c
8
, c
9
, c
12
(y
3
− 5y
2
+ 6y − 1)(y
42
− 34y
41
+ ··· − 18y + 1)
15
