12n
0229
(K12n
0229
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 11 9 3 6 7 12 5 10
Solving Sequence
3,8 4,5,11
6 9 12 2 1 7 10
c
3
c
5
c
8
c
11
c
2
c
1
c
7
c
10
c
4
, c
6
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h4.74944 × 10
17
u
17
+ 1.40015 × 10
18
u
16
+ ··· + 6.24112 × 10
19
d − 1.05622 × 10
18
,
− 6.60139 × 10
16
u
17
− 1.14793 × 10
18
u
16
+ ··· + 1.24822 × 10
20
c + 5.64891 × 10
19
,
− 5.68457 × 10
17
u
17
− 8.64985 × 10
17
u
16
+ ··· + 1.24822 × 10
20
b − 1.55459 × 10
19
,
2.99690 × 10
17
u
17
+ 2.72458 × 10
17
u
16
+ ··· + 2.49645 × 10
20
a − 2.46906 × 10
20
, u
18
+ 3u
17
+ ··· + 32u + 32i
I
u
2
= h6226u
9
a + 7765u
9
+ ··· − 39596a − 22790, 19798u
9
a + 1477u
9
+ ··· − 86484a − 5134,
1447u
9
a + 65u
9
+ ··· − 7346a − 3206, −22391u
9
a + 7563u
9
+ ··· + 121770a − 50482,
u
10
− u
9
− 7u
8
+ 8u
7
+ 13u
6
− 14u
5
− 2u
4
− 2u
3
+ 13u
2
− 12u + 4i
I
v
1
= hc, d + v, b, a − 1, v
2
− v + 1i
I
v
2
= ha, d + v, av + c − v + 1, b − 1, v
2
− v + 1i
I
v
3
= ha, d + 1, c + a, b − 1, v + 1i
I
v
4
= ha, d
2
a − d
2
v − dc + dv + d − v − 1, d
2
v
2
− v
2
d − dv + v
2
+ 2v + 1,
dca − dcv − da + dv − c
2
+ cv − av + 2c − a − 1, v
2
dc − v
2
d − v
2
c + v
2
a − cv + 2av + a,
dav + da − dv − cv − c + v + 1, c
2
v
2
− v
2
ca + a
2
v
2
− cav − v
2
c + 2a
2
v − v
2
a + a
2
− av + v
2
, b − 1i
* 5 irreducible components of dim
C
= 0, with total 43 representations.
* 1 irreducible components of dim
C
= 1
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
= h4.75×10
17
u
17
+1.40×10
18
u
16
+· · ·+6.24×10
19
d−1.06×10
18
, −6.60×
10
16
u
17
− 1.15 × 10
18
u
16
+ · · · + 1.25 × 10
20
c + 5.65 × 10
19
, −5.68 ×
10
17
u
17
− 8.65 × 10
17
u
16
+ · · · + 1.25 × 10
20
b − 1.55 × 10
19
, 3.00 × 10
17
u
17
+
2.72 × 10
17
u
16
+ · · · + 2.50 × 10
20
a − 2.47 × 10
20
, u
18
+ 3u
17
+ · · · + 32u + 32i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
5
=
−0.00120047u
17
− 0.00109138u
16
+ ··· − 0.0893825u + 0.989028
0.00455413u
17
+ 0.00692973u
16
+ ··· + 0.245124u + 0.124544
a
11
=
0.000528863u
17
+ 0.00919651u
16
+ ··· + 0.525376u − 0.452556
−0.00760992u
17
− 0.0224344u
16
+ ··· + 0.469479u + 0.0169236
a
6
=
−0.00389201u
17
− 0.00712189u
16
+ ··· + 1.21746u + 0.120580
0.00251002u
17
+ 0.00451441u
16
+ ··· + 1.02744u + 0.0384150
a
9
=
0.00640203u
17
+ 0.0116363u
16
+ ··· − 0.190018u − 0.0821645
0.00251002u
17
+ 0.00451441u
16
+ ··· + 1.02744u + 0.0384150
a
12
=
0.0117438u
17
+ 0.0288644u
16
+ ··· − 0.134994u − 0.795004
0.00684312u
17
+ 0.0134766u
16
+ ··· + 0.331617u + 0.354667
a
2
=
−0.00120047u
17
− 0.00109138u
16
+ ··· − 0.0893825u + 0.989028
−0.00756978u
17
− 0.0124143u
16
+ ··· − 0.287029u − 0.204865
a
1
=
−0.00877025u
17
− 0.0135056u
16
+ ··· − 0.376412u + 0.784163
−0.00756978u
17
− 0.0124143u
16
+ ··· − 0.287029u − 0.204865
a
7
=
u
u
a
10
=
0.0131347u
17
+ 0.0229449u
16
+ ··· − 0.168830u + 0.0635675
0.00924267u
17
+ 0.0158230u
16
+ ··· + 1.04863u + 0.184147
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1881106086253954753
31205580083057755580
u
17
−
5887773742508132609
62411160166115511160
u
16
+ ··· −
57261478582730965292
7801395020764438895
u −
64355080374530213256
7801395020764438895
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
+ 29u
17
+ ··· + 26u + 1
c
2
, c
4
, c
6
c
8
, c
9
u
18
− 5u
17
+ ··· + 2u − 1
c
3
, c
7
u
18
− 3u
17
+ ··· − 32u + 32
c
5
, c
11
u
18
− u
17
+ ··· + 12u + 4
c
10
, c
12
u
18
− 5u
17
+ ··· + 136u + 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 69y
17
+ ··· − 166y + 1
c
2
, c
4
, c
6
c
8
, c
9
y
18
− 29y
17
+ ··· − 26y + 1
c
3
, c
7
y
18
− 15y
17
+ ··· − 2048y + 1024
c
5
, c
11
y
18
+ 5y
17
+ ··· − 136y + 16
c
10
, c
12
y
18
+ 17y
17
+ ··· − 38944y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.078440 + 0.216619I
a = 0.492205 − 0.156710I
b = 0.844681 + 0.587317I
c = 1.077070 − 0.430910I
d = 1.068210 − 0.698024I
−3.61986 − 3.92600I −13.3379 + 5.7849I
u = −1.078440 − 0.216619I
a = 0.492205 + 0.156710I
b = 0.844681 − 0.587317I
c = 1.077070 + 0.430910I
d = 1.068210 + 0.698024I
−3.61986 + 3.92600I −13.3379 − 5.7849I
u = 0.709201 + 0.274453I
a = 0.515734 + 0.082365I
b = 0.890761 − 0.301961I
c = 0.436964 + 0.773316I
d = −0.097657 − 0.668363I
−3.12578 − 1.29944I −14.10514 + 0.79844I
u = 0.709201 − 0.274453I
a = 0.515734 − 0.082365I
b = 0.890761 + 0.301961I
c = 0.436964 − 0.773316I
d = −0.097657 + 0.668363I
−3.12578 + 1.29944I −14.10514 − 0.79844I
u = −0.610909 + 0.417338I
a = 0.768504 + 0.302779I
b = 0.126387 − 0.443779I
c = −0.48208 − 1.41304I
d = −0.884219 − 0.662050I
1.20916 + 1.63680I −1.95124 − 5.83411I
u = −0.610909 − 0.417338I
a = 0.768504 − 0.302779I
b = 0.126387 + 0.443779I
c = −0.48208 + 1.41304I
d = −0.884219 + 0.662050I
1.20916 − 1.63680I −1.95124 + 5.83411I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.555399
a = 0.739573
b = 0.352132
c = −0.371975
d = 0.206595
−0.726383 −14.1310
u = −0.072203 + 0.503217I
a = 1.330050 + 0.161709I
b = −0.259101 − 0.090079I
c = −0.46842 + 1.35904I
d = 0.650071 + 0.333845I
−0.39079 − 2.25423I −1.75748 + 3.62098I
u = −0.072203 − 0.503217I
a = 1.330050 − 0.161709I
b = −0.259101 + 0.090079I
c = −0.46842 − 1.35904I
d = 0.650071 − 0.333845I
−0.39079 + 2.25423I −1.75748 − 3.62098I
u = −1.83506 + 0.34828I
a = −1.318640 − 0.296832I
b = −1.72178 + 0.16248I
c = 0.10743 + 1.64261I
d = 0.76923 + 2.97688I
−11.72250 + 5.21750I −12.21552 − 2.94469I
u = −1.83506 − 0.34828I
a = −1.318640 + 0.296832I
b = −1.72178 − 0.16248I
c = 0.10743 − 1.64261I
d = 0.76923 − 2.97688I
−11.72250 − 5.21750I −12.21552 + 2.94469I
u = −1.70473 + 1.04671I
a = −0.961354 − 0.702659I
b = −1.67800 + 0.49555I
c = −0.21746 − 1.42452I
d = −1.86176 − 2.20079I
19.5607 + 13.8899I −13.2954 − 6.2001I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.70473 − 1.04671I
a = −0.961354 + 0.702659I
b = −1.67800 − 0.49555I
c = −0.21746 + 1.42452I
d = −1.86176 + 2.20079I
19.5607 − 13.8899I −13.2954 + 6.2001I
u = −0.16477 + 2.05598I
a = 0.354039 − 0.009486I
b = 1.82253 + 0.07562I
c = −0.653183 − 0.249237I
d = −0.62005 + 1.30187I
−15.4858 − 3.5329I −13.90580 + 2.19457I
u = −0.16477 − 2.05598I
a = 0.354039 + 0.009486I
b = 1.82253 − 0.07562I
c = −0.653183 + 0.249237I
d = −0.62005 − 1.30187I
−15.4858 + 3.5329I −13.90580 − 2.19457I
u = 2.12691
a = −1.17023
b = −1.85453
c = 0.262059
d = −0.557378
−16.6053 −15.4680
u = 1.91575 + 0.96837I
a = −0.965214 + 0.561225I
b = −1.77427 − 0.45020I
c = −0.245361 + 0.187449I
d = 0.651569 − 0.121506I
18.1284 − 6.9769I −14.6320 + 1.8700I
u = 1.91575 − 0.96837I
a = −0.965214 − 0.561225I
b = −1.77427 + 0.45020I
c = −0.245361 − 0.187449I
d = 0.651569 + 0.121506I
18.1284 + 6.9769I −14.6320 − 1.8700I
7
II. I
u
2
= h6226au
9
+ 7765u
9
+ · · · − 3.96 × 10
4
a − 2.28 × 10
4
, 1.98 × 10
4
au
9
+
1477u
9
+· · ·−8.65×10
4
a−5134, 1447au
9
+65u
9
+· · ·−7346a−3206, −2.24×
10
4
au
9
+ 7563u
9
+ · · · + 1.22 × 10
5
a − 5.05 × 10
4
, u
10
− u
9
+ · · · − 12u + 4i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
4
=
1
u
2
a
5
=
a
−0.422112au
9
− 0.0189615u
9
+ ··· + 2.14294a + 0.935239
a
11
=
−1.44384au
9
− 0.107716u
9
+ ··· + 6.30718a + 0.374417
−0.908110au
9
− 1.13258u
9
+ ··· + 5.77538a + 3.32410
a
6
=
3673
6856
u
9
a +
1
4
u
9
+ ··· −
1823
3428
a − 3
1.03574u
9
− 0.613623u
8
+ ··· + 10.7148u − 6.53180
a
9
=
−0.535735au
9
+ 0.785735u
9
+ ··· + 0.531797a − 3.53180
1.03574u
9
− 0.613623u
8
+ ··· + 10.7148u − 6.53180
a
12
=
−0.663652au
9
− 0.107716u
9
+ ··· + 2.73337a + 0.374417
−0.682614au
9
− 0.637544u
9
+ ··· + 3.66861a + 1.89177
a
2
=
a
0.422112au
9
+ 0.0189615u
9
+ ··· − 2.14294a − 0.935239
a
1
=
0.422112au
9
+ 0.0189615u
9
+ ··· − 1.14294a − 0.935239
0.422112au
9
+ 0.0189615u
9
+ ··· − 2.14294a − 0.935239
a
7
=
u
u
a
10
=
−0.681009au
9
+ 0.785735u
9
+ ··· + 2.22025a − 3.53180
−0.145274au
9
+ 1.03574u
9
+ ··· + 1.68845a − 6.53180
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
3875
1714
u
9
+
183
1714
u
8
+
26957
1714
u
7
−
2248
857
u
6
−
51811
1714
u
5
−
541
857
u
4
+
185
857
u
3
+
9943
857
u
2
−
27495
1714
u −
882
857
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
+ 19u
19
+ ··· − 1248u + 256
c
2
, c
4
, c
6
c
8
, c
9
u
20
− 3u
19
+ ··· + 8u + 16
c
3
, c
7
(u
10
+ u
9
− 7u
8
− 8u
7
+ 13u
6
+ 14u
5
− 2u
4
+ 2u
3
+ 13u
2
+ 12u + 4)
2
c
5
, c
11
(u
10
− 2u
9
+ 3u
8
− 2u
7
+ 4u
6
− 3u
5
+ 3u
4
+ 3u
2
− u + 1)
2
c
10
, c
12
(u
10
− 2u
9
+ 9u
8
− 14u
7
+ 28u
6
− 31u
5
+ 35u
4
− 20u
3
+ 15u
2
− 5u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
20
− 39y
19
+ ··· − 4268544y + 65536
c
2
, c
4
, c
6
c
8
, c
9
y
20
− 19y
19
+ ··· + 1248y + 256
c
3
, c
7
(y
10
− 15y
9
+ ··· − 40y + 16)
2
c
5
, c
11
(y
10
+ 2y
9
+ 9y
8
+ 14y
7
+ 28y
6
+ 31y
5
+ 35y
4
+ 20y
3
+ 15y
2
+ 5y + 1)
2
c
10
, c
12
(y
10
+ 14y
9
+ ··· + 5y + 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.620250 + 0.748934I
a = 0.448932 − 0.060647I
b = 1.187590 + 0.295523I
c = −0.036785 + 1.027380I
d = 0.50487 + 1.48189I
−4.43566 + 1.46073I −14.6593 − 3.2864I
u = −0.620250 + 0.748934I
a = −0.77388 − 2.52919I
b = −1.110620 + 0.361536I
c = −0.84252 + 1.37187I
d = 0.746622 + 0.664780I
−4.43566 + 1.46073I −14.6593 − 3.2864I
u = −0.620250 − 0.748934I
a = 0.448932 + 0.060647I
b = 1.187590 − 0.295523I
c = −0.036785 − 1.027380I
d = 0.50487 − 1.48189I
−4.43566 − 1.46073I −14.6593 + 3.2864I
u = −0.620250 − 0.748934I
a = −0.77388 + 2.52919I
b = −1.110620 − 0.361536I
c = −0.84252 − 1.37187I
d = 0.746622 − 0.664780I
−4.43566 − 1.46073I −14.6593 + 3.2864I
u = 0.793271 + 0.121626I
a = 0.549929 + 0.112131I
b = 0.745831 − 0.355977I
c = −0.79610 − 1.70490I
d = −2.03769 − 3.21838I
−2.87696 + 2.81207I −12.88002 − 4.64391I
u = 0.793271 + 0.121626I
a = −4.13892 + 0.99173I
b = −1.228490 − 0.054749I
c = 3.11748 + 3.57912I
d = 0.42416 + 1.44928I
−2.87696 + 2.81207I −12.88002 − 4.64391I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.793271 − 0.121626I
a = 0.549929 − 0.112131I
b = 0.745831 + 0.355977I
c = −0.79610 + 1.70490I
d = −2.03769 + 3.21838I
−2.87696 − 2.81207I −12.88002 + 4.64391I
u = 0.793271 − 0.121626I
a = −4.13892 − 0.99173I
b = −1.228490 + 0.054749I
c = 3.11748 − 3.57912I
d = 0.42416 − 1.44928I
−2.87696 − 2.81207I −12.88002 + 4.64391I
u = 0.413972 + 0.524496I
a = 0.920372 − 0.380673I
b = −0.072202 + 0.383745I
c = −1.62004 + 0.89776I
d = −0.357634 − 0.319019I
−1.39065 + 0.79591I −7.22040 + 0.81155I
u = 0.413972 + 0.524496I
a = 0.475648 + 0.039205I
b = 1.088210 − 0.172121I
c = 0.706375 − 0.124338I
d = 1.141520 + 0.478061I
−1.39065 + 0.79591I −7.22040 + 0.81155I
u = 0.413972 − 0.524496I
a = 0.920372 + 0.380673I
b = −0.072202 − 0.383745I
c = −1.62004 − 0.89776I
d = −0.357634 + 0.319019I
−1.39065 − 0.79591I −7.22040 − 0.81155I
u = 0.413972 − 0.524496I
a = 0.475648 − 0.039205I
b = 1.088210 + 0.172121I
c = 0.706375 + 0.124338I
d = 1.141520 − 0.478061I
−1.39065 − 0.79591I −7.22040 − 0.81155I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.88200 + 0.46774I
a = −1.236340 + 0.360963I
b = −1.74531 − 0.21760I
c = −0.930133 + 0.846762I
d = −1.17593 + 1.51598I
−12.6890 − 7.4068I −12.74326 + 4.41038I
u = 1.88200 + 0.46774I
a = 0.385819 − 0.297883I
b = 0.623883 + 1.253760I
c = 0.399930 − 0.904911I
d = 2.14658 − 1.15854I
−12.6890 − 7.4068I −12.74326 + 4.41038I
u = 1.88200 − 0.46774I
a = −1.236340 − 0.360963I
b = −1.74531 + 0.21760I
c = −0.930133 − 0.846762I
d = −1.17593 − 1.51598I
−12.6890 + 7.4068I −12.74326 − 4.41038I
u = 1.88200 − 0.46774I
a = 0.385819 + 0.297883I
b = 0.623883 − 1.253760I
c = 0.399930 + 0.904911I
d = 2.14658 + 1.15854I
−12.6890 + 7.4068I −12.74326 − 4.41038I
u = −1.96899 + 0.18613I
a = −1.262570 − 0.138704I
b = −1.78259 + 0.08597I
c = −0.815769 + 0.005529I
d = −0.287282 + 0.794814I
−13.15130 + 0.50253I −13.49701 + 0.08773I
u = −1.96899 + 0.18613I
a = 0.381016 + 0.259317I
b = 0.79370 − 1.22078I
c = −0.182431 + 0.386420I
d = −1.60521 + 0.16272I
−13.15130 + 0.50253I −13.49701 + 0.08773I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.96899 − 0.18613I
a = −1.262570 + 0.138704I
b = −1.78259 − 0.08597I
c = −0.815769 − 0.005529I
d = −0.287282 − 0.794814I
−13.15130 − 0.50253I −13.49701 − 0.08773I
u = −1.96899 − 0.18613I
a = 0.381016 − 0.259317I
b = 0.79370 + 1.22078I
c = −0.182431 − 0.386420I
d = −1.60521 − 0.16272I
−13.15130 − 0.50253I −13.49701 − 0.08773I
14
III. I
v
1
= hc, d + v, b, a − 1, v
2
− v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
4
=
1
0
a
5
=
1
0
a
11
=
0
−v
a
6
=
1
v − 1
a
9
=
v − 1
−v + 1
a
12
=
v
−v
a
2
=
1
0
a
1
=
1
0
a
7
=
v
0
a
10
=
−1
−v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v − 11
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
u
2
c
5
, c
10
u
2
+ u + 1
c
6
(u − 1)
2
c
8
, c
9
(u + 1)
2
c
11
, c
12
u
2
− u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
y
2
c
5
, c
10
, c
11
c
12
y
2
+ y + 1
c
6
, c
8
, c
9
(y − 1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 1.00000
b = 0
c = 0
d = −0.500000 − 0.866025I
−1.64493 − 2.02988I −9.00000 + 3.46410I
v = 0.500000 − 0.866025I
a = 1.00000
b = 0
c = 0
d = −0.500000 + 0.866025I
−1.64493 + 2.02988I −9.00000 − 3.46410I
18
IV. I
v
2
= ha, d + v, av + c − v + 1, b − 1, v
2
− v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
4
=
1
0
a
5
=
0
1
a
11
=
v − 1
−v
a
6
=
v
0
a
9
=
v
0
a
12
=
v − 1
−1
a
2
=
1
−1
a
1
=
0
−1
a
7
=
v
0
a
10
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 7
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
6
, c
7
c
8
, c
9
u
2
c
4
(u + 1)
2
c
5
, c
12
u
2
− u + 1
c
10
, c
11
u
2
+ u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
2
c
3
, c
6
, c
7
c
8
, c
9
y
2
c
5
, c
10
, c
11
c
12
y
2
+ y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = 1.00000
c = −0.500000 + 0.866025I
d = −0.500000 − 0.866025I
−1.64493 + 2.02988I −9.00000 − 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = 1.00000
c = −0.500000 − 0.866025I
d = −0.500000 + 0.866025I
−1.64493 − 2.02988I −9.00000 + 3.46410I
22
V. I
v
3
= ha, d + 1, c + a, b − 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
−1
0
a
4
=
1
0
a
5
=
0
1
a
11
=
0
−1
a
6
=
0
1
a
9
=
−1
−1
a
12
=
0
−1
a
2
=
1
−1
a
1
=
0
−1
a
7
=
−1
0
a
10
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
u − 1
c
3
, c
5
, c
7
c
10
, c
11
, c
12
u
c
4
, c
8
, c
9
u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
8
, c
9
y − 1
c
3
, c
5
, c
7
c
10
, c
11
, c
12
y
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 1.00000
c = 0
d = −1.00000
−3.28987 −12.0000
26
VI.
I
v
4
= ha, −d
2
v +dv +· · ·+d−1, d
2
v
2
−dv
2
+· · ·+2v +1, −cdv +dv +· · ·−a−
1, cdv
2
−dv
2
+· · ·+2av+a, adv−dv+· · ·−c+1, c
2
v
2
−acv
2
+· · ·−av+a
2
, b−1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
4
=
1
0
a
5
=
0
1
a
11
=
c
d
a
6
=
−c + 1
−dc + 1
a
9
=
c + v − 1
dc − 1
a
12
=
c
d + c
a
2
=
1
−1
a
1
=
0
−1
a
7
=
v
0
a
10
=
c − 1
dc − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = d
2
c − d
2
− 2dc + v
2
+ 4c − 15
(iv) u-Polynomials at the component : It cannot be defined for a positive
dimension component.
(v) Riley Polynomials at the component : It cannot be defined for a positive
dimension component.
27
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
−3.28987 + 2.02988I −12.35599 + 3.42923I
28
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u − 1)
3
(u
18
+ 29u
17
+ ··· + 26u + 1)
· (u
20
+ 19u
19
+ ··· − 1248u + 256)
c
2
, c
6
u
2
(u − 1)
3
(u
18
− 5u
17
+ ··· + 2u − 1)(u
20
− 3u
19
+ ··· + 8u + 16)
c
3
, c
7
u
5
(u
10
+ u
9
+ ··· + 12u + 4)
2
· (u
18
− 3u
17
+ ··· − 32u + 32)
c
4
, c
8
, c
9
u
2
(u + 1)
3
(u
18
− 5u
17
+ ··· + 2u − 1)(u
20
− 3u
19
+ ··· + 8u + 16)
c
5
, c
11
u(u
2
− u + 1)(u
2
+ u + 1)
· (u
10
− 2u
9
+ 3u
8
− 2u
7
+ 4u
6
− 3u
5
+ 3u
4
+ 3u
2
− u + 1)
2
· (u
18
− u
17
+ ··· + 12u + 4)
c
10
u(u
2
+ u + 1)
2
· (u
10
− 2u
9
+ 9u
8
− 14u
7
+ 28u
6
− 31u
5
+ 35u
4
− 20u
3
+ 15u
2
− 5u + 1)
2
· (u
18
− 5u
17
+ ··· + 136u + 16)
c
12
u(u
2
− u + 1)
2
· (u
10
− 2u
9
+ 9u
8
− 14u
7
+ 28u
6
− 31u
5
+ 35u
4
− 20u
3
+ 15u
2
− 5u + 1)
2
· (u
18
− 5u
17
+ ··· + 136u + 16)
29
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
2
(y − 1)
3
(y
18
− 69y
17
+ ··· − 166y + 1)
· (y
20
− 39y
19
+ ··· − 4268544y + 65536)
c
2
, c
4
, c
6
c
8
, c
9
y
2
(y − 1)
3
(y
18
− 29y
17
+ ··· − 26y + 1)
· (y
20
− 19y
19
+ ··· + 1248y + 256)
c
3
, c
7
y
5
(y
10
− 15y
9
+ ··· − 40y + 16)
2
(y
18
− 15y
17
+ ··· − 2048y + 1024)
c
5
, c
11
y(y
2
+ y + 1)
2
· (y
10
+ 2y
9
+ 9y
8
+ 14y
7
+ 28y
6
+ 31y
5
+ 35y
4
+ 20y
3
+ 15y
2
+ 5y + 1)
2
· (y
18
+ 5y
17
+ ··· − 136y + 16)
c
10
, c
12
y(y
2
+ y + 1)
2
(y
10
+ 14y
9
+ ··· + 5y + 1)
2
· (y
18
+ 17y
17
+ ··· − 38944y + 256)
30
