11a
173
(K11a
173
)
A knot diagram
1
Linearized knot diagam
5 1 9 6 2 10 4 11 7 3 8
Solving Sequence
1,5
2 3 6
4,8
7 11 9 10
c
1
c
2
c
5
c
4
c
7
c
11
c
8
c
10
c
3
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−14767307395u
27
+ 20235323073u
26
+ ··· + 98330713818b + 33355375098,
32428293291u
27
− 21218621420u
26
+ ··· + 196661427636a + 204360671755,
u
28
− 2u
27
+ ··· − 3u − 4i
I
u
2
= h−u
4
a − u
3
a + 14u
4
− 2u
2
a − 5u
3
− 4au − 10u
2
+ 19b + 9a − u + 26,
5u
4
a − 2u
3
a + 16u
4
− u
2
a − 8u
3
+ a
2
− au − 5u
2
+ 9a − 3u + 30, u
5
− u
4
+ 2u − 1i
I
u
3
= h19u
15
a + 23u
15
+ ··· + 20a + 27, 2u
15
a + 6u
15
+ ··· + a
2
− 4,
u
16
− u
15
− 2u
14
+ 3u
13
+ 4u
12
− 7u
11
− 3u
10
+ 10u
9
− 9u
7
+ 3u
6
+ 5u
5
− 4u
4
+ 2u
2
− 2u + 1i
I
u
4
= hb − 1, 2a − 2u + 1, u
3
+ u
2
− 1i
I
u
5
= hb − a − 1, a
2
+ a + 2, u + 1i
I
u
6
= h2b − a + 1, a
2
− 2a + 5, u − 1i
* 6 irreducible components of dim
C
= 0, with total 77 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−1.48×10
10
u
27
+2.02×10
10
u
26
+· · ·+9.83×10
10
b+3.34×10
10
, 3.24×
10
10
u
27
−2.12×10
10
u
26
+· · ·+1.97×10
11
a+2.04×10
11
, u
28
−2u
27
+· · ·−3u−4i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
4
=
u
3
u
5
− u
3
+ u
a
8
=
−0.164894u
27
+ 0.107894u
26
+ ··· − 2.21519u − 1.03915
0.150180u
27
− 0.205788u
26
+ ··· + 0.595130u − 0.339216
a
7
=
−0.160609u
27
+ 0.110297u
26
+ ··· − 2.13491u − 1.03465
0.227707u
27
− 0.221295u
26
+ ··· + 0.789310u − 0.0177292
a
11
=
0.206489u
27
− 0.182794u
26
+ ··· + 1.38239u + 1.44504
−0.198851u
27
+ 0.240301u
26
+ ··· + 0.0000310478u + 0.278301
a
9
=
−0.312509u
27
+ 0.216909u
26
+ ··· − 2.81796u − 1.93782
0.373802u
27
− 0.449982u
26
+ ··· + 0.400981u − 0.382402
a
10
=
0.137090u
27
− 0.0589378u
26
+ ··· + 1.47329u + 1.50912
−0.199975u
27
+ 0.238265u
26
+ ··· − 0.339747u + 0.201391
a
10
=
0.137090u
27
− 0.0589378u
26
+ ··· + 1.47329u + 1.50912
−0.199975u
27
+ 0.238265u
26
+ ··· − 0.339747u + 0.201391
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
138939169865
196661427636
u
27
−
31573928977
196661427636
u
26
+ ··· −
326662110881
16388452303
u −
420010681258
49165356909
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
28
+ 2u
27
+ ··· + 3u − 4
c
2
, c
4
u
28
+ 10u
27
+ ··· + 97u + 16
c
3
u
28
+ 3u
27
+ ··· + 736u + 128
c
6
, c
8
, c
9
c
11
u
28
− 3u
27
+ ··· − 5u − 1
c
7
, c
10
8(8u
28
− 12u
27
+ ··· + 4u + 2)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
28
− 10y
27
+ ··· − 97y + 16
c
2
, c
4
y
28
+ 18y
27
+ ··· + 8543y + 256
c
3
y
28
− 5y
27
+ ··· − 238592y + 16384
c
6
, c
8
, c
9
c
11
y
28
+ 11y
27
+ ··· − 51y + 1
c
7
, c
10
64(64y
28
+ 176y
27
+ ··· + 40y + 4)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.566116 + 0.813544I
a = 0.534639 − 0.137883I
b = −0.471357 + 0.915613I
1.74883 − 2.81556I −1.14300 + 4.42775I
u = −0.566116 − 0.813544I
a = 0.534639 + 0.137883I
b = −0.471357 − 0.915613I
1.74883 + 2.81556I −1.14300 − 4.42775I
u = 0.805429 + 0.748611I
a = 1.99187 + 0.34421I
b = −1.193820 + 0.462931I
4.99503 − 1.79073I −1.05075 − 2.61493I
u = 0.805429 − 0.748611I
a = 1.99187 − 0.34421I
b = −1.193820 − 0.462931I
4.99503 + 1.79073I −1.05075 + 2.61493I
u = 0.679059 + 0.893968I
a = −0.932511 − 0.786849I
b = 0.600465 + 1.265070I
−0.89815 + 10.64770I −3.82752 − 5.52190I
u = 0.679059 − 0.893968I
a = −0.932511 + 0.786849I
b = 0.600465 − 1.265070I
−0.89815 − 10.64770I −3.82752 + 5.52190I
u = 0.167815 + 0.852338I
a = −0.800362 + 0.593310I
b = 0.442426 − 1.154500I
−3.88792 − 6.82425I −4.62158 + 6.71855I
u = 0.167815 − 0.852338I
a = −0.800362 − 0.593310I
b = 0.442426 + 1.154500I
−3.88792 + 6.82425I −4.62158 − 6.71855I
u = −0.838400
a = −0.287249
b = −1.20069
0.271501 −23.7360
u = −1.156720 + 0.209637I
a = −0.79174 + 1.21845I
b = 0.465804 + 1.280600I
−8.43358 + 10.19260I −10.18832 − 7.63922I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.156720 − 0.209637I
a = −0.79174 − 1.21845I
b = 0.465804 − 1.280600I
−8.43358 − 10.19260I −10.18832 + 7.63922I
u = 0.928400 + 0.721425I
a = 1.19972 + 1.35918I
b = −1.278550 − 0.388894I
4.61539 − 3.79849I −3.70384 + 8.50950I
u = 0.928400 − 0.721425I
a = 1.19972 − 1.35918I
b = −1.278550 + 0.388894I
4.61539 + 3.79849I −3.70384 − 8.50950I
u = −0.878060 + 0.825409I
a = −0.366900 + 0.450231I
b = 0.338313 − 0.571686I
3.34352 + 1.62496I −2.45048 + 1.41829I
u = −0.878060 − 0.825409I
a = −0.366900 − 0.450231I
b = 0.338313 + 0.571686I
3.34352 − 1.62496I −2.45048 − 1.41829I
u = 1.214650 + 0.097151I
a = −0.222900 − 0.987308I
b = −0.155309 − 0.849372I
−4.05629 + 0.93128I −2.23485 − 6.88947I
u = 1.214650 − 0.097151I
a = −0.222900 + 0.987308I
b = −0.155309 + 0.849372I
−4.05629 − 0.93128I −2.23485 + 6.88947I
u = −0.903785 + 0.845201I
a = −1.078650 − 0.117582I
b = 0.379054 + 0.705257I
3.28350 + 4.57627I −2.13594 − 7.47854I
u = −0.903785 − 0.845201I
a = −1.078650 + 0.117582I
b = 0.379054 − 0.705257I
3.28350 − 4.57627I −2.13594 + 7.47854I
u = 1.168360 + 0.434244I
a = 0.627774 + 0.344147I
b = 0.309881 + 1.145950I
−7.10420 + 2.17526I −9.93897 − 4.23335I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.168360 − 0.434244I
a = 0.627774 − 0.344147I
b = 0.309881 − 1.145950I
−7.10420 − 2.17526I −9.93897 + 4.23335I
u = −1.074080 + 0.691225I
a = 1.41798 − 0.69280I
b = −0.422318 − 1.038380I
0.23866 + 8.48658I −4.72348 − 9.14479I
u = −1.074080 − 0.691225I
a = 1.41798 + 0.69280I
b = −0.422318 + 1.038380I
0.23866 − 8.48658I −4.72348 + 9.14479I
u = 1.050060 + 0.753206I
a = −2.17570 − 0.35594I
b = 0.60850 − 1.30717I
−2.0462 − 16.7456I −5.37386 + 9.80445I
u = 1.050060 − 0.753206I
a = −2.17570 + 0.35594I
b = 0.60850 + 1.30717I
−2.0462 + 16.7456I −5.37386 − 9.80445I
u = 0.682847
a = −0.725706
b = 0.129567
−0.926639 −11.5880
u = −0.357231 + 0.322552I
a = 0.478268 − 0.914294I
b = −0.587531 − 0.365743I
1.12674 + 1.01957I 4.42993 − 4.67672I
u = −0.357231 − 0.322552I
a = 0.478268 + 0.914294I
b = −0.587531 + 0.365743I
1.12674 − 1.01957I 4.42993 + 4.67672I
7
II.
I
u
2
= h−u
4
a+14u
4
+· · ·+9a+26, 5u
4
a+16u
4
+· · ·+9a+30, u
5
−u
4
+2u−1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
4
=
u
3
u
4
− u
3
− u + 1
a
8
=
a
0.0526316au
4
− 0.736842u
4
+ ··· − 0.473684a − 1.36842
a
7
=
0.368421au
4
− 0.157895u
4
+ ··· + 0.684211a + 0.421053
−u
4
− au + u
2
+ u − 2
a
11
=
0.736842au
4
+ 5.68421u
4
+ ··· + 1.36842a + 10.8421
0.210526au
4
− 0.947368u
4
+ ··· + 0.105263a − 1.47368
a
9
=
u
4
− u
3
− u
2
− u + 2
−u
4
+ u
2
+ u − 1
a
10
=
0.473684au
4
+ 4.36842u
4
+ ··· + 0.736842a + 7.68421
−0.105263au
4
− 1.52632u
4
+ ··· − 0.0526316a − 2.26316
a
10
=
0.473684au
4
+ 4.36842u
4
+ ··· + 0.736842a + 7.68421
−0.105263au
4
− 1.52632u
4
+ ··· − 0.0526316a − 2.26316
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
4
+ 4u
3
+ 4u
2
− 10
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
5
+ u
4
+ 2u + 1)
2
c
2
, c
4
(u
5
+ u
4
+ 4u
3
+ 2u
2
+ 4u + 1)
2
c
3
(u
5
− u
4
+ 2u − 1)
2
c
6
, c
8
, c
9
c
11
u
10
+ u
9
+ 2u
8
+ 4u
7
+ 4u
6
+ 5u
5
+ 3u
4
+ u
3
+ u
2
+ 1
c
7
, c
10
u
10
+ 4u
9
+ 8u
8
+ 6u
7
+ 6u
6
+ 7u
5
+ 25u
4
+ 43u
3
+ 56u
2
+ 36u + 8
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
(y
5
− y
4
+ 4y
3
− 2y
2
+ 4y −1)
2
c
2
, c
4
(y
5
+ 7y
4
+ 20y
3
+ 26y
2
+ 12y −1)
2
c
6
, c
8
, c
9
c
11
y
10
+ 3y
9
+ 4y
8
− 4y
7
− 12y
6
− 3y
5
+ 11y
4
+ 13y
3
+ 7y
2
+ 2y + 1
c
7
, c
10
y
10
+ 28y
8
+ ··· − 400y + 64
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.760506 + 0.815892I
a = −0.686158 + 0.302307I
b = 0.386464 − 0.809421I
3.01208 + 1.13825I 0.09602 − 2.34058I
u = −0.760506 + 0.815892I
a = 0.658201 − 0.065826I
b = −0.473774 − 0.431559I
3.01208 + 1.13825I 0.09602 − 2.34058I
u = −0.760506 − 0.815892I
a = −0.686158 − 0.302307I
b = 0.386464 + 0.809421I
3.01208 − 1.13825I 0.09602 + 2.34058I
u = −0.760506 − 0.815892I
a = 0.658201 + 0.065826I
b = −0.473774 + 0.431559I
3.01208 − 1.13825I 0.09602 + 2.34058I
u = 1.001870 + 0.741764I
a = −1.06668 − 1.09068I
b = 1.129990 + 0.183434I
1.49357 − 10.61130I −2.76481 + 7.85454I
u = 1.001870 + 0.741764I
a = 2.24279 + 0.22903I
b = −0.67647 + 1.30286I
1.49357 − 10.61130I −2.76481 + 7.85454I
u = 1.001870 − 0.741764I
a = −1.06668 + 1.09068I
b = 1.129990 − 0.183434I
1.49357 + 10.61130I −2.76481 − 7.85454I
u = 1.001870 − 0.741764I
a = 2.24279 − 0.22903I
b = −0.67647 − 1.30286I
1.49357 + 10.61130I −2.76481 − 7.85454I
u = 0.517281
a = −4.14815 + 3.15299I
b = 0.133790 − 1.026500I
−4.07650 −8.66240
u = 0.517281
a = −4.14815 − 3.15299I
b = 0.133790 + 1.026500I
−4.07650 −8.66240
11
III. I
u
3
=
h19u
15
a+23u
15
+· · ·+20a+27, 2u
15
a+6u
15
+· · ·+a
2
−4, u
16
−u
15
+· · ·−2u+1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
−u
3
+ u
a
4
=
u
3
u
5
− u
3
+ u
a
8
=
a
−0.358491au
15
− 0.433962u
15
+ ··· − 0.377358a − 0.509434
a
7
=
0.943396au
15
+ 0.773585u
15
+ ··· + 0.150943a − 1.39623
−0.811321au
15
− 1.24528u
15
+ ··· − 0.169811a + 0.320755
a
11
=
0.433962au
15
+ 2.73585u
15
+ ··· + 0.509434a + 1.03774
−0.339623au
15
− 0.358491u
15
+ ··· − 0.0943396a − 1.37736
a
9
=
2u
14
+ u
13
+ ··· − u + 2
u
15
− 2u
14
+ ··· + 2u − 2
a
10
=
−0.377358au
15
+ 1.49057u
15
+ ··· + 1.33962a + 0.358491
0.509434au
15
− 0.962264u
15
+ ··· − 0.358491a − 0.433962
a
10
=
−0.377358au
15
+ 1.49057u
15
+ ··· + 1.33962a + 0.358491
0.509434au
15
− 0.962264u
15
+ ··· − 0.358491a − 0.433962
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
12
−8u
10
+ 16u
8
−4u
7
−16u
6
+ 8u
5
+ 12u
4
−8u
3
−4u
2
+ 4u −6
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
16
+ u
15
+ ··· + 2u + 1)
2
c
2
, c
4
(u
16
+ 5u
15
+ ··· − 4u
2
+ 1)
2
c
3
(u
16
− u
15
+ ··· − 2u + 1)
2
c
6
, c
8
, c
9
c
11
u
32
+ 5u
31
+ ··· + 8u + 1
c
7
, c
10
u
32
+ u
31
+ ··· − 402u + 73
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
(y
16
− 5y
15
+ ··· − 4y
2
+ 1)
2
c
2
, c
4
(y
16
+ 11y
15
+ ··· − 8y + 1)
2
c
6
, c
8
, c
9
c
11
y
32
+ 21y
31
+ ··· + 6y + 1
c
7
, c
10
y
32
− 15y
31
+ ··· − 89626y + 5329
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.017320 + 0.191091I
a = 0.77304 − 1.40886I
b = −0.436018 − 1.310650I
−4.37117 + 5.29622I −8.10789 − 6.28296I
u = −1.017320 + 0.191091I
a = −0.080344 + 0.145257I
b = 0.930500 + 0.053773I
−4.37117 + 5.29622I −8.10789 − 6.28296I
u = −1.017320 − 0.191091I
a = 0.77304 + 1.40886I
b = −0.436018 + 1.310650I
−4.37117 − 5.29622I −8.10789 + 6.28296I
u = −1.017320 − 0.191091I
a = −0.080344 − 0.145257I
b = 0.930500 − 0.053773I
−4.37117 − 5.29622I −8.10789 + 6.28296I
u = 0.908738 + 0.252477I
a = 0.160770 − 1.402060I
b = 0.185966 + 0.248413I
−3.61825 − 0.25270I −6.38985 + 0.96511I
u = 0.908738 + 0.252477I
a = −1.69112 − 0.97289I
b = −0.058000 − 1.114600I
−3.61825 − 0.25270I −6.38985 + 0.96511I
u = 0.908738 − 0.252477I
a = 0.160770 + 1.402060I
b = 0.185966 − 0.248413I
−3.61825 + 0.25270I −6.38985 − 0.96511I
u = 0.908738 − 0.252477I
a = −1.69112 + 0.97289I
b = −0.058000 + 1.114600I
−3.61825 + 0.25270I −6.38985 − 0.96511I
u = 0.708362 + 0.611401I
a = −1.56409 + 0.56471I
b = 0.153564 − 1.382420I
−3.61825 + 0.25270I −6.38985 − 0.96511I
u = 0.708362 + 0.611401I
a = −1.17703 − 1.58536I
b = 0.608496 + 0.923549I
−3.61825 + 0.25270I −6.38985 − 0.96511I
15
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.708362 − 0.611401I
a = −1.56409 − 0.56471I
b = 0.153564 + 1.382420I
−3.61825 − 0.25270I −6.38985 + 0.96511I
u = 0.708362 − 0.611401I
a = −1.17703 + 1.58536I
b = 0.608496 − 0.923549I
−3.61825 − 0.25270I −6.38985 + 0.96511I
u = 0.724199 + 0.826388I
a = 0.873040 + 1.019050I
b = −0.667529 − 1.233440I
2.34449 + 4.73566I −1.11364 − 2.91588I
u = 0.724199 + 0.826388I
a = −1.62577 − 0.21392I
b = 1.060700 − 0.232760I
2.34449 + 4.73566I −1.11364 − 2.91588I
u = 0.724199 − 0.826388I
a = 0.873040 − 1.019050I
b = −0.667529 + 1.233440I
2.34449 − 4.73566I −1.11364 + 2.91588I
u = 0.724199 − 0.826388I
a = −1.62577 + 0.21392I
b = 1.060700 + 0.232760I
2.34449 − 4.73566I −1.11364 + 2.91588I
u = −0.866890 + 0.696274I
a = 1.92331 + 0.56041I
b = −0.212635 + 1.014820I
−0.93480 + 2.67607I −0.38861 − 3.32415I
u = −0.866890 + 0.696274I
a = 2.69221 − 1.74930I
b = −0.171716 − 1.089490I
−0.93480 + 2.67607I −0.38861 − 3.32415I
u = −0.866890 − 0.696274I
a = 1.92331 − 0.56041I
b = −0.212635 − 1.014820I
−0.93480 − 2.67607I −0.38861 + 3.32415I
u = −0.866890 − 0.696274I
a = 2.69221 + 1.74930I
b = −0.171716 + 1.089490I
−0.93480 − 2.67607I −0.38861 + 3.32415I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.960503 + 0.654282I
a = 0.874727 − 0.511465I
b = 0.27490 + 1.49232I
−4.37117 − 5.29622I −8.10789 + 6.28296I
u = 0.960503 + 0.654282I
a = −2.47726 − 0.17457I
b = 0.723528 − 1.103510I
−4.37117 − 5.29622I −8.10789 + 6.28296I
u = 0.960503 − 0.654282I
a = 0.874727 + 0.511465I
b = 0.27490 − 1.49232I
−4.37117 + 5.29622I −8.10789 − 6.28296I
u = 0.960503 − 0.654282I
a = −2.47726 + 0.17457I
b = 0.723528 + 1.103510I
−4.37117 + 5.29622I −8.10789 − 6.28296I
u = −0.977539 + 0.749941I
a = 0.262243 − 0.231216I
b = −0.494890 + 0.256259I
2.34449 + 4.73566I −1.11364 − 2.91588I
u = −0.977539 + 0.749941I
a = −1.72382 + 0.29569I
b = 0.336437 + 0.940681I
2.34449 + 4.73566I −1.11364 − 2.91588I
u = −0.977539 − 0.749941I
a = 0.262243 + 0.231216I
b = −0.494890 − 0.256259I
2.34449 − 4.73566I −1.11364 + 2.91588I
u = −0.977539 − 0.749941I
a = −1.72382 − 0.29569I
b = 0.336437 − 0.940681I
2.34449 − 4.73566I −1.11364 + 2.91588I
u = 0.059947 + 0.622852I
a = 0.467003 − 0.890621I
b = −0.378599 + 1.075260I
−0.93480 − 2.67607I −0.38861 + 3.32415I
u = 0.059947 + 0.622852I
a = −1.186920 + 0.555131I
b = 0.645301 + 0.131928I
−0.93480 − 2.67607I −0.38861 + 3.32415I
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.059947 − 0.622852I
a = 0.467003 + 0.890621I
b = −0.378599 − 1.075260I
−0.93480 + 2.67607I −0.38861 − 3.32415I
u = 0.059947 − 0.622852I
a = −1.186920 − 0.555131I
b = 0.645301 − 0.131928I
−0.93480 + 2.67607I −0.38861 − 3.32415I
18
IV. I
u
4
= hb − 1, 2a − 2u + 1, u
3
+ u
2
− 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
−u
2
+ 1
u
2
a
6
=
−u
u
2
+ u − 1
a
4
=
−u
2
+ 1
u
2
a
8
=
u −
1
2
1
a
7
=
1
2
u
1
2
u
2
+
1
2
u +
1
2
a
11
=
u +
1
2
1
a
9
=
2u
2
a
10
=
3
2
u
−
1
2
u
2
−
1
2
u +
3
2
a
10
=
3
2
u
−
1
2
u
2
−
1
2
u +
3
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =
17
4
u
2
+
17
4
u +
7
4
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
+ u
2
− 1
c
2
u
3
+ u
2
+ 2u + 1
c
3
u
3
c
4
u
3
− u
2
+ 2u − 1
c
5
u
3
− u
2
+ 1
c
6
, c
8
(u + 1)
3
c
7
8(8u
3
+ 4u
2
+ 4u + 1)
c
9
, c
11
(u − 1)
3
c
10
8(8u
3
− 4u
2
+ 4u − 1)
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
3
− y
2
+ 2y −1
c
2
, c
4
y
3
+ 3y
2
+ 2y −1
c
3
y
3
c
6
, c
8
, c
9
c
11
(y −1)
3
c
7
, c
10
64(64y
3
+ 48y
2
+ 8y −1)
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = −1.37744 + 0.74486I
b = 1.00000
4.66906 + 2.82812I −1.06503 − 2.38969I
u = −0.877439 − 0.744862I
a = −1.37744 − 0.74486I
b = 1.00000
4.66906 − 2.82812I −1.06503 + 2.38969I
u = 0.754878
a = 0.254878
b = 1.00000
0.531480 7.38010
22
V. I
u
5
= hb − a − 1, a
2
+ a + 2, u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
−1
a
2
=
1
1
a
3
=
0
1
a
6
=
1
0
a
4
=
−1
−1
a
8
=
a
a + 1
a
7
=
a + 1
a + 2
a
11
=
−1
a − 1
a
9
=
−1
−2
a
10
=
−1
a
a
10
=
−1
a
(ii) Obstruction class = −1
(iii) Cusp Shapes = −14
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
c
10
(u − 1)
2
c
2
, c
3
, c
4
(u + 1)
2
c
6
, c
8
, c
9
c
11
u
2
+ u + 2
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
7
c
10
(y −1)
2
c
6
, c
8
, c
9
c
11
y
2
+ 3y + 4
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.50000 + 1.32288I
b = 0.50000 + 1.32288I
−8.22467 −14.0000
u = −1.00000
a = −0.50000 − 1.32288I
b = 0.50000 − 1.32288I
−8.22467 −14.0000
26
VI. I
u
6
= h2b − a + 1, a
2
− 2a + 5, u − 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
1
a
2
=
1
1
a
3
=
0
1
a
6
=
−1
0
a
4
=
1
1
a
8
=
a
1
2
a −
1
2
a
7
=
1
2
a −
1
2
−1
a
11
=
1
2
a −
3
2
−1
a
9
=
1
2
a −
1
2
0
a
10
=
1
2
a −
3
2
−
1
2
a +
1
2
a
10
=
1
2
a −
3
2
−
1
2
a +
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u − 1)
2
c
2
, c
5
(u + 1)
2
c
3
, c
6
, c
8
c
9
, c
11
u
2
+ 1
c
7
u
2
− 2u + 2
c
10
u
2
+ 2u + 2
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
(y −1)
2
c
3
, c
6
, c
8
c
9
, c
11
(y + 1)
2
c
7
, c
10
y
2
+ 4
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 1.00000 + 2.00000I
b = 1.000000I
−4.93480 −12.0000
u = 1.00000
a = 1.00000 − 2.00000I
b = − 1.000000I
−4.93480 −12.0000
30
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
3
+ u
2
− 1)(u
5
+ u
4
+ 2u + 1)
2
(u
16
+ u
15
+ ··· + 2u + 1)
2
· (u
28
+ 2u
27
+ ··· + 3u − 4)
c
2
(u + 1)
4
(u
3
+ u
2
+ 2u + 1)(u
5
+ u
4
+ 4u
3
+ 2u
2
+ 4u + 1)
2
· ((u
16
+ 5u
15
+ ··· − 4u
2
+ 1)
2
)(u
28
+ 10u
27
+ ··· + 97u + 16)
c
3
u
3
(u + 1)
2
(u
2
+ 1)(u
5
− u
4
+ 2u − 1)
2
(u
16
− u
15
+ ··· − 2u + 1)
2
· (u
28
+ 3u
27
+ ··· + 736u + 128)
c
4
(u − 1)
2
(u + 1)
2
(u
3
− u
2
+ 2u − 1)(u
5
+ u
4
+ 4u
3
+ 2u
2
+ 4u + 1)
2
· ((u
16
+ 5u
15
+ ··· − 4u
2
+ 1)
2
)(u
28
+ 10u
27
+ ··· + 97u + 16)
c
5
(u − 1)
2
(u + 1)
2
(u
3
− u
2
+ 1)(u
5
+ u
4
+ 2u + 1)
2
· ((u
16
+ u
15
+ ··· + 2u + 1)
2
)(u
28
+ 2u
27
+ ··· + 3u − 4)
c
6
, c
8
(u + 1)
3
(u
2
+ 1)(u
2
+ u + 2)
· (u
10
+ u
9
+ 2u
8
+ 4u
7
+ 4u
6
+ 5u
5
+ 3u
4
+ u
3
+ u
2
+ 1)
· (u
28
− 3u
27
+ ··· − 5u − 1)(u
32
+ 5u
31
+ ··· + 8u + 1)
c
7
64(u − 1)
2
(u
2
− 2u + 2)(8u
3
+ 4u
2
+ 4u + 1)
· (u
10
+ 4u
9
+ 8u
8
+ 6u
7
+ 6u
6
+ 7u
5
+ 25u
4
+ 43u
3
+ 56u
2
+ 36u + 8)
· (8u
28
− 12u
27
+ ··· + 4u + 2)(u
32
+ u
31
+ ··· − 402u + 73)
c
9
, c
11
(u − 1)
3
(u
2
+ 1)(u
2
+ u + 2)
· (u
10
+ u
9
+ 2u
8
+ 4u
7
+ 4u
6
+ 5u
5
+ 3u
4
+ u
3
+ u
2
+ 1)
· (u
28
− 3u
27
+ ··· − 5u − 1)(u
32
+ 5u
31
+ ··· + 8u + 1)
c
10
64(u − 1)
2
(u
2
+ 2u + 2)(8u
3
− 4u
2
+ 4u − 1)
· (u
10
+ 4u
9
+ 8u
8
+ 6u
7
+ 6u
6
+ 7u
5
+ 25u
4
+ 43u
3
+ 56u
2
+ 36u + 8)
· (8u
28
− 12u
27
+ ··· + 4u + 2)(u
32
+ u
31
+ ··· − 402u + 73)
31
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y −1)
4
(y
3
− y
2
+ 2y −1)(y
5
− y
4
+ 4y
3
− 2y
2
+ 4y −1)
2
· ((y
16
− 5y
15
+ ··· − 4y
2
+ 1)
2
)(y
28
− 10y
27
+ ··· − 97y + 16)
c
2
, c
4
(y −1)
4
(y
3
+ 3y
2
+ 2y −1)(y
5
+ 7y
4
+ 20y
3
+ 26y
2
+ 12y −1)
2
· ((y
16
+ 11y
15
+ ··· − 8y + 1)
2
)(y
28
+ 18y
27
+ ··· + 8543y + 256)
c
3
y
3
(y −1)
2
(y + 1)
2
(y
5
− y
4
+ 4y
3
− 2y
2
+ 4y −1)
2
· ((y
16
− 5y
15
+ ··· − 4y
2
+ 1)
2
)(y
28
− 5y
27
+ ··· − 238592y + 16384)
c
6
, c
8
, c
9
c
11
(y −1)
3
(y + 1)
2
(y
2
+ 3y + 4)
· (y
10
+ 3y
9
+ 4y
8
− 4y
7
− 12y
6
− 3y
5
+ 11y
4
+ 13y
3
+ 7y
2
+ 2y + 1)
· (y
28
+ 11y
27
+ ··· − 51y + 1)(y
32
+ 21y
31
+ ··· + 6y + 1)
c
7
, c
10
4096(y −1)
2
(y
2
+ 4)(64y
3
+ 48y
2
+ 8y −1)
· (y
10
+ 28y
8
+ ··· − 400y + 64)(64y
28
+ 176y
27
+ ··· + 40y + 4)
· (y
32
− 15y
31
+ ··· − 89626y + 5329)
32
