12a
1225
(K12a
1225
)
A knot diagram
1
Linearized knot diagam
5 6 8 10 11 3 12 4 1 2 7 9
Solving Sequence
1,9 4,10
5 2 11 8 3 12 7 6
c
9
c
4
c
1
c
10
c
8
c
3
c
12
c
7
c
6
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h7.20918 × 10
393
u
111
+ 5.54525 × 10
394
u
110
+ ··· + 1.43090 × 10
397
b − 3.89590 × 10
397
,
− 1.74511 × 10
396
u
111
− 9.01477 × 10
395
u
110
+ ··· + 1.21484 × 10
400
a − 9.13035 × 10
401
,
u
112
+ 9u
111
+ ··· − 90142u − 1132i
I
u
2
= h−1343140997u
15
− 3388091310u
14
+ ··· + 6660374991b + 2076426241,
265614140u
15
+ 2980660587u
14
+ ··· + 6660374991a + 17049769085, u
16
+ 5u
15
+ ··· − 2u − 1i
I
u
3
= h−a
3
+ b − 4a − 1, a
4
+ a
3
+ 4a
2
+ 4a + 1, u − 1i
I
u
4
= hb + 1, a + 1, u − 1i
I
u
5
= hb
5
− 2b
4
a + b
3
a
2
− 3b
3
+ 4b
2
a − a
2
b + b − a + 1, u − 1i
I
v
1
= ha, b
4
+ b
3
− 1, v − 1i
I
v
2
= ha, b − 1, v − 1i
* 6 irreducible components of dim
C
= 0, with total 138 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
= h7.21 × 10
393
u
111
+ 5.55 × 10
394
u
110
+ · · · + 1.43 × 10
397
b − 3.90 ×
10
397
, −1.75 × 10
396
u
111
− 9.01 × 10
395
u
110
+ · · · + 1.21 × 10
400
a − 9.13 ×
10
401
, u
112
+ 9u
111
+ · · · − 90142u − 1132i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
4
=
0.000143650u
111
+ 0.0000742056u
110
+ ··· + 1183.64u + 75.1571
−0.000503820u
111
− 0.00387535u
110
+ ··· + 132.583u + 2.72269
a
10
=
1
u
2
a
5
=
−0.00163818u
111
− 0.0140914u
110
+ ··· + 1425.91u + 79.2593
−0.00251920u
111
− 0.0199229u
110
+ ··· + 299.210u + 4.84051
a
2
=
0.000256671u
111
+ 0.00161270u
110
+ ··· + 1043.43u + 70.8299
0.000551878u
111
+ 0.00433234u
110
+ ··· − 57.9556u + 0.0777320
a
11
=
0.000976338u
111
+ 0.00910943u
110
+ ··· − 1193.78u − 61.3082
−0.000854627u
111
− 0.00682138u
110
+ ··· + 94.3398u + 0.548443
a
8
=
−0.000398981u
111
− 0.00415660u
110
+ ··· + 1073.25u + 68.4436
0.000742676u
111
+ 0.00637617u
110
+ ··· − 273.417u − 2.86495
a
3
=
−0.00139747u
111
− 0.0104758u
110
+ ··· − 147.808u + 8.40896
−0.00107238u
111
− 0.00755752u
110
+ ··· − 265.251u − 3.49103
a
12
=
u
u
a
7
=
−0.000769701u
111
− 0.00710499u
110
+ ··· + 1097.78u + 68.7355
0.000371956u
111
+ 0.00342777u
110
+ ··· − 248.882u − 2.57307
a
6
=
−0.000217324u
111
− 0.00370821u
110
+ ··· + 1742.49u + 88.6486
0.000823128u
111
+ 0.00586181u
110
+ ··· + 199.870u + 3.76570
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0107685u
111
+ 0.0968647u
110
+ ··· − 5066.55u − 61.6765
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
16(16u
112
+ 8u
111
+ ··· − 57723u + 15987)
c
2
, c
6
u
112
+ 9u
111
+ ··· − 90142u − 1132
c
3
, c
8
16(16u
112
− 8u
111
+ ··· − 75u + 75)
c
4
48(48u
112
− 48u
111
+ ··· − 1592u − 64)
c
5
48(48u
112
+ 48u
111
+ ··· + 1592u − 64)
c
7
, c
11
16(16u
112
+ 8u
111
+ ··· + 75u + 75)
c
9
, c
12
u
112
− 9u
111
+ ··· + 90142u − 1132
c
10
16(16u
112
− 8u
111
+ ··· + 57723u + 15987)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
256(256y
112
− 5152y
111
+ ··· − 1.30933 × 10
10
y + 2.55584 × 10
8
)
c
2
, c
6
, c
9
c
12
y
112
− 75y
111
+ ··· − 5045677580y + 1281424
c
3
, c
7
, c
8
c
11
256(256y
112
− 16672y
111
+ ··· − 439725y + 5625)
c
4
, c
5
2304(2304y
112
− 11424y
111
+ ··· − 1092032y + 4096)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.076594 + 0.998674I
a = 0.231384 + 0.192595I
b = −1.092480 + 0.313140I
3.25749 − 3.93133I 0
u = −0.076594 − 0.998674I
a = 0.231384 − 0.192595I
b = −1.092480 − 0.313140I
3.25749 + 3.93133I 0
u = 0.989446 + 0.111155I
a = −0.06785 − 2.70572I
b = 0.26976 − 1.69355I
−0.179102 + 1.361240I 0
u = 0.989446 − 0.111155I
a = −0.06785 + 2.70572I
b = 0.26976 + 1.69355I
−0.179102 − 1.361240I 0
u = 1.03475
a = −0.678980
b = −0.837668
−1.64218 0
u = −0.928213 + 0.201967I
a = 0.799418 − 0.944826I
b = 1.170730 − 0.590714I
0.866138 + 0.769169I 0
u = −0.928213 − 0.201967I
a = 0.799418 + 0.944826I
b = 1.170730 + 0.590714I
0.866138 − 0.769169I 0
u = 0.012899 + 1.051640I
a = −0.263753 − 0.403519I
b = 1.333720 − 0.114397I
8.41416 − 6.54605I 0
u = 0.012899 − 1.051640I
a = −0.263753 + 0.403519I
b = 1.333720 + 0.114397I
8.41416 + 6.54605I 0
u = −0.033862 + 0.928112I
a = −0.140232 + 0.039291I
b = 1.281230 − 0.478890I
5.94038 − 4.98070I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.033862 − 0.928112I
a = −0.140232 − 0.039291I
b = 1.281230 + 0.478890I
5.94038 + 4.98070I 0
u = −0.842253 + 0.386957I
a = 0.47697 − 1.50961I
b = 0.239501 + 0.060068I
0.62344 + 9.53417I 0
u = −0.842253 − 0.386957I
a = 0.47697 + 1.50961I
b = 0.239501 − 0.060068I
0.62344 − 9.53417I 0
u = −1.042910 + 0.349738I
a = −0.383966 + 1.323600I
b = −0.281312 + 0.605442I
−2.67525 + 4.55404I 0
u = −1.042910 − 0.349738I
a = −0.383966 − 1.323600I
b = −0.281312 − 0.605442I
−2.67525 − 4.55404I 0
u = −0.808934 + 0.384457I
a = 0.15671 + 1.60302I
b = 0.780624 + 0.552924I
1.13362 + 2.05532I 0
u = −0.808934 − 0.384457I
a = 0.15671 − 1.60302I
b = 0.780624 − 0.552924I
1.13362 − 2.05532I 0
u = 1.048220 + 0.374459I
a = −0.869926 − 0.251124I
b = −0.291121 − 0.253138I
−0.866138 + 0.769169I 0
u = 1.048220 − 0.374459I
a = −0.869926 + 0.251124I
b = −0.291121 + 0.253138I
−0.866138 − 0.769169I 0
u = 1.072650 + 0.309982I
a = 0.08998 + 2.27104I
b = −0.829938 + 0.206066I
0.179102 − 1.361240I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.072650 − 0.309982I
a = 0.08998 − 2.27104I
b = −0.829938 − 0.206066I
0.179102 + 1.361240I 0
u = 0.771213 + 0.378608I
a = −0.583767 + 0.056030I
b = −0.859928 − 0.546705I
−2.02176 + 0.22367I 0
u = 0.771213 − 0.378608I
a = −0.583767 − 0.056030I
b = −0.859928 + 0.546705I
−2.02176 − 0.22367I 0
u = −0.229968 + 0.823116I
a = 0.053000 − 0.318049I
b = −1.397590 − 0.020177I
9.29392 − 0.40910I 0
u = −0.229968 − 0.823116I
a = 0.053000 + 0.318049I
b = −1.397590 + 0.020177I
9.29392 + 0.40910I 0
u = 0.473129 + 1.051400I
a = 0.199711 − 0.300992I
b = 1.198560 + 0.396998I
5.00780 + 5.56131I 0
u = 0.473129 − 1.051400I
a = 0.199711 + 0.300992I
b = 1.198560 − 0.396998I
5.00780 − 5.56131I 0
u = −1.145040 + 0.158811I
a = 0.12713 − 1.42460I
b = −1.228560 − 0.577397I
−5.94038 + 4.98070I 0
u = −1.145040 − 0.158811I
a = 0.12713 + 1.42460I
b = −1.228560 + 0.577397I
−5.94038 − 4.98070I 0
u = −1.155800 + 0.143605I
a = −0.04341 + 1.85196I
b = 1.184810 + 0.664213I
−1.99720 + 9.98062I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.155800 − 0.143605I
a = −0.04341 − 1.85196I
b = 1.184810 − 0.664213I
−1.99720 − 9.98062I 0
u = 0.497490 + 0.652853I
a = 0.568345 + 0.080588I
b = −0.127788 − 0.410063I
−1.13362 − 2.05532I 0
u = 0.497490 − 0.652853I
a = 0.568345 − 0.080588I
b = −0.127788 + 0.410063I
−1.13362 + 2.05532I 0
u = 0.941206 + 0.736070I
a = 0.381307 + 1.186970I
b = −1.056170 + 0.634618I
−1.25247 − 5.17059I 0
u = 0.941206 − 0.736070I
a = 0.381307 − 1.186970I
b = −1.056170 − 0.634618I
−1.25247 + 5.17059I 0
u = −1.084390 + 0.505444I
a = −0.510177 − 1.293310I
b = −1.270000 − 0.369732I
6.78188 + 5.23022I 0
u = −1.084390 − 0.505444I
a = −0.510177 + 1.293310I
b = −1.270000 + 0.369732I
6.78188 − 5.23022I 0
u = −1.190100 + 0.153253I
a = 0.178297 + 0.610262I
b = 1.38897 + 0.33779I
−1.46756 + 0.33645I 0
u = −1.190100 − 0.153253I
a = 0.178297 − 0.610262I
b = 1.38897 − 0.33779I
−1.46756 − 0.33645I 0
u = −0.122047 + 0.779373I
a = −0.114156 + 0.418854I
b = −0.527172 + 0.483285I
2.67525 − 4.55404I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.122047 − 0.779373I
a = −0.114156 − 0.418854I
b = −0.527172 − 0.483285I
2.67525 + 4.55404I 0
u = 1.069800 + 0.576020I
a = 0.14524 − 1.44287I
b = 1.36776 − 0.79349I
3.04906 − 11.28170I 0
u = 1.069800 − 0.576020I
a = 0.14524 + 1.44287I
b = 1.36776 + 0.79349I
3.04906 + 11.28170I 0
u = −0.023540 + 1.254960I
a = 0.449621 − 0.002989I
b = −1.059750 + 0.329925I
1.25247 − 5.17059I 0
u = −0.023540 − 1.254960I
a = 0.449621 + 0.002989I
b = −1.059750 − 0.329925I
1.25247 + 5.17059I 0
u = −0.150701 + 1.283400I
a = 0.141625 − 0.115575I
b = −1.253310 − 0.414045I
4.91352 + 13.09700I 0
u = −0.150701 − 1.283400I
a = 0.141625 + 0.115575I
b = −1.253310 + 0.414045I
4.91352 − 13.09700I 0
u = 1.267280 + 0.341348I
a = 0.60742 − 1.44572I
b = 0.895900 − 0.360926I
−1.28303 − 3.24310I 0
u = 1.267280 − 0.341348I
a = 0.60742 + 1.44572I
b = 0.895900 + 0.360926I
−1.28303 + 3.24310I 0
u = 1.303300 + 0.294422I
a = −0.11471 − 1.55010I
b = −0.07325 − 1.51517I
−4.13502 − 12.09070I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.303300 − 0.294422I
a = −0.11471 + 1.55010I
b = −0.07325 + 1.51517I
−4.13502 + 12.09070I 0
u = 1.194340 + 0.660141I
a = 0.210808 + 0.809537I
b = −0.763792 + 0.253689I
−1.72504 − 2.62810I 0
u = 1.194340 − 0.660141I
a = 0.210808 − 0.809537I
b = −0.763792 − 0.253689I
−1.72504 + 2.62810I 0
u = −1.263900 + 0.516886I
a = −0.03228 − 1.44001I
b = −0.829618 − 0.750072I
−0.62344 + 9.53417I 0
u = −1.263900 − 0.516886I
a = −0.03228 + 1.44001I
b = −0.829618 + 0.750072I
−0.62344 − 9.53417I 0
u = 1.334180 + 0.314698I
a = 0.081026 + 1.235020I
b = 0.198328 + 1.226370I
−8.41416 − 6.54605I 0
u = 1.334180 − 0.314698I
a = 0.081026 − 1.235020I
b = 0.198328 − 1.226370I
−8.41416 + 6.54605I 0
u = 0.328035 + 0.535610I
a = −1.188290 + 0.333926I
b = 1.095590 − 0.102708I
2.02176 − 0.22367I 4.79873 + 0.86633I
u = 0.328035 − 0.535610I
a = −1.188290 − 0.333926I
b = 1.095590 + 0.102708I
2.02176 + 0.22367I 4.79873 − 0.86633I
u = −1.352620 + 0.255718I
a = −0.196044 + 1.169210I
b = −0.118555 + 1.122180I
−6.78188 + 5.23022I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.352620 − 0.255718I
a = −0.196044 − 1.169210I
b = −0.118555 − 1.122180I
−6.78188 − 5.23022I 0
u = −1.298990 + 0.466389I
a = 0.37182 + 1.60795I
b = 1.35303 + 0.86227I
1.99720 + 9.98062I 0
u = −1.298990 − 0.466389I
a = 0.37182 − 1.60795I
b = 1.35303 − 0.86227I
1.99720 − 9.98062I 0
u = −1.385620 + 0.052575I
a = 0.73344 + 1.28348I
b = 0.485042 + 1.057350I
−4.28714 − 3.78788I 0
u = −1.385620 − 0.052575I
a = 0.73344 − 1.28348I
b = 0.485042 − 1.057350I
−4.28714 + 3.78788I 0
u = −1.310370 + 0.516292I
a = −0.21364 − 1.43619I
b = −1.092980 − 0.635421I
−0.61110 + 9.33643I 0
u = −1.310370 − 0.516292I
a = −0.21364 + 1.43619I
b = −1.092980 + 0.635421I
−0.61110 − 9.33643I 0
u = 1.37817 + 0.36293I
a = −0.84923 + 1.26582I
b = −1.240840 + 0.469570I
4.28714 − 3.78788I 0
u = 1.37817 − 0.36293I
a = −0.84923 − 1.26582I
b = −1.240840 − 0.469570I
4.28714 + 3.78788I 0
u = −1.43190 + 0.15558I
a = −0.203034 − 0.989310I
b = −0.080939 − 0.939558I
−9.29392 + 0.40910I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43190 − 0.15558I
a = −0.203034 + 0.989310I
b = −0.080939 + 0.939558I
−9.29392 − 0.40910I 0
u = 1.41028 + 0.32457I
a = 0.757729 − 0.381296I
b = 0.925369 + 0.082252I
1.46756 + 0.33645I 0
u = 1.41028 − 0.32457I
a = 0.757729 + 0.381296I
b = 0.925369 − 0.082252I
1.46756 − 0.33645I 0
u = −0.365915 + 0.412674I
a = −0.14055 + 2.53139I
b = 0.253914 − 0.136115I
1.72504 + 2.62810I 9.23789 − 9.47130I
u = −0.365915 − 0.412674I
a = −0.14055 − 2.53139I
b = 0.253914 + 0.136115I
1.72504 − 2.62810I 9.23789 + 9.47130I
u = −1.35458 + 0.51347I
a = 0.44715 + 1.41303I
b = 1.219040 + 0.364948I
4.13502 + 12.09070I 0
u = −1.35458 − 0.51347I
a = 0.44715 − 1.41303I
b = 1.219040 − 0.364948I
4.13502 − 12.09070I 0
u = −1.09380 + 0.98488I
a = −0.223478 + 0.718541I
b = 0.664565 − 0.021277I
−2.08701 + 3.74779I 0
u = −1.09380 − 0.98488I
a = −0.223478 − 0.718541I
b = 0.664565 + 0.021277I
−2.08701 − 3.74779I 0
u = −0.42099 + 1.41567I
a = 0.249353 + 0.126700I
b = −0.968329 − 0.139295I
2.08701 − 3.74779I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.42099 − 1.41567I
a = 0.249353 − 0.126700I
b = −0.968329 + 0.139295I
2.08701 + 3.74779I 0
u = −1.37062 + 0.55200I
a = −0.063610 − 1.279610I
b = −1.31742 − 0.59639I
−3.04906 + 11.28170I 0
u = −1.37062 − 0.55200I
a = −0.063610 + 1.279610I
b = −1.31742 + 0.59639I
−3.04906 − 11.28170I 0
u = 0.349248 + 0.305350I
a = 0.768121 + 0.016112I
b = 0.739773 + 0.980194I
1.28303 − 3.24310I 3.29814 + 8.40281I
u = 0.349248 − 0.305350I
a = 0.768121 − 0.016112I
b = 0.739773 − 0.980194I
1.28303 + 3.24310I 3.29814 − 8.40281I
u = 1.48918 + 0.38329I
a = 0.061872 − 0.544415I
b = −0.413632 − 0.594403I
−4.00511 − 0.72764I 0
u = 1.48918 − 0.38329I
a = 0.061872 + 0.544415I
b = −0.413632 + 0.594403I
−4.00511 + 0.72764I 0
u = −0.046450 + 0.453850I
a = 0.824444 − 0.751338I
b = 0.115446 − 0.445470I
− 1.27033I 0. + 4.50236I
u = −0.046450 − 0.453850I
a = 0.824444 + 0.751338I
b = 0.115446 + 0.445470I
1.27033I 0. − 4.50236I
u = 1.44276 + 0.57759I
a = −0.298746 + 1.328770I
b = −1.41290 + 0.70903I
− 19.5476I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.44276 − 0.57759I
a = −0.298746 − 1.328770I
b = −1.41290 − 0.70903I
19.5476I 0
u = 1.45797 + 0.63871I
a = 0.181999 − 1.166490I
b = 1.31547 − 0.65832I
−4.91352 − 13.09700I 0
u = 1.45797 − 0.63871I
a = 0.181999 + 1.166490I
b = 1.31547 + 0.65832I
−4.91352 + 13.09700I 0
u = −0.309714 + 0.264226I
a = 2.48579 − 1.07022I
b = 0.452397 + 0.657328I
0.61110 + 9.33643I −0.22464 − 7.70849I
u = −0.309714 − 0.264226I
a = 2.48579 + 1.07022I
b = 0.452397 − 0.657328I
0.61110 − 9.33643I −0.22464 + 7.70849I
u = −1.50628 + 0.58589I
a = 0.154270 + 0.911151I
b = 1.33432 + 0.49940I
−5.00780 + 5.56131I 0
u = −1.50628 − 0.58589I
a = 0.154270 − 0.911151I
b = 1.33432 − 0.49940I
−5.00780 − 5.56131I 0
u = −0.19099 + 1.61396I
a = −0.1113280 + 0.0382015I
b = 1.103820 + 0.299690I
5.74733I 0
u = −0.19099 − 1.61396I
a = −0.1113280 − 0.0382015I
b = 1.103820 − 0.299690I
− 5.74733I 0
u = 1.35740 + 0.90914I
a = 0.128278 + 0.818090I
b = −1.105390 + 0.487764I
−1.96231 − 5.07117I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.35740 − 0.90914I
a = 0.128278 − 0.818090I
b = −1.105390 − 0.487764I
−1.96231 + 5.07117I 0
u = 1.52288 + 0.59787I
a = 0.375475 − 0.409323I
b = 1.356790 − 0.132401I
4.00511 + 0.72764I 0
u = 1.52288 − 0.59787I
a = 0.375475 + 0.409323I
b = 1.356790 + 0.132401I
4.00511 − 0.72764I 0
u = −1.63935
a = −0.478929
b = −0.242092
−10.3706 0
u = −1.07002 + 1.27061I
a = 0.030202 − 0.435703I
b = −0.927485 + 0.155970I
1.96231 − 5.07117I 0
u = −1.07002 − 1.27061I
a = 0.030202 + 0.435703I
b = −0.927485 − 0.155970I
1.96231 + 5.07117I 0
u = −0.290654 + 0.105986I
a = −3.69871 + 1.83262I
b = −0.514232 − 0.449850I
−3.25749 + 3.93133I −6.45843 − 5.67906I
u = −0.290654 − 0.105986I
a = −3.69871 − 1.83262I
b = −0.514232 + 0.449850I
−3.25749 − 3.93133I −6.45843 + 5.67906I
u = −0.187718
a = −1.90046
b = −1.73335
10.3706 42.9970
u = −1.89629
a = −0.683881
b = −1.58737
3.86997 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.92194
a = 0.611878
b = 0.823316
−3.86997 0
u = −0.0160460
a = 57.9682
b = 0.897203
1.64218 6.13430
16
II.
I
u
2
= h−1.34 × 10
9
u
15
− 3.39 × 10
9
u
14
+ · · · + 6.66 × 10
9
b + 2.08 × 10
9
, 2.66 ×
10
8
u
15
+2.98×10
9
u
14
+· · ·+6.66×10
9
a+1.70×10
10
, u
16
+5u
15
+· · ·−2u−1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
4
=
−0.0398798u
15
− 0.447521u
14
+ ··· + 3.28976u − 2.55988
0.201661u
15
+ 0.508694u
14
+ ··· − 2.48637u − 0.311758
a
10
=
1
u
2
a
5
=
−0.101874u
15
− 0.843672u
14
+ ··· + 1.33952u − 2.62352
0.238671u
15
+ 0.717261u
14
+ ··· − 2.72072u − 0.397940
a
2
=
−1.09064u
15
− 4.10646u
14
+ ··· − 4.87264u − 0.0808389
−1.78150u
15
− 7.66429u
14
+ ··· + 1.33234u + 0.954948
a
11
=
1.60822u
15
+ 6.56169u
14
+ ··· − 5.97915u − 3.48691
1.35300u
15
+ 5.70439u
14
+ ··· + 0.670822u − 1.19245
a
8
=
−0.734918u
15
− 2.29797u
14
+ ··· + 3.65342u + 0.892857
−1.12368u
15
− 4.52412u
14
+ ··· + 7.25559u + 2.58191
a
3
=
−3.67851u
15
− 15.2266u
14
+ ··· + 17.3498u + 3.61819
−2.38855u
15
− 9.62679u
14
+ ··· + 7.40411u + 5.18039
a
12
=
u
u
a
7
=
−0.522788u
15
− 1.42424u
14
+ ··· + 2.70001u + 0.610534
−0.911553u
15
− 3.65039u
14
+ ··· + 6.30217u + 2.29959
a
6
=
−4.10790u
15
− 17.4344u
14
+ ··· + 10.0290u + 1.74411
−3.10934u
15
− 13.4400u
14
+ ··· − 3.71620u + 3.21349
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −
10698032698
2220124997
u
15
−
54625834408
2220124997
u
14
+ ··· −
124965329986
2220124997
u −
22261582578
2220124997
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
+ 4u
15
+ ··· + 3u + 1
c
2
, c
12
u
16
− 5u
15
+ ··· + 2u − 1
c
3
, c
11
u
16
− 3u
15
+ ··· − 3u + 1
c
4
u
16
− 4u
15
+ ··· + 4u + 1
c
5
u
16
+ 4u
15
+ ··· − 4u + 1
c
6
, c
9
u
16
+ 5u
15
+ ··· − 2u − 1
c
7
, c
8
u
16
+ 3u
15
+ ··· + 3u + 1
c
10
u
16
− 4u
15
+ ··· − 3u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
10
y
16
− 10y
15
+ ··· − 13y + 1
c
2
, c
6
, c
9
c
12
y
16
− 11y
15
+ ··· − 8y + 1
c
3
, c
7
, c
8
c
11
y
16
− 19y
15
+ ··· − 23y + 1
c
4
, c
5
y
16
− 8y
15
+ ··· − 6y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.855691
a = −2.79932
b = −2.68688
−0.711120 9.81610
u = −1.146170 + 0.462459I
a = −0.12388 + 1.84991I
b = 1.020380 + 0.753532I
11.5750I 0. − 11.00303I
u = −1.146170 − 0.462459I
a = −0.12388 − 1.84991I
b = 1.020380 − 0.753532I
− 11.5750I 0. + 11.00303I
u = 1.148830 + 0.492284I
a = 0.034064 − 1.246620I
b = 0.798811 − 0.208995I
−1.07726 − 2.17718I 0.53151 + 1.42089I
u = 1.148830 − 0.492284I
a = 0.034064 + 1.246620I
b = 0.798811 + 0.208995I
−1.07726 + 2.17718I 0.53151 − 1.42089I
u = −1.05468 + 0.98904I
a = 0.448465 − 0.820018I
b = −1.008820 − 0.471438I
−1.83679 + 5.66055I −4.0106 − 15.0207I
u = −1.05468 − 0.98904I
a = 0.448465 + 0.820018I
b = −1.008820 + 0.471438I
−1.83679 − 5.66055I −4.0106 + 15.0207I
u = 0.541515
a = 4.23654
b = −1.11420
0.711120 −9.81610
u = −0.51345 + 1.54946I
a = −0.175161 + 0.081391I
b = 1.000850 − 0.273809I
1.83679 − 5.66055I 4.0106 + 15.0207I
u = −0.51345 − 1.54946I
a = −0.175161 − 0.081391I
b = 1.000850 + 0.273809I
1.83679 + 5.66055I 4.0106 − 15.0207I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.65977
a = −0.515660
b = −0.366311
−10.2737 39.7580
u = 0.322309
a = −0.530108
b = −1.75057
10.2737 −39.7580
u = −0.165504 + 0.248141I
a = −3.21855 + 0.57876I
b = 0.527246 + 0.683816I
1.07726 − 2.17718I −0.53151 + 1.42089I
u = −0.165504 − 0.248141I
a = −3.21855 − 0.57876I
b = 0.527246 − 0.683816I
1.07726 + 2.17718I −0.53151 − 1.42089I
u = −1.79107
a = 0.276801
b = −0.335027
−4.73200 −13.1350
u = 1.90466
a = −0.598131
b = −1.42394
4.73200 13.1350
21
III. I
u
3
= h−a
3
+ b − 4a − 1, a
4
+ a
3
+ 4a
2
+ 4a + 1, u − 1i
(i) Arc colorings
a
1
=
0
1
a
9
=
1
0
a
4
=
a
a
3
+ 4a + 1
a
10
=
1
1
a
5
=
a
3
+ 4a + 1
2a
3
+ 7a + 2
a
2
=
3a
3
+ a
2
+ 11a + 4
5a
3
+ 2a
2
+ 19a + 8
a
11
=
5a
3
+ 2a
2
+ 19a + 9
6a
3
+ 2a
2
+ 23a + 10
a
8
=
−a
3
− 3a
−3a
3
− a
2
− 11a − 4
a
3
=
−3a
3
− a
2
− 11a − 4
−5a
3
− 2a
2
− 19a − 8
a
12
=
1
1
a
7
=
−3a
3
− a
2
− 11a − 4
−5a
3
− 2a
2
− 19a − 8
a
6
=
−3a
3
− a
2
− 11a − 4
−5a
3
− 2a
2
− 19a − 8
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− u
3
− 2u
2
+ 1
c
2
, c
6
u
4
c
3
, c
8
u
4
+ u
3
− 2u
2
+ 1
c
4
u
4
+ u
2
+ 4u + 1
c
5
, c
7
, c
10
c
11
u
4
− u
3
− 1
c
9
, c
12
(u + 1)
4
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
8
y
4
− 5y
3
+ 6y
2
− 4y + 1
c
2
, c
6
y
4
c
4
y
4
+ 2y
3
+ 3y
2
− 14y + 1
c
5
, c
7
, c
10
c
11
y
4
− y
3
− 2y
2
+ 1
c
9
, c
12
(y − 1)
4
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.655786
b = −1.90517
−1.64493 −6.00000
u = 1.00000
a = −0.401572
b = −0.671044
−1.64493 −6.00000
u = 1.00000
a = 0.02868 + 1.94846I
b = 0.788105 + 0.401358I
−1.64493 −6.00000
u = 1.00000
a = 0.02868 − 1.94846I
b = 0.788105 − 0.401358I
−1.64493 −6.00000
25
IV. I
u
4
= hb + 1, a + 1, u − 1i
(i) Arc colorings
a
1
=
0
1
a
9
=
1
0
a
4
=
−1
−1
a
10
=
1
1
a
5
=
−1
−1
a
2
=
−1
0
a
11
=
2
1
a
8
=
2
1
a
3
=
1
0
a
12
=
1
1
a
7
=
1
0
a
6
=
1
0
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u − 1
c
2
, c
4
, c
6
u
c
3
, c
5
, c
7
c
8
, c
9
, c
10
c
11
, c
12
u + 1
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y − 1
c
2
, c
4
, c
6
y
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = −1.00000
−1.64493 −6.00000
29
V. I
u
5
= hb
5
− 2b
4
a + b
3
a
2
− 3b
3
+ 4b
2
a − a
2
b + b − a + 1, u − 1i
(i) Arc colorings
a
1
=
0
1
a
9
=
1
0
a
4
=
a
b
a
10
=
1
1
a
5
=
b
2b − a
a
2
=
−b
2
−2b
2
+ ba + 1
a
11
=
−b
4
+ b
3
a + b
2
+ 1
−2b
4
+ 3b
3
a − b
2
a
2
+ 3b
2
− 2ba
a
8
=
ba + 1
b
2
a
3
=
−b
2
a − b + a
−b
3
+ b
a
12
=
1
1
a
7
=
b
2
2b
2
− ba − 1
a
6
=
−b
2
a + b
2
− b + a
−b
3
+ 2b
2
− ba + b − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
(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.
30
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = ···
a = ···
b = ···
0 0
31
VI. I
v
1
= ha, b
4
+ b
3
− 1, v − 1i
(i) Arc colorings
a
1
=
1
0
a
9
=
1
0
a
4
=
0
b
a
10
=
1
0
a
5
=
b
b
a
2
=
b
2
+ 1
b
2
a
11
=
b
3
− b
2
b
3
− 1
a
8
=
1
b
2
a
3
=
−b
−b
3
+ b
a
12
=
1
0
a
7
=
b
2
+ 1
b
2
a
6
=
b
2
− b + 1
−b
3
+ b
2
+ b
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
8
u
4
+ u
3
− 1
c
2
, c
6
(u − 1)
4
c
5
u
4
+ u
2
− 4u + 1
c
7
, c
11
u
4
− u
3
− 2u
2
+ 1
c
9
, c
12
u
4
c
10
u
4
+ u
3
− 2u
2
+ 1
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
8
y
4
− y
3
− 2y
2
+ 1
c
2
, c
6
(y − 1)
4
c
5
y
4
+ 2y
3
+ 3y
2
− 14y + 1
c
7
, c
10
, c
11
y
4
− 5y
3
+ 6y
2
− 4y + 1
c
9
, c
12
y
4
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −0.219447 + 0.914474I
1.64493 6.00000
v = 1.00000
a = 0
b = −0.219447 − 0.914474I
1.64493 6.00000
v = 1.00000
a = 0
b = 0.819173
1.64493 6.00000
v = 1.00000
a = 0
b = −1.38028
1.64493 6.00000
35
VII. I
v
2
= ha, b − 1, v − 1i
(i) Arc colorings
a
1
=
1
0
a
9
=
1
0
a
4
=
0
1
a
10
=
1
0
a
5
=
1
1
a
2
=
2
1
a
11
=
−1
−1
a
8
=
1
1
a
3
=
−1
0
a
12
=
1
0
a
7
=
2
1
a
6
=
1
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
, c
7
c
8
, c
11
u − 1
c
5
, c
9
, c
12
u
c
10
u + 1
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
, c
7
c
8
, c
10
, c
11
y − 1
c
5
, c
9
, c
12
y
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
1.64493 6.00000
39
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
16(u − 1)
2
(u
4
− u
3
− 2u
2
+ 1)(u
4
+ u
3
− 1)(u
16
+ 4u
15
+ ··· + 3u + 1)
· (16u
112
+ 8u
111
+ ··· − 57723u + 15987)
c
2
u
5
(u − 1)
5
(u
16
− 5u
15
+ ··· + 2u − 1)
· (u
112
+ 9u
111
+ ··· − 90142u − 1132)
c
3
16(u − 1)(u + 1)(u
4
+ u
3
− 1)(u
4
+ u
3
− 2u
2
+ 1)(u
16
− 3u
15
+ ··· − 3u + 1)
· (16u
112
− 8u
111
+ ··· − 75u + 75)
c
4
48(u)(u − 1)(u
4
+ u
2
+ 4u + 1)(u
4
+ u
3
− 1)(u
16
− 4u
15
+ ··· + 4u + 1)
· (48u
112
− 48u
111
+ ··· − 1592u − 64)
c
5
48(u)(u + 1)(u
4
+ u
2
− 4u + 1)(u
4
− u
3
− 1)(u
16
+ 4u
15
+ ··· − 4u + 1)
· (48u
112
+ 48u
111
+ ··· + 1592u − 64)
c
6
u
5
(u − 1)
5
(u
16
+ 5u
15
+ ··· − 2u − 1)
· (u
112
+ 9u
111
+ ··· − 90142u − 1132)
c
7
16(u − 1)(u + 1)(u
4
− u
3
− 1)(u
4
− u
3
− 2u
2
+ 1)(u
16
+ 3u
15
+ ··· + 3u + 1)
· (16u
112
+ 8u
111
+ ··· + 75u + 75)
c
8
16(u − 1)(u + 1)(u
4
+ u
3
− 1)(u
4
+ u
3
− 2u
2
+ 1)(u
16
+ 3u
15
+ ··· + 3u + 1)
· (16u
112
− 8u
111
+ ··· − 75u + 75)
c
9
u
5
(u + 1)
5
(u
16
+ 5u
15
+ ··· − 2u − 1)
· (u
112
− 9u
111
+ ··· + 90142u − 1132)
c
10
16(u + 1)
2
(u
4
− u
3
− 1)(u
4
+ u
3
− 2u
2
+ 1)(u
16
− 4u
15
+ ··· − 3u + 1)
· (16u
112
− 8u
111
+ ··· + 57723u + 15987)
c
11
16(u − 1)(u + 1)(u
4
− u
3
− 1)(u
4
− u
3
− 2u
2
+ 1)(u
16
− 3u
15
+ ··· − 3u + 1)
· (16u
112
+ 8u
111
+ ··· + 75u + 75)
c
12
u
5
(u + 1)
5
(u
16
− 5u
15
+ ··· + 2u − 1)
· (u
112
− 9u
111
+ ··· + 90142u − 1132)
40
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
10
256(y − 1)
2
(y
4
− 5y
3
+ 6y
2
− 4y + 1)(y
4
− y
3
− 2y
2
+ 1)
· (y
16
− 10y
15
+ ··· − 13y + 1)
· (256y
112
− 5152y
111
+ ··· − 13093319163y + 255584169)
c
2
, c
6
, c
9
c
12
y
5
(y − 1)
5
(y
16
− 11y
15
+ ··· − 8y + 1)
· (y
112
− 75y
111
+ ··· − 5045677580y + 1281424)
c
3
, c
7
, c
8
c
11
256(y − 1)
2
(y
4
− 5y
3
+ 6y
2
− 4y + 1)(y
4
− y
3
− 2y
2
+ 1)
· (y
16
− 19y
15
+ ··· − 23y + 1)
· (256y
112
− 16672y
111
+ ··· − 439725y + 5625)
c
4
, c
5
2304y(y − 1)(y
4
− y
3
− 2y
2
+ 1)(y
4
+ 2y
3
+ 3y
2
− 14y + 1)
· (y
16
− 8y
15
+ ··· − 6y + 1)
· (2304y
112
− 11424y
111
+ ··· − 1092032y + 4096)
41
