464 Index
resolution, 434
set, 107
Cell-like Approximation Theorem, 366
cellular, 59
map, 60
move, 146
set, 59
cellularity criterion, 73, 106
center line of a solid torus, 44
closed
n-cell complement, 410
manifold, 2
cocore of a handle, 329
codimension, xvii
collapse, 100
(j, )−, 254
collar
for an end, 428
of a ball pair, 285
of a subset, 64
pinched, 92
singular, 405
complementary domains, 26
completion
of a manifold, 428
of map, 432
complex
CW, xiv
simplicial, xiv
concordance, 198
concordant, 199
Cone Unknotting Theorem, 201
Relative, 215
connected
k-connected pair, 11
k-connected space, 10
locally k-co-connected, 31
locally k-connected, 10
continuous relation, 383
contractible retraction, 213
controlled engulfing, 115
generalized, 119, 213, 262, 266, 354, 359,
362
coordinate neighborhood, xiv
core of a handle, 329
covering isotopy, 209
Theorem
Relative, 216
theorem, 210
covering transformations, 298
cube, 1, 131
crumpled, 410
with handles, 84
CW complex, xiv
DDP, 367
deck transformations, 298
decomposition space, 55
deficiency of a group, 283
defining sequence
abstract, 172
compatible, 176
geometric, 173
degree, 405
of a Laurent polynomial, 312
Dehn’s Theorem, 282
Delta structure, 236, 388
(δ, h)-cobordism over X, 433
δ-homotopy, 118
δ-product structure over X, 433
demension, 125
diameter of a homotopy, 432
dimension
of a topological space, 14
of embedding, 125
theorem, 8
disjoint disks property, 367
disk, 1
bundle neighborhood, 346
dominated by a finite complex, 429
double Fox-Artin arc, 77
Double Suspension Theorem, 423, 443
dual
face of a cube, 133
skeleton of a cube, 133
skeleton of a triangulation, 98
Duality Theorem, 6, 8, 317
dunce hat, 189
embedded space, xiv
embedding, xiv
dimension, 125, 160
relation, 383
cell-like, 383
Embedding Existence Theorems, 162, 182,
185, 190, 191, 194, 217, 237, 274, 290,
325, 327, 335, 391, 438
end
of a manifold, 428
of a map, 432
End Theorem, 433
engulfing, 97
Bryant-Seebeck, 115
controlled, 115
generalized, 119
radial, 123
Stallings, 99
Zeeman, 105
-mapping, 14
-mapping cylinder neighborhood, 129
-push, 115
-regular neighborhood, 124
-tame, 157
equivalent
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