Index 465
embeddings, xiv
Euclidean space, xiii
Eventual Hurewicz Theorem, 16
everywhere wild, 73
Existence Problem, xvi
exotic homology manifold, 437
expansion, 185
exterior of a link, 302
eyebolt, 84
face of a cube, 131
faithful
embedding of boundary manifolds, 194
map of ∂-manifolds, 38
map of pairs, 201
fiber
of an embedding of
Dj
, 249
preserving, 209, 249
fine homotopy equivalence, 110
flat, xv
cell, 26, 27, 66, 164, 264, 382
locally, 201
locally flat modulo A, 164
sphere, 26, 27, 62, 64, 93, 164, 264, 278,
284, 289, 399, 404
twice, 92
Flatness Problem, xv
Flattening Theorems, 26, 27, 29, 62, 64, 66,
93, 201, 264, 284, 289, 293, 295, 356,
366, 382, 399, 404, 418
Fox-Artin
arc, 75
double, 77
sphere, 79
fractal, 137
framing of a handle, 329
full
subcomplex, 98
subset of Emb(X, M), 158
fundamental group of the end, 429
Generalized Sch¨ onflies Theorem, 62, 64
h-Cobordism Theorem, 425
Thin, 434
Weak, 105
handle theory, 276
handle-like decomposition, 220
Hauptvermutung, 283, 439
Hausdorff
dimension, 137
measure, 137
Hawaiian earring, 5
homeomorphically approximated, 404
homogeneously embedded, 83
strongly, 421
homologically tame, 432
homology
∂-manifold, 437
cobordant, 313
manifold, 435
homotopy group
boundary operator, 11
definition, 9
induced homorphism, 10
relative, 10
homotopy sequence of a pair, 11
Hopf link, 28, 211
Hurewicz Isomorphism Theorem
global, 16
Local (or Eventual), 16
Relative, 17
icosahedron, 18
index of a homology manifold, 435
Index Theorem, 435
induced homomorphism, 10
infinite cyclic cover, 298
inflation, 414
interior of a ∂-manifold, 2
Invariance of Domain, 2
inverse limit of groups, 428
inverse set, 61
isolated end, 428
isotopy
covering, 209
extension, 209
(j, )-collapse, 254
Jordan
Curve Theorem, 19
Separation Theorem, 8
k-connected
pair, 11
space, 10
Kawauchi invariant, 314
Kirby calculus, 329
Klee trick, 66
knotted, xv
Laurent polynomial, 299
degree, 312
LCk,
10
Levine’s Unknotting Theorem, 282
limited by a collection, 427
link calculus, 329
linking number, 302
local
coefficients, 275
contractibility, 358
locally
1-alg, 31
co-connected, 31
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