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