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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