466 Index collared, 64 connected in dimension k, 10 constant fundamental group, 432 flat, xvi, 32, 201, 436 flat modulo A, 164 homotopically unknotted, 31 solvable, 158 spanned, 409 tame, 33 longitude, 28, 302, 329 Main Problem, xiv manifold, 2 factor, 436 topological, 162 manifold-with-boundary, 2 map r-connected, 185 1-UV, 168 proper, 58 mapping cylinder, 123 neighborhood, 129, 417 reduced, 185 retraction, 186 simplicial, 124, 185 torus, 326 Matsumoto link, 307 manifold, 333 Mazur swindle, 95 meets boundary regularly, 201 Menger continuum, 138, 141, 233, 374 modified, 132 standard, 131 sponge, 131 meridian, 28, 302, 329 mesh of a cover, 137 metastable range, 192, 193 mildly wild arc, 79 Milnor duality, 317 sequence, 276, 299 mismatch property, 413 modified Menger continuum, 132 Monotone Union Theorem, 285 Relative, 285 near-homeomorphism, 56 neighborhood, 2 of an end of a manifold, 428 of an end of a map, 432 Newman contractible manifold, 19 nice immersion, 228 nondegeneracy set, 58 null sequence, 372 one-point union, 1 one-sided, 350 orbit space, 413 order ideal, 300 of a module, 300 ordinary polynomial, 312 organization of this book, xvi orientable, 6 orientation, 405 orthogonal complement, 323 pillbox, 47 pinched bicollar, 93 collar, 92 PL, xiv, xv almost, 265 locally flat, 279, 402 modulo a point, 92 on an open subset, 265 Sch¨ onflies Conjecture, 26 Structure Theorem, 347 plug, 84 Poincar´ e Theorem PL, 425 Weak, 99 Poincar´ e-Lefschetz duality, 6 polyhedron, xiv presentation matrix, 300 preserve fibers, 209 primary decomposition, 315 submodule, 314 Product Neighborhood Theorem, 201 Relative, 215 projective class group, 430 module, 430 proper mapping, 58 relation, 383 property 1-UV, 168 pseudo-isotopy, 154, 162 quotient map, 55 R-diameter, 385 R-disk, 385 radial engulfing, 123 ratio-changing general position, 151 regular neighborhood -, 124 abstract, 213, 219 meets boundary regularly, 201 regular value, 225 relation, 383
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