Index 467 cell-like embedding, 383 continuous, 383 Relative Covering Isotopy Theorem, 216 Hurewicz Isomorphism Theorem, 17 Monotone Union Theorem, 285 Product Neighborhood Theorem, 215 relative homotopy group, 10 relatively 2-connected at infinity, 426 removing a 2-handle, 329 resolvable, 434 retract absolute, 12 neighborhood, 12 retraction contractible, 213 Rochlin invariant, 444 s-Cobordism Theorem, 426 saturated set, 55 Sch¨ onflies Conjecture, 26 Theorem Generalized, 62, 64 PL, 19 topological, 19 Seifert matrix, 305 surface, 302 Seifert-van Kampen Theorem, 3, 21 semi-capped surface, 236, 388 semifree action, 415 sewing crumpled cubes, 411 shadow, 100, 217 shrinkability criterion, 56 shrinkable decomposition, 56 fixing C, 58 strongly, 58 Sierpi´ nski carpet, 131 curve, 374 simple closed curve, 19 simple-homotopy equivalence, 185 simplicial complement, 98 complex, xiv mapping cylinder, 124, 185 triangulation, 443 simply connected at infinity, 106 sin(1/x)-continuum, 59 singular collar, 405 singular set of a map, 100 skeleton dual, 98 of a cube, 131 of a triangulation, 98 slice knot, 278 slice-trivial, 385 sliced map, 217 Slicing Lemma, 217 solid torus, 42 solvable, 152 locally, 158, 161 sphere, xiv spinning, 36, 281 Stability of Embedding Theorem, 217 stable fundamental group at an end, 429 homeomorphism, 439, 441 inverse sequence, 428 manifold, 441 stably free, 430 isomorphic, 430 Stallings engulfing, 99, 108, 194, 289 modified, 104, 108, 289 standard n-cube, 130 Menger continuum, 132 mistake, 125, 130 ˇ Stan ko complex, 236, 388 move, 235, 388 strongly homogeneously embedded, 421 shrinkable, 58 sunny collapsing, 211 supporting isotopy, 115 surjection, 53 suspension, 35 symmetrically situated, 182 tame -tame, 157 as a subspace, xv Cantor set, 42 compactum, 227 embedding, xv end of a manifold, 429 end of a map, 432 locally, 33 Taming Problem, xv Taming Theorems, 158, 160, 161, 261, 263, 265, 347, 402 template, 235, 388 Thin h-Cobordism Theorem, 434 topological embedding, xiv manifold, xiv, 162 topologically rigid, 442 torsion, 426 submodule, 301

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