464 Index resolution, 434 set, 107 Cell-like Approximation Theorem, 366 cellular, 59 map, 60 move, 146 set, 59 cellularity criterion, 73, 106 center line of a solid torus, 44 closed n-cell complement, 410 manifold, 2 cocore of a handle, 329 codimension, xvii collapse, 100 (j, )−, 254 collar for an end, 428 of a ball pair, 285 of a subset, 64 pinched, 92 singular, 405 complementary domains, 26 completion of a manifold, 428 of map, 432 complex CW, xiv simplicial, xiv concordance, 198 concordant, 199 Cone Unknotting Theorem, 201 Relative, 215 connected k-connected pair, 11 k-connected space, 10 locally k-co-connected, 31 locally k-connected, 10 continuous relation, 383 contractible retraction, 213 controlled engulfing, 115 generalized, 119, 213, 262, 266, 354, 359, 362 coordinate neighborhood, xiv core of a handle, 329 covering isotopy, 209 Theorem Relative, 216 theorem, 210 covering transformations, 298 cube, 1, 131 crumpled, 410 with handles, 84 CW complex, xiv DDP, 367 deck transformations, 298 decomposition space, 55 deficiency of a group, 283 defining sequence abstract, 172 compatible, 176 geometric, 173 degree, 405 of a Laurent polynomial, 312 Dehn’s Theorem, 282 Delta structure, 236, 388 (δ, h)-cobordism over X, 433 δ-homotopy, 118 δ-product structure over X, 433 demension, 125 diameter of a homotopy, 432 dimension of a topological space, 14 of embedding, 125 theorem, 8 disjoint disks property, 367 disk, 1 bundle neighborhood, 346 dominated by a finite complex, 429 double Fox-Artin arc, 77 Double Suspension Theorem, 423, 443 dual face of a cube, 133 skeleton of a cube, 133 skeleton of a triangulation, 98 Duality Theorem, 6, 8, 317 dunce hat, 189 embedded space, xiv embedding, xiv dimension, 125, 160 relation, 383 cell-like, 383 Embedding Existence Theorems, 162, 182, 185, 190, 191, 194, 217, 237, 274, 290, 325, 327, 335, 391, 438 end of a manifold, 428 of a map, 432 End Theorem, 433 engulfing, 97 Bryant-Seebeck, 115 controlled, 115 generalized, 119 radial, 123 Stallings, 99 Zeeman, 105 -mapping, 14 -mapping cylinder neighborhood, 129 -push, 115 -regular neighborhood, 124 -tame, 157 equivalent

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