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Kirby R.C., Siebenmann L.C. — Foundational Essays on Topological Manifolds, Smoothing and Triangulations |
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Предметный указатель |
191
, 221
234 238
224
imbedded 146
266
264
, 163
( = Hausdorff) 69
near 46
-set 278
233
221
234
279
282
236
and ) 164
Annulus conjecture 291
Approximation (for majorant topology) 46—54
Block transverse 98 102
Blocked equivalence (of s-decompositions) 130
Bundle theorem 70 217
Cairns — Hirsch theorem 37
Cardinal fact (about STABLE structures) 139
Casson — Sullivan periodicity 327 278
cat 10
Chart 7
Chart, product 59
Chart, submersion 59
Classical smoothing theory 156 209
Classical smoothing theory, cf. 169—171
Classification theorems for CAT structures 155 176 194 313
Clean collaring 40
Clean submanifold 12
Cobordism, oriented 322
Cobordism, relative 19
Cobordism, spin 325
Cobordism, unoriented 324
Cofibration 127
Collapsing Lemma 256
Collaring theorems 40—42
Composed microbundle 203
Compressible (neighborhood) 66
Concordance extension theorem 3 26
Concordance implies isotopy theorem 3 25 316
Concordance implies sliced concordance lemma 110
Concordance of CAT structures on a manifold 3 12 24
Concordance of CAT structures on a microbundle 162
Concordance of CAT structures on a microbundle, stable 163
Concordance of microbundles 203
Concordance, sliced 12
Concordance, sliced -parametered 73
Conditioned (homotopy, concordance, etc.) 11 76
Corner set 8
Corners 7 8 29 119
Critical point 108
CSS 220
DEM 146
diff 6
DIFF transversality theorem 85
DIFF triangulation 9
Differential 221
Elementary engulfing lemma 257
Elementary expansion 117
Embed = imbed 6
expansion 118
Farrell’s fibration theorem 211
Finiteness of compact types 301 123 117
Fully normal space 46
G/CAT 103 265—267;
G/TOP 102 103 273ff 318 326 327ff
General position 147—149
Generalized Klein bottle 284
Geometric realisation (of a css set) 222
Gradient like field 112
Handle 15 104
Handle lemma 74
Handle problem 15
Handlebody 104
Handlebody decomposition 104
Handlebody theorem 104
Hauptvermutimg 213 292 299 308
hole 257
Homotopy 11
Homotopy real projective space 331 338
Homotopy theorem for microbundles 161
Homotopy tori 208 264ff 275 287 291
Homotopy, conditioned 11
Homotopy, support of 11
Homotopy-CAT structure 265
Imbed = embed 6
Immersion of ( - point) in 43
Immersion theoretic method 220—230 256—263
Involutions 331—333 337 338
Isotopy 11;
Isotopy approximation theorem 78
Isotopy extension lemma 206
Isotopy, microbundle 203
K-LC imbedded ( = k-LCC ) 146
K-smooth homeomorphism 198
Kan fibration 223
Kister — Mazur theorem 159
L(X), 269 278
Local collaring 40
Local collaring, uniqueness of 40
Local finiteness theorem 123
Locally CAT transverse 90
Locally flat submanifold 13
| Locally tame 143
Main diagram 16 297 302
Majorant topology, source 52
Majorant topology, target 46
Micro-identical 159
Micro-isomorphism 159
Microbundle 10 159
Microbundle homotopy 162
Microbundle isotopy 203
Microbundle map 161
Microbundle, composed 203
Microbundle, concordance of 203
Microbundle, reduction of 162
Microbundle, rooted 182
Microflexible 260
Morlet’s theorem 241
Morse function 108
N(X) 265
Normal (cobordism, invariant, map) 265
Normal microbundle 160 203—208
Periodicity theorem for G/TOP 277
Periodicity theorem of Wall 266—267
Periodicity theorem, structure 283
Pinching lemma 86
PL 6
Poly-Z of rank n 284
Product along P near a point (or a subset) 10 11
Product structure theorem 3 31 315
Product structure theorem, local version 36
Proper map 47
Pseudo-group on a space 7
Pull back rule 166
Punctured torus 43
Reduction of bundle structure 120 187
Reduction of microbundle structure 162 220
Regular homotopy (of open immersions) 147
Rel = fixing a neighborhood of 11
Relative cobordism 19
Rohlin’s signature theorem 210
Rooted microbundle 182
S(X) 264
s-cobordism theorem 4
S-cobordism theorem, non-compact 19
S-decomposition 128
S-decomposition, block equivalehce of 130
S-decomposition, complete 130
S-decomposition, TOP 131
Sharply relative 161
Sheaf of quasi-spaces 259
Sheaf of sets 48
Shortcut 65
Simple space 118
simple type 118
Simple type of a TOP manifold 117 119 126ff 301 318
Simple type, recent theorems on 117
sliced 12 57
Sliced ( -parametered) concordance 73
Sliced concordance 12
Sliced concordance extension theorem 77
Sliced concordance theorem 73
Sliced concordance theorem, alternate 74
Sliced concordance theorem, variant of 77
Smoothed (handle which can be) 15
Smoothing lemma (for open immersions) 149
Smoothing rule 167
Spaced simple block decomposition 128; see s-decomposition
Spine 107
Stability (of solvability of handle problem) 23
Stability theorem (for ) 192 247 305 317
STABLE homeomorphism 33 139 291
Stable manifold 5 139 140
Stable normal microbundles (stable existence and stable uniqueness) 204ff
Stably microbundle transverse () 100 102
Stanko homotopy dimension of imbedding 146
Straightening corners 119
Straightening handles 15
Straightening polyhedra in codimension 143
Strongly flexible 232
Structure, CAT manifold 7
Structure, CAT microbundle 220
Submersion 10
Submersion chart 59
Submersion of the punctured torus 43
Sullivan — Wall exact sequence 269
Surgery 113 (§3.4) 139 145 151 15 264—289
Tangent microbundle 163
Technical bundle theorem 60
Top 6
TOP/CAT 192 196 200ff 246ff 317ff
Torsion, topological invariance of 117 119 126ff 301 318
Transversality lemma for surgery 151
Transversality theorem for surgery 145ff
Transversality theorem, DIFF 85
Transversality theorem, first 85
Transversality theorem, general 100
Transversality theorem, general (for map) 102
Transversality theorem, PL imbedded block bundle 98
Transversality theorem, PL imbedded micro-bundle 94
Transversality theorem, TOP imbedded micro-bundle 91
Transverse (to a microbundle) 84
Transverse, imbedded 91
Triangulation Conjecture 213 292 299 308ff
Triangulation Conjecture, unrestricted 312
Triangulation Conjecture, unrestricted, for manifolds 10
Unbending corners 119
Wandering point 231
Weak stability lemma 192
Whitehead compatible 10
Whitehead triangulation 9
Windowblind Lemma 35
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