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Kirby R.C., Siebenmann L.C. — Foundational Essays on Topological Manifolds, Smoothing and Triangulations
Kirby R.C., Siebenmann L.C. — Foundational Essays on Topological Manifolds, Smoothing and Triangulations

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Название: Foundational Essays on Topological Manifolds, Smoothing and Triangulations

Авторы: Kirby R.C., Siebenmann L.C.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1977

Количество страниц: 372

Добавлена в каталог: 25.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$B_{CAT}$      191
$CAT(\xi)$, $\mathbf{CAT}(\xi)$      221
$CAT^{cls}(\xi)$      234 238
$CAT_M(A)$      224
$LC^k$ imbedded      146
$L_m(\pi)$      266
$S_0(X)$      264
$TOP/CAT(\xi)$ , $TOP/CAT(\xi\mathrm{ rel }C,\eta)$      163
$T_2$ ( = Hausdorff)      69
$U$ near      46
$\Delta$-set      278
$\gamma^m_{TOP}$      233
$\mathbf{CAT}(\hat\tau)$      221
$\mathbf{CAT}(\xi\mathrm{ near }A)$      234
$\mathbf{N}(X)$      279
$\mathbf{S}(X)$      282
$\mathcal{B}^{cls}_{CAT}$      236
$\mathcal{S}_{CAT}(M)$ and $\mathcal{S}_{CAT}(M\mathrm{ rel }C , \Sigma_0$)      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 $\Delta$-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 ($T^n$ - point) in $R^n$      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), $L(\pi)$      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 ( $\Delta$-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 $\pi_k(TOP_n/CAT_n)$)      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 ($\between$)      100 102
Stanko homotopy dimension of imbedding      146
Straightening corners      119
Straightening handles      15
Straightening polyhedra in codimension $\ge3$      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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