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Candel A., Conlon L. — Foliations I

Candel A., Conlon L. — Foliations I

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Название: Foliations I

Авторы: Candel A., Conlon L.

Аннотация:

This is the first of two volumes on the qualitative theory of foliations. This volume is divided into three parts. It is extensively illustrated throughout and provides a large number of examples. Part 1 is intended as a "primer" in foliation theory. A working knowledge of manifold theory and topology is a prerequisite. Fundamental definitions and theorems are explained to prepare the reader for further exploration of the topic. This section places considerable emphasis on the construction of examples, which are accompanied by many illustrations.
Part 2 considers foliations of codimension one. Using very hands-on geometric methods, the path leads to a complete structure theory (the theory of levels), which was established by Conlon along with Cantwell, Hector, Duminy, Nishimori, Tsuchiya, et al. Presented here is the first and only full treatment of the theory of levels in a textbook.
Part 3 is devoted to foliations of higher codimension, including abstract laminations (foliated spaces). The treatment emphasizes the methods of ergodic theory: holonomy-invariant measures and entropy. Featured are Sullivan's theory of foliation cycles, Plante's theory of growth of leaves, and the Ghys, Langevin, Walczak theory of geometric entropy.
This comprehensive volume has something to offer a broad spectrum of readers: from beginners to advanced students to professional researchers. Packed with a wealth of illustrations and copious examples at varying degrees of difficulty, this highly-accessible text offers the first full treatment in the literature of the theory of levels for foliated manifolds of codimension one. It would make an elegant supplementary text for a topics course at the advanced graduate level. Foliations II is Volume 60 in the AMS in the Graduate Studies in Mathematics series.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 398

Добавлена в каталог: 21.11.2013

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Предметный указатель

$B_{m}$       19 276
$B_{\tau}$       19 276
$C^{k}$ norm      232
$C^{r}(M)$ (for foliated spaces)      279
$C_{k}$       192
$Gl_{+}(n, \mathbb{R})$       287
$H^{DR}_{p}$       237
$M_{*}$       189
$M_{0}$       189
$M_{k}$       189
$M_{\infty}$       189
$\alpha$ -limit set      158
$\delta W$       127
$\mathbb{F}^{p}$       19
$\mathbb{H}^{n}$       15
$\mathcal{B}_{\mathcal{F}}$       240
$\mathcal{C}_{\mathcal{F}}$       231 239—245
$\mathcal{D}^{'}_{p}$       233
$\mathcal{D}^{c}_{p}$       247
$\mathcal{D}^{k}_{p}$       232
$\mathcal{D}_{p}$       231
$\mathcal{O}(\mathcal{F})$       126
$\mathcal{Z}_{\mathcal{F}}$       240
$\omega$ -limit set      46 157
$\partial_{m}$       20
$\partial_{\tau}$       20
$\preceq$       159
$\succeq$       149 311
$\widehat{\mathcal{C}}_{\mathcal{F}}$       240
(n, $\epsilon$ )-separation by $G_{1}$       351
(n, $\epsilon$ )-separation by $\Gamma_{1}$       352
(n, $\epsilon$ )-separation by $\mathcal{U}$       356
(n, $\epsilon$ )-separation by a map      348
(n, $\epsilon$ )-spanning set      349
(R, $\epsilon$ )-separation by g      360
2-holed torus      17
2nd countable      24
A(L)      145
Accessible set      145
Action of a Lie group      284
Adjoint      237
Ahlfors, L.      343
Alexander horned sphere      111
Almost periodic function      285
Annihilator of a distribution      36
Annihilator, ideal      34 36
Architecture (of foliations)      166
ARM      131
Arnol'd, V.I.      218
Asymptote of a leaf      115
Asymptote of an end      115
Asymptotic      103 115 116
Atlas(es), foliated      23—33 275—281
Atlas(es), foliated, associated to a foliation      21
Atlas(es), foliated, class $C^{r}$       23 278
Atlas(es), foliated, coherence of      25 278
Atlas(es), foliated, coherent regular refinement of      29 278
Atlas(es), foliated, regular      27 278
Atlas(es), laminated      235
Attie, O.      194 340
Averaging sequence      251—253 339 343
Averaging sequence, definition of      252
Averaging sequence, topological      331
Bebutov, M.      273 286
Biregular cover      123 125
Biregular foliated atlas      121 125
Blank, S.      225
Bohr, H.      275
Bonding map      281
Border      127
Border plaque      127
Border plaque, special      127
Boundary operator on currents      237
Boundary, tangential      20 22
Boundary, transverse      20 22
Bounded linear map on $\mathcal{D}_{p}$       233
Bounded subset of $\mathcal{D}^{'}_{p}$       237
Bounded subset of $\mathcal{D}_{p}$       233
Bundle, flat      54
Bundle, foliated      46—55
Bundle, structure cocycle for      54
Bundle, structure group of      54
Bundle, structure group of, reduction of      54
Bundle-like metric      362
C(M)      279
Candel, A.      342
Cantor set      18 104 108 275 276 283 291
Cantor set of ends      111
Cantwell, J.      142 165 171
Category      62
Category, morphism of      62
Category, object of      62
Chart(s), coherently foliated      23 25 276
Chart(s), foliated      19 276
Chart(s), foliated, codimension of      19
Chart(s), foliated, transversal of      20 276
Circle at infinity      12 104
Cobordism (of foliations)      100
Cocycle conditions      28 280
Cocycle holonomy      28 280
Codimension of foliated chart      19
Codimension of foliation      6 21
Codimension, arbitrary      229—386
Codimension, one      121—225
Coherence of foliated atlases      25 278
Coherence of invariant measures      302
Collar      82
Collar, foliated      82
Completely integrable system      34
Completeness      50
Compressible      307
Concordance (of foliations)      99
Conforma, metrics, class of      342
Conformal metrics      294 341
Conformal Riemann surfaces      294
Conlon, L.      165 171
Connes, A.      345
Contraction, linear      183
Contraction, Sacksteder      183
Convolution      288
Corner      19
Critical point      152
Critical point, nondegenerate      152
Cross section      46 49
Cross section, local      286
Current      231
Current of degree 0      236
Current of integration      234
Current, closed      237
Current, de Rham      229
Current, diffuse      233
Current, Dirac      233
Current, exact      237
Current, foliation      231 239—245
Current, foliation cycle      235 240
Current, foliation cycle as a holonomy-invariant measure      245—251
Current, foliation, Dirac      239
Current, holonomy-invariant measure for a foliation      234
Current, holonomy-invariant measure for a lamination      235
Current, p-      233
Current, p-boundary      237
Current, p-cycle      237
Current, singular      233
Current, singular submanifold      234
Cut and paste      3
Cycle foliation      229 231 235 240
Cycle foliation as a holonomy-invariant measure      245—251
Cycle foliation in foliated spaces      303
Cycle limit      158
Cycle, asymptotic      253

Cylindrical coordinates      90
de Rham cohomology in foliated spaces      303
De Rham current      229
de Rham homology      237
de Rham homology of foliated spaces      304
de Rham theorem      238
Deadend component      267
Deadend component, generalized      268
Deformation of a foliation      17 95—101
Denjoy's example      107—108 205
Denjoy's foliation      166 184
Denjoy's theorem      166 217
Denjoy, A.      108 166 184
Depth      192
Derived set      114
Diagonal action      76
Diffeomorphism in foliated spaces      277
Differentiability class of a foliated atlas      21 278
Differentiability class of a foliated manifold      21
Differentiability class of a foliated space      279
Differentiability class of a foliation      21
Differential graded ideal      37
Dippolito semistability theorem      134
Dippolito, P.      134
Dirac current      233
Dirac foliation current      239
Distance in a $\Gamma$ -orbit      320
Distance, leafwise      299
Distance, leafwise, Riemannian      299
distribution      34
Distribution, completely integrable      36
Distribution, involutive      36
Distribution, k-plane      34 36
Dominate      311
Dominate, strictly      312
Double along $\partial_{m} M$       126
Duminy's theorem on ends      118 184 199
Duminy's vanishing theorem      66 184 193 208 218 325 372 379
Duminy, G.      66 118 165 184 193 199 372 379
End(s)      90 110—118
End(s) of leaves      115—118
End(s) of manifolds      110—115
End(s), Cantor set of      111 372
End(s), definition of      111
End(s), fundamental neighborhood system of      112
End(s), periodic      198
End(s), proper      116
End(s), totally proper      116
entropy      229 347—386
Entropy of a flow      352
Entropy of a foliation      356—358
Entropy of a foliation, relative to a foliated atlas      356—357
Entropy of a map      348—351
Entropy of a pseudogroup      352—355
Entropy of a transformation group      351—352
Entropy, geometric of a foliated manifold      358—368
Entropy, geometric of a foliated space      368—370
Entropy, geometric, definition for foliated manifolds      360
Epstein, D.B.A.      65
Ergodic flow-invariant measure      253
Ergodic theorem      254
Escher, M.C.      86
Euclidean half space      15
Euler characteristic of a foliated space      342
Euler characteristic, average      331
Euler characteristic, average, nonzero      331
Euler characteristic, average, zero      331
Euler class      147 340
Exotic characteristic class      38
Expanding map      284 296 373
Expansion of a regular foliated atlas      280
Exploding ball      258
Exploding disk      258
Exploding plateau      258
Fiber bundle      5
Fiber bundle, base of      5
Fiber bundle, fiber of      5
Fiber bundle, foliated      46—55
Fiber bundle, total space of      5
Finite depth      197—204
First return map      45
First return time      47
Flow on a metric space      273 285 352
Flow, entropy of      352
Flow, local      8
Flow, Sacksteder      214—217
Flowbox      337
Flowline      8
Foelner condition      252 306 326
Foliated atlas      23 275—281
Foliated atlas, class $C^{r}$       23 278
Foliated atlas, coherent regular refinement of      29 278
Foliated atlas, regular      27 278
Foliated bundle      46—55 283
Foliated bundle, incomplete      49
Foliated chart      19 276
Foliated chart, transversal of      20 276
Foliated manifold      5—23
Foliated manifold, definition of      21
Foliated manifold, differentiability class of      21
Foliated manifold, geometrically taut      261
Foliated manifold, harmonic      261
Foliated normal neighborhood      63
Foliated product      126
Foliated space      32 273—307
Foliated space, orientable      279
Foliated space, transverse model of      275
Foliation(s) as a coherence class of foliated atlases      31 279
Foliation(s) as a maximal foliated atlas      31 279
Foliation(s) as an equivalence relation      22 279
Foliation(s) of class $C^{0}$       31
Foliation(s) of class $C^{r, 0+}$       32
Foliation(s) of class $C^{r, k}$       32
Foliation(s) of finite depth      197
Foliation(s) of manifolds with boundary      15
Foliation(s) without holonomy      205
Foliation(s), analytic      162
Foliation(s), boundary      240
Foliation(s), cobordant      100
Foliation(s), codimension of      6 21
Foliation(s), concordant      99
Foliation(s), current      231
Foliation(s), cycle      229 231 235 240
Foliation(s), cycle in foliated spaces      303
Foliation(s), defined by a closed, nonsingular 1-form      40
Foliation(s), definition of      20—21 279
Foliation(s), differentiability class of      21 279
Foliation(s), dimension of      6 21 279
Foliation(s), entropy      229
Foliation(s), geometrically taut      261
Foliation(s), harmonic      261
Foliation(s), homologically taut      266
Foliation(s), homotopic      98
Foliation(s), induced on $\partial_{m} M$       31
Foliation(s), induced on $\partial_{\tau} M$       31
Foliation(s), infinitesimally trivial at the boundary      91
Foliation(s), integrably homotopic      96
Foliation(s), integral to a $C^{0}$ hyperplane field      32 123—126
Foliation(s), integral to a $C^{0}$ plane field      32
Foliation(s), leafwise orientable      89
Foliation(s), lifted by covering map      81
Foliation(s), minimal      103
Foliation(s), normal bundle of      28
Foliation(s), smooth leaved      31
Foliation(s), tangent to submanifold      15
Foliation(s), taut, arbitrary codimension      261—272
Foliation(s), taut, codimension one      146
Foliation(s), taut, codimension-one      257—261
Foliation(s), transverse G-structure of      33
Foliation(s), transverse to submanifold      15

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