Margalef-Roig J., Outerelo Dominguez E. — Differential topology :: Электронная библиотека попечительского совета мехмата МГУ

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Margalef-Roig J., Outerelo Dominguez E. — Differential topology

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Название: Differential topology

Авторы: Margalef-Roig J., Outerelo Dominguez E.

Аннотация:

...there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated are Banach manifolds with corners. Corners add to the complications and the authors have carefully fathomed the validity of all main results at corners. Even in finite dimensions some results at corners are more complete and better thought out here than elsewhere in the literature. The proofs are correct and with all details. I see this book as a reliable monograph of a well-defined subject; the possibility to fall back to it adds to the feeling of security when climbing in the more dangerous realms of infinite dimensional differential geometry.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1

Год издания: 1992

Количество страниц: 618

Добавлена в каталог: 23.10.2010

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Предметный указатель

$C^{p}$ -homotopy      465 466
$C^{p}$ -representation      409
$D_{n}$ as manifold      30
$S^{n}$ as a manifold      30
$T_{1}$ axiom      42
$T_{3}$ axiom      46
$T_{c^{0}}$ topology      449
$T_{c}$ topology      435
$T_{D}(p,k)$ topology      469
$T_{D}(\infty)$ topology      487
$T_{F}^{d^{'}}$ topology      440
$T_{p}$ topology      435
$T_{s}$ topology      436
$T_{u}$ topology      440
$T_{W}(p,k)$ topology      471
$T_{W}(\infty)$ topology      487
$T_{W}^{*}(\infty)$ topology      490
$z^{\infty}$ -set      337
$z^{\infty}$ -space      337 479
$[0,1]^{n}$ as manifold      31
$\sigma$ -proper map      402
Actions of Lie Groups on manifolds      294 295
Actions of Lie Groups, free      295
Actions of Lie Groups, proper      295
Actions of Lie Groups, transitive      295
Algebra      286
Atlas of a manifold      19
Atlas of class p      18
Atlas on a set      18
Axiom of Hausdorff      43
Baire space      44
Banach algebra      286
Banach space      2
Banach space of continuous linear maps      3
Banach space of continuous multilinear maps      5
Banach space of continuous n-linear maps      6
Banachable space      6
Basis of the strong topology $\bar{\mathcal{B}}_{s}^{***}$       446
Basis of the strong topology $\bar{\mathcal{B}}_{s}^{*}$       438
Basis of the strong topology $\mathcal{B}_{s}$       436
Basis of the strong topology $\mathcal{B}_{s}^{***}$       445
Basis of the strong topology $\mathcal{B}_{s}^{**}$       438
Basis of the strong topology $\mathcal{B}_{s}^{*}$       437
Basis of the strong topology $\mathcal{B}_{s}^{d^{'}}$       442
Boundary      28
Boundary invariance      25 38
Boundary of a differentiable manifold      22 28
Boundary of an open set of a quadrant      23
Brown theorem      372
Butt map (b)      428
Cauchy — Schwarz inequality      2
Centered chart      28
Chain rule formula      430
Change of variable      87
Characterization of closed embeddings      149 150
Characterization of closed submanifolds by embeddings      150
Characterization of embeddings      148
Characterization of immersions      132 134 137 140
Characterization of invertible jets      519
Characterization of local diffeomorphisms      103
Characterization of subimmersions      229 231 232 233 273 275 278
Characterization of submanifolds by embeddings      149
Characterization of submanifolds by immersions      130
Characterization of submersions      164 167 168
Characterization of topological spaces that admit differentiable structures      257 258 270
Characterization of transversal maps to a submanifold      313
Chart of a manifold      19
Chart on a set      18
Chart, adapted      113 114
Classification of 1-dimensional manifolds      373
Closed embedding      149
Codimension of a submanifold at a point      117
Coincidence of the topologies $T_{c^{0}}$ and $T_{s}$       451
Coincidence of the topologies $T_{c}$ and $T_{s}$       439
Coincidence of the topologies $T_{D}(p,k)$ and $T_{W}(p,k)$       477 478
Coincidence of the topologies $T_{D}(\infty)$ and $T_{W}(\infty)$       491 492
Coincidence of the topologies $T_{F}^{d^{'}}$ and $T_{s}$       441 442
Coindex of a non-degenerate critical point      572
Collar neighbourhoods      259 263
Compact operator      383
Compact-open topology      435
Compatible charts      18
Complete metric space      45
Complete topological linear space      6
Completely metrizable manifold      45
Composition of differentiable maps      11
Composition of Fredholm maps      392
Composition of Fredholm operators      388
Composition of immersions      142 143
Composition of jets      509 510
Composition of maps of class p      37
Composition of submersions      161
Connected manifolds      43
Contact of order larger than or equal to k      427
Continuity of the composition of maps in $T_{D}(p,k)$       510
Continuity of the composition of maps in $T_{W}(p,k)$       512
Continuity of the evaluation      513
Continuity of the fixed point      107
Continuous linear maps      3
Continuous multilinear maps      5
Convergence of sequences in $T_{s}$       454
Convergence of sequences in $T_{W}(p,k)$       482
Convergence of sequences in $T_{W}(\infty)$       495
Converse Taylor theorem      78 79
Convolution      524 525
Convolution kernel      524
Corank of a $C^{p}-map$       362
Corank of a jet      560
Cotangent space      180
Covering dimension      48
Covering dimension of differentiable manifolds      48
Covering projection      210
Critical point      362
Critical value      363
Density of $(LD)^{s}(X,X^{'})$ in $(LD)^{r}(X,X^{'})$ (s>r)      531
Density of $C^{p}(X,X^{'})$ in $C(X,X^{'})$       462
Density of $C^{s}(X,X^{'})$ in $C^{r}(X,X^{'})$ (s>r)      529 535
Density of $Diff^{s}(X,X^{'})$ in $Diff^{r}(X,X^{'})$ (s>r)      532
Density of $Emb^{s}(X,X^{'})$ in $Emb^{r}(X,X^{'})$ (s>r)      532 537
Density of $Emb_{c}^{s}(X,X^{'})$ in $Emb^(X,X^{'})$ (s>r)      532 538
Density of $Im^{s}(X,X^{'})$ in $Im^{r}(X,X^{'})$ (s>r)      531 537
Density of $Prop^{s}(X,X^{'})$ in $Prop^{r}(X,X^{'})$ (s>r)      532 537
Density of $Sub^{s}(X,X^{'})$ in $Sub^{r}(X,X^{'})$ (s>r)      531 537
Diffeomorphisms between manifolds      37
Diffeomorphisms of open sets of quadrants      24
Diffeomorphisms, induced on the smooth boundary      39
Diffeomorphisms, preserving index      38
Differentiable manifold      19
Differentiable map      10
Differentiable map at a point      9
Differentiable map locally constant      64
Differentiable map of Fredholm      391
Differentiable map of left Fredholm      391
Differentiable map on an open set      9
Differentiable structure of $S^{n}$       30
Differentiable structure of a closed ball      30
Differentiable structure of a quadrant      30
Differentiable structure of a submanifold      115
Differentiable structure of an open set      30
Differentiable structure of class p      19
Differentiable structure of n-cube      31
Differentiable structure of the Boundary $(\partial X)$       29
Differentiable structure of the interior of a manifold      29
Differentiable structure of the k-boundary $(B_{k}X)$       29
Differential      9 180
Differential of a composition      11
Differential of order p      12
Dimension of a manifold at a point      20
Divisible space      448
Domain of a chart      18

Double splitting operator      381
Elevation of the class of a manifold      538 540
Embedding      148
Embedding of manifolds in Banach spaces      152
Embedding of manifolds in Euclidean spaces      157
Embedding of manifolds in Hilbert spaces      152
Equivalence relations preserving boundary      190
Equivalent atlases      18
Equivalent norms      4
Euclidean space      3
Excellent Morse function      565 566
Existence of differentiable partitions of unity      51 61
Existence of fibered product of manifolds      332
Factorization of the subimmersions      277
Fibered product existence      332
Fibered product of manifolds      331 332
Fine topology      440
Finite order jets      427 428
Finite order weak topology      469
Finite order Whitney topology      470
Finite-dimensional operator      383
First axiom of countability      42
First category set      356
First theorem of Sard      372
Fixed point theorem      107
Fredholm map      391
Fredholm operator      381
Functional of class p      570
Fundamental theorem about quotient manifolds      191 205 206
Fundamental theorem of algebra      184
General Position Lemma      424 425
Germs of submanifolds      272 276 277
Gluing of manifolds      112
Godement lemma      244
Graph of a differentiable map      157
Graph topology      436
Grassmann F-manifolds      34
Grassmann manifolds      31
Groups of transformations      208
Groups of transformations acting discontinuously      209
Groups of transformations acting effectively      209
Groups of transformations acting freely      209
hessian      567 572
Hilbert direct sum (finite case)      150
Hilbert direct sum (infinite case)      151
Hilbert group      291
Hilbert manifold      157
Hilbert space      3
Homogeneous spaces      293
Homotopic maps      460 461 465 466 467 468
Homotopy of class p      465 466 467 468
Immersion      128
Immersion at a point      128
Immersion of a compact-manifold in a euclidean space      157
Immersion of a manifold in a Banach space      152
Immersion of a manifold in a Hilbert space      157
Immersion of a n-dimensional manifold in $\mathbb{R}^{2n}$       565
Implicit function theorem      108 109
Implicit function theorem, injective version      131
Implicit function theorem, surjective version      163
Index of a Fredholm map      391
Index of a Fredholm operator      381
Index of a left Fredholm map      391
Index of a left Fredholm operator      381
Index of a non-degenerate critical point      572
Index of a point in a manifold      27
Index of a point in a quadrant      22 23
Index of an inner tangent vector      137
Index of Kronecker      8
Infinite order jets      486
Injective version of the implicit mapping theorem      131
Inner product      2
Inner tangent vector      68
integral      86
Interior of a manifold      28
Interior of an open set of a quadrant      23
Invariance of sets of measure zero under $C^{1}$ -maps      348 356
Invariance of the boundary under diffeomorphisms      25 38
Invariance of the index under diffeomorphisms      25 38
Inverse image of a submanifold by means of a submersion      174 176 177 179 182
Inverse image of a submanifold by means of a transversal map      319 325
Inverse mapping theorem      100 101 102 103
Invertible jet      518
Jets of finite order      428
Jets of infinite order      486
K-boundary      28
Klein bottle      213
Kupka example      401
Left Fredholm map      391
Left Fredholm operator      381
Left limit      85
Leibnitz's rule      73
Lens manifolds      213
Lie group      283
Lie group homomorphisms      288
Lie subgroups      289
Linear reduction of a differentiable map      176
Local characterization of the subimmersions      273
Local compactness in manifolds      43
Local connection in manifolds      43
Local diffeomorphisms      102
Locally closed maps      395
Locally compact space      43
Locally connected space      43
Locally Lipschitz maps      349
Locally path-connected space      43
Locally proper maps      394
m-cube      345
m-rectangle      345
Manifold of germs of submanifolds      277
Manifold of jets      432
Manifold of Stiefel      305
Map of class p      15
Map of class p between manifolds      36
Map of Morse      565
Maps, $j^{k}$       434
Maps, $j^{k}(f)$       434
Maps, $j^{\infty}$       486
Maps, $j^{\infty}(f)$       486
Maps, $r^{\infty}_{k}$       486
Maps, $r_{k^{'}}^{k}$       429
Maps, b      428
Maps, s      428
Measure zero set      345 354
Metric associated to a norm      2
Metrizable manifold      45 46
Moebioeus strip      212
Morphism of a chart      18
Morse function      565
Morse lemma      572
n-dimensional torus      212
Neat submanifold      118
Non-degenerate critical point      572
Norm      1
Norm associated to an inner product      2
Normal bundle manifold      238
Normed real linear space      1
Nowhere dense subset      351 355
On the smooth boundary      29
Open linear maps      4
Open manifold      30
Open set of a quadrant      9
Open submanifold      116
Openness of closed embeddings      507
Openness of diffeomorphisms      507
Openness of embeddings      503
Openness of immersions      497
Openness of local diffeomorphisms      498
Openness of proper maps in $T_{s}$       458
Openness of submersions      497

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