Differential Topology

Leopoldo Nachbin (Eds.)0444884343, 9780444884343, 9780080872841

…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.
Peter W. Michor

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Table of contents :
Content:
Edited by
Page ii

Copyright page
Page iv

Dedication
Page v

Preface
Pages ix-x
Peter W. Michor

Introduction
Pages xi-xv

Chapter 1 Real Differentiable Manifolds with Corners
Pages 1-72

Chapter 2 The Whitney Extension Theorem and the Inverse Mapping Theorem for Differentiable Manifolds with Corners
Pages 73-112

Chapter 3 Submanifolds and Immersions
Pages 113-158

Chapter 4 Submersions and Quotient Manifolds
Pages 159-213

Chapter 5 Subimmersions
Pages 215-281

Chapter 6 Lie Groups
Pages 283-308

Chapter 7 Transversality
Pages 309-343

Chapter 8 Parametrized Theorems of the Density of the Transversality
Pages 345-425

Chapter 9 Spaces of Differentiable Maps
Pages 427-522

Chapter 10 Approximation of Differentiable Maps
Pages 523-541

Chapter 11 Openness and Density of the Transversality
Pages 543-573

Bibliography
Pages 575-587

Index
Pages 589-603