...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
Author(s): Leopoldo Nachbin (Eds.)
Series: North-Holland Mathematics Studies 173
Edition: 1
Publisher: North Holland
Year: 1992
Language: English
Pages: ii-xv, 1-603
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
