Differential Topology

" ... 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 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 ...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