Lectures on Morse Homology

Augustin Banyaga, David Hurtubise - Collection Kluwer Texts in the Mathematical Sciences

324 pages, parution le 14/02/2005

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Résumé

This book presents in great detail all the results one needs to prove the Morse Homology Theorem using classical techniques from algebraic topology and homotopy theory. Most of these results can be found scattered throughout the literature dating from the mid to late 1900's in some form or other, but often the results are proved in different contexts with a multitude of different notations and different goals. This book collects all these results together into a single reference with complete and detailed proofs.

The core material in this book includes CW-complexes, Morse theory, hyperbolic dynamical systems (the Lamba-Lemma, the Stable/Unstable Manifold Theorem), transversality theory, the Morse-Smale-Witten boundary operator, and Conley index theory. More advanced topics include Morse theory on Grassmann manifolds and Lie groups, and an overview of Floer homology theories. With the stress on completeness and by its elementary approach to Morse homology, this book is suitable as a textbook for a graduate level course, or as a reference for working mathematicians and physicists.

Sommaire

Preface
Introduction
The CW-Homology Theorem
Basic Morse Theory
The Stable/Unstable Manifold Theorem
Basic Differential Topology
Morse-Smale Functions
The Morse Homology Theorem
Morse Theory on Grassmann Manifolds
An Overview of Floer Homology Theories
Hints and References for Selected Problems

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	PAPIER
Éditeur(s)	Kluwer Academic Publishers
Auteur(s)	Augustin Banyaga, David Hurtubise
Collection	Kluwer Texts in the Mathematical Sciences
Parution	14/02/2005
Nb. de pages	324
Format	16,5 x 24,5
Couverture	Relié
Poids	726g
Intérieur	Noir et Blanc
EAN13	9781402026959