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Morse Homology

  • Matthias Schwarz

Part of the Progress in Mathematics book series (PM, volume 111)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Matthias Schwarz
    Pages 1-19
  3. Matthias Schwarz
    Pages 21-101
  4. Matthias Schwarz
    Pages 103-132
  5. Matthias Schwarz
    Pages 133-198
  6. Matthias Schwarz
    Pages 199-206
  7. Back Matter
    Pages 207-236

About this book

Introduction

1.1 Background The subject of this book is Morse homology as a combination of relative Morse theory and Conley's continuation principle. The latter will be useda s an instrument to express the homology encoded in a Morse complex associated to a fixed Morse function independent of this function. Originally, this type of Morse-theoretical tool was developed by Andreas Floer in order to find a proof of the famous Arnold conjecture, whereas classical Morse theory turned out to fail in the infinite-dimensional setting. In this framework, the homological variant of Morse theory is also known as Floer homology. This kind of homology theory is the central topic of this book. But first, it seems worthwhile to outline the standard Morse theory. 1.1.1 Classical Morse Theory The fact that Morse theory can be formulated in a homological way is by no means a new idea. The reader is referred to the excellent survey paper by Raoul Bott [Bol.

Keywords

Finite Manifold Morphism Topology calculus function geometry proof theorem

Authors and affiliations

  • Matthias Schwarz
    • 1
  1. 1.MathematikETH ZentrumZürichSwitzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-8577-5
  • Copyright Information Birkhäuser Verlag Basel 1993
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-0348-9688-7
  • Online ISBN 978-3-0348-8577-5
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site