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  • © 1993

Morse Homology

Birkhäuser

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

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  • ISBN: 978-3-0348-8577-5
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Table of contents (5 chapters)

  1. Front Matter

    Pages i-ix
  2. Introduction

    • Matthias Schwarz
    Pages 1-19
  3. The Trajectory Spaces

    • Matthias Schwarz
    Pages 21-101
  4. Orientation

    • Matthias Schwarz
    Pages 103-132
  5. Morse Homology Theory

    • Matthias Schwarz
    Pages 133-198
  6. Extensions

    • Matthias Schwarz
    Pages 199-206
  7. Back Matter

    Pages 207-236

About this book

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

Reviews

    "The proofs are written with great care, and Schwarz motivates all ideas with great skill...This is an excellent book."   
  - Bulletin of the AMS   

Authors and Affiliations

  • Mathematik, ETH Zentrum, Zürich, Switzerland

    Matthias Schwarz

Bibliographic Information

  • Book Title: Morse Homology

  • Authors: Matthias Schwarz

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-8577-5

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel 1993

  • Hardcover ISBN: 978-3-7643-2904-4

  • Softcover ISBN: 978-3-0348-9688-7

  • eBook ISBN: 978-3-0348-8577-5

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: IX, 236

  • Topics: Topology, Analysis, Geometry

Buying options

eBook USD 69.99
Price excludes VAT (USA)
  • ISBN: 978-3-0348-8577-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 89.99
Price excludes VAT (USA)
Hardcover Book USD 89.99
Price excludes VAT (USA)