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Introduction

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

Abstract

The subject of this book is Morse homology as a combination of relative Morse theory and Conley’s continuation principle. The latter will be used as 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.

Keywords

Homology Group Fredholm Operator Morse Index Morse Theory Morse Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 1993

Authors and Affiliations

  1. 1.MathematikETH ZentrumZürichSwitzerland

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