ENGLISH

Morse Homology

By Matthias Schwarz (auth.)

Book information

Publisher
Birkhäuser Basel
Year
1993
ISBN
978-3-0348-9688-7, 978-3-0348-8577-5
DOI
10.1007/978-3-0348-8577-5
Language
english
Format
PDF
Filesize
4 MB (4710513 bytes)
Series
Progress in Mathematics 111
Edition
1
Pages
236\242
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Analysis; Geometry; Topology

Description

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.

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