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Morse Functions Read chapter Read first chapter

2014 | OriginalPaper | Chapter

4. Morse Homology, Applications

Authors : Michèle Audin, Mihai Damian

Published in: Morse Theory and Floer Homology

Publisher: Springer London

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Abstract

We give a few computations and a few applications of Morse homology: the Knnneth formula for products, the Poincaré duality, the Euler characteristic (and the Morse inequalities), the link with the connectedness and the simple connectedness of the manifold in question. We also show the functoriality of Morse homology and present a long exact sequence for a pair consisting of a manifold and a submanifold.

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previous chapter The Morse Complex
next chapter What You Need to Know About Symplectic Geometry
Appendix
Available only for authorised users
Footnotes
1
The existence of such a diffeomorphism can be proved by integrating a suitable vector field on the disk D N , an exercise whose details are left to the readers (Exercise 19 on p. 122).
 
2
For the readers who know what this is, it is indeed the relative homology obtained by excision; see for example [25].
 
3
Recall that we can obtain such an i using the flow of a vector field that points inward.
 
4
For another point of view, we refer to Laudenbach’s appendix in [12].
 
Metadata
Title
Morse Homology, Applications
Authors
Michèle Audin
Mihai Damian
Copyright Year
2014
Publisher
Springer London
Book
Morse Theory and Floer Homology

Print ISBN: 978-1-4471-5495-2

Electronic ISBN: 978-1-4471-5496-9

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-1-4471-5496-9_4

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