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About this book
The homotopy index theory was developed by Charles Conley for two sided flows on compact spaces. The homotopy or Conley index, which provides an algebraic-topologi cal measure of an isolated invariant set, is defined to be the ho motopy type of the quotient space N /N , where is a certain 1 2 1 2 compact pair, called an index pair. Roughly speaking, N1 isolates the invariant set and N2 is the "exit ramp" of N . 1 It is shown that the index is independent of the choice of the in dex pair and is invariant under homotopic perturbations of the flow. Moreover, the homotopy index generalizes the Morse index of a nQnde generate critical point p with respect to a gradient flow on a com pact manifold. In fact if the Morse index of p is k, then the homo topy index of the invariant set {p} is Ik - the homotopy type of the pointed k-dimensional unit sphere.
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Table of contents (3 chapters)
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Front Matter
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Back Matter
Authors and Affiliations
Bibliographic Information
Book Title: The Homotopy Index and Partial Differential Equations
Authors: Krzysztof P. Rybakowski
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-642-72833-4
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1987
Softcover ISBN: 978-3-540-18067-8Published: 24 August 1987
eBook ISBN: 978-3-642-72833-4Published: 06 December 2012
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XII, 208
Topics: Manifolds and Cell Complexes (incl. Diff.Topology), Analysis