Topological Methods in Nonlinear Analysis

The Conley index and the critical groups via an extension of Gromoll-Meyer theory

K. C. Chang and N. Ghoussoub

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Abstract

We investigate, in a variational setting, the relationship between the Gromoll-Meyer pairs of a dynamically isolated critical set and the Conley index pairs of its isolating invariant neighbourhoods. We show that the information given by the critical groups of such a set is equivalent to that given by the Conley index. This allows us to derive - in a non-compact setting - various invariance properties for the Conley index from those of the critical groups, as well as a formula relating the degree of a gradient vector field in an isolating neighbourhood to the Conley index pair associated with it.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 7, Number 1 (1996), 77-93.

Dates
First available in Project Euclid: 16 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1479265320

Mathematical Reviews number (MathSciNet)
MR1422006

Zentralblatt MATH identifier
0898.58006

Citation

Chang, K. C.; Ghoussoub, N. The Conley index and the critical groups via an extension of Gromoll-Meyer theory. Topol. Methods Nonlinear Anal. 7 (1996), no. 1, 77--93. https://projecteuclid.org/euclid.tmna/1479265320


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