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.
Citation
K. C. Chang. N. Ghoussoub. "The Conley index and the critical groups via an extension of Gromoll-Meyer theory." Topol. Methods Nonlinear Anal. 7 (1) 77 - 93, 1996.
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