Poincaré-Lefschetz duality for the homology Conley index

Author:
Christopher McCord

Journal:
Trans. Amer. Math. Soc. **329** (1992), 233-252

MSC:
Primary 58F25; Secondary 55N20, 58F09

MathSciNet review:
1036005

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Abstract | References | Similar Articles | Additional Information

Abstract: The Conley index for continuous dynamical systems is defined for (one-sided) semiflows. For (two-sided) flows, there are two indices defined: one for the forward flow; and one for the reverse flow. In general, the two indices give different information about the flow; but for flows on orientable manifolds, there is a duality isomorphism between the homology Conley indices of the forward and reverse flows. This duality preserves the algebraic structure of many of the constructions of the Conley index theory: sums and products; continuation; attractor-repeller sequences and connection matrices.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1992-1036005-X

Keywords:
Conley index,
homology Conley index,
Poincaré duality

Article copyright:
© Copyright 1992
American Mathematical Society