Poincaré-Lefschetz duality for the homology Conley index

McCord, Christopher

doi:10.1090/S0002-9947-1992-1036005-X

Poincaré-Lefschetz duality for the homology Conley index
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Trans. Amer. Math. Soc. 329 (1992), 233-252 Request permission

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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