Abstract
In [J. Topol. Anal. 6 (2014), 305–338], we have developed a homology theory (Morse–Conley–Floer homology) for isolated invariant sets of arbitrary flows on finite-dimensional manifolds. In this paper, we investigate functoriality and duality of this homology theory. As a preliminary, we investigate functoriality in Morse homology. Functoriality for Morse homology of closed manifolds is known, but the proofs use isomorphisms to other homology theories. We give direct proofs by analyzing appropriate moduli spaces. The notions of isolated map and flow map allow the results to generalize to local Morse homology and Morse–Conley–Floer homology. We prove Poincaré-type duality statements for local Morse homology and Morse–Conley–Floer homology.
Highlights
We address functoriality and duality properties of Morse homology, local Morse homology and Morse–Conley–Floer homology
The functoriality of Morse homology on closed manifolds is known [1, 2, 3, 9, 15], no proofs are given through the analysis of moduli spaces
Duality in Morse–Conley–Floer homology In Section 8 we prove a Poincare-type duality theorem for Morse–Conley– Floerhomology
Summary
The functoriality of Morse homology on closed manifolds is known [1, 2, 3, 9, 15], no proofs are given through the analysis of moduli spaces. Is a detailed description of the results in this paper
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