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Functoriality and duality in Morse-Conley-Floer homology | T.O. Rot
; R.C.A.M. Vandervorst
; | Date: |
16 Sep 2014 | Abstract: | In~cite{rotvandervorst} a homology theory --Morse-Conley-Floer homology--
for isolated invariant sets of arbitrary flows on finite dimensional manifolds
is developed. 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~cite{abbondandoloschwarz, aizenbudzapolski,audindamian,
kronheimermrowka, schwarz}, but the proofs use isomorphisms to other homology
theories. We give direct proofs by analyzing appropriate moduli spaces. The
notions of isolating map and flow map allows the results to generalize to local
Morse homology and Morse-Conley-Floer homology. We prove Poincar’e type
duality statements for local Morse homology and Morse-Conley-Floer homology. | Source: | arXiv, 1409.4649 | Services: | Forum | Review | PDF | Favorites |
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