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Rot, T. O. and Vandervorst, R. C. A. M. (2014). Functoriality and duality in Morse-Conley-Floer homology. J. Fixed Point Theory Appl., 16 (1-2). S. 437 - 477. BASEL: SPRINGER BASEL AG. ISSN 1661-7746

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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 Poincar,-type duality statements for local Morse homology and Morse-Conley-Floer homology.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Rot, T. O. UNSPECIFIED UNSPECIFIED UNSPECIFIED Vandervorst, R. C. A. M. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-421011
DOI:	10.1007/s11784-015-0223-6
Journal or Publication Title:	J. Fixed Point Theory Appl.
Volume:	16
Number:	1-2
Page Range:	S. 437 - 477
Date:	2014
Publisher:	SPRINGER BASEL AG
Place of Publication:	BASEL
ISSN:	1661-7746
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language INDEX Multiple languages Mathematics, Applied; Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/42101