Discrete Morse theory and extended L² homology

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dc.contributor.authorVarghese, M.
dc.contributor.authorYates, S.
dc.date.issued1999
dc.description.abstractA brief overview of Forman's discrete Morse theory is presented, from which analogues of the main results of classical Morse theory can be derived for discrete Morse functions, these being functions mapping the set of cells of a CW complex to the real numbers satisfying some combinatorial relations. The discrete analogue of the strong Morse inequality was proved by Forman for finite CW complexes using a Witten deformation technique. This deformation argument is adapted to provide strong Morse inequalities for infinite CW complexes which have a finite cellular domain under the free cellular action of a discrete group. The inequalities derived are analogous to the L<sup>2</sup> Morse inequalities of Novikov and Shubin and the asymptotic L<sup>2</sup> Morse inequalities of an inexact Morse 1-form as derived by Mathai and Shubin. We also obtain quantitative lower bounds for the Morse numbers whenever the spectrum of the Laplacian contains zero, using the extended category of Farber. © 1999 Academic Press.
dc.identifier.citationJournal of Functional Analysis, 1999; 168(1):84-110
dc.identifier.doi10.1006/jfan.1999.3439
dc.identifier.issn0022-1236
dc.identifier.issn1096-0783
dc.identifier.orcidVarghese, M. [0000-0002-1100-3595]
dc.identifier.urihttp://hdl.handle.net/2440/3597
dc.language.isoen
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE
dc.source.urihttps://doi.org/10.1006/jfan.1999.3439
dc.titleDiscrete Morse theory and extended L² homology
dc.title.alternativeDiscrete Morse theory and extended L(2) homology
dc.typeJournal article
pubs.publication-statusPublished

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