Volume 9, issue 2 (2009)

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Morse inequalities for orbifold cohomology

Richard Hepworth

Algebraic & Geometric Topology 9 (2009) 1105–1175
Abstract

This paper begins the study of Morse theory for orbifolds, or equivalently for differentiable Deligne–Mumford stacks. The main result is an analogue of the Morse inequalities that relates the orbifold Betti numbers of an almost-complex orbifold to the critical points of a Morse function on the orbifold. We also show that a generic function on an orbifold is Morse. In obtaining these results we develop for differentiable Deligne–Mumford stacks those tools of differential geometry and topology—flows of vector fields, the strong topology—that are essential to the development of Morse theory on manifolds.

Keywords
Morse theory, orbifolds
Mathematical Subject Classification 2000
Primary: 57N65, 57R70
References
Publication
Received: 14 November 2008
Revised: 2 May 2009
Accepted: 7 May 2009
Published: 2 June 2009
Authors
Richard Hepworth
Department of Pure Mathematics
University of Sheffield
Sheffield
United Kingdom
http://www.hepworth.staff.shef.ac.uk/