Morse inequalities for orbifold cohomology

Hepworth, Richard

doi:10.2140/agt.2009.9.1105

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Morse inequalities for orbifold cohomology

Richard Hepworth

Algebraic & Geometric Topology 9 (2009) 1105–1175

DOI: 10.2140/agt.2009.9.1105

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/

Volume 9, issue 2 (2009)