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2009 Morse inequalities for orbifold cohomology
Richard Hepworth
Algebr. Geom. Topol. 9(2): 1105-1175 (2009). 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.

Citation

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Richard Hepworth. "Morse inequalities for orbifold cohomology." Algebr. Geom. Topol. 9 (2) 1105 - 1175, 2009. https://doi.org/10.2140/agt.2009.9.1105

Information

Received: 14 November 2008; Revised: 2 May 2009; Accepted: 7 May 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1175.55004
MathSciNet: MR2511141
Digital Object Identifier: 10.2140/agt.2009.9.1105

Subjects:
Primary: 57N65, 57R70

Keywords: Morse theory, orbifolds

Rights: Copyright © 2009 Mathematical Sciences Publishers

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Vol.9 • No. 2 • 2009
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