Morse Inequalities for Orbifold Cohomology

Research output: Contribution to journalArticle

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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.
Original languageEnglish
Pages (from-to)1105-1175
Number of pages71
JournalAlgebraic & Geometric Topology
Volume9
Issue number2
DOIs
Publication statusPublished - 2 Jun 2009

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Morse Inequalities
Orbifold
Cohomology
Morse Theory
Differentiable
Morse Function
Betti numbers
Differential Geometry
Critical point
Vector Field
Analogue

Cite this

Morse Inequalities for Orbifold Cohomology. / Hepworth, Richard.

In: Algebraic & Geometric Topology, Vol. 9, No. 2, 02.06.2009, p. 1105-1175.

Research output: Contribution to journalArticle

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