Algebraic & Geometric Topology

Morse inequalities for orbifold cohomology

Richard Hepworth

Full-text: Open access

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.

Article information

Source
Algebr. Geom. Topol., Volume 9, Number 2 (2009), 1105-1175.

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513797010

Digital Object Identifier
doi:10.2140/agt.2009.9.1105

Mathematical Reviews number (MathSciNet)
MR2511141

Zentralblatt MATH identifier
1175.55004

Subjects
Primary: 57N65: Algebraic topology of manifolds 57R70: Critical points and critical submanifolds

Keywords
Morse theory orbifolds

Citation

Hepworth, Richard. Morse inequalities for orbifold cohomology. Algebr. Geom. Topol. 9 (2009), no. 2, 1105--1175. doi:10.2140/agt.2009.9.1105. https://projecteuclid.org/euclid.agt/1513797010


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