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Morse Inequalities for Orbifold Cohomology

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  • Richard A. Hepworth
This paper begins the study of Morse theory for orbifolds, or more precisely 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.
OriginalsprogEngelsk
TidsskriftAlgebraic & Geometric Topology
Vol/bind9
Udgave nummer2
Sider (fra-til)1105-1175
ISSN1472-2747
DOI
StatusUdgivet - 2009

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