Morse Inequalities for Orbifold Cohomology
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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.
Originalsprog | Engelsk |
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Tidsskrift | Algebraic & Geometric Topology |
Vol/bind | 9 |
Udgave nummer | 2 |
Sider (fra-til) | 1105-1175 |
ISSN | 1472-2747 |
DOI | |
Status | Udgivet - 2009 |
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