Morse Inequalities for Orbifold Cohomology

Details Morse Inequalities for Orbifold Cohomology Morse Inequalities for Orbifold Cohomology

2007-12-14

arxiv.org/abs/0712.2432v1

Algebr. Geom. Topol. 9 (2009), no. 2, 1105-1175

Mathematics

Algebraic Topology

Scientific paper

10.2140/agt.2009.9.1105

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.

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