Morse inequalities for orbifold cohomology

Richard Hepworth
2009 Algebraic and Geometric Topology  
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
more » ... metry and topology -- flows of vector fields, the strong topology -- that are essential to the development of Morse theory on manifolds.
doi:10.2140/agt.2009.9.1105 fatcat:ts2vt2pym5hjbnh6jkiseuif3m