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Abstract: This paper begins the study of Morse theory for orbifolds, or more preciselyfor differentiable Deligne-Mumford stacks. The main result is an analogue ofthe Morse inequalities that relates the orbifold Betti numbers of analmost-complex orbifold to the critical points of a Morse function on theorbifold. We also show that a generic function on an orbifold is Morse. Inobtaining these results we develop for differentiable Deligne-Mumford stacksthose tools of differential geometry and topology - flows of vector fields,the strong topology - that are essential to the development of Morse theory onmanifolds.



Autor: Richard A. Hepworth

Fuente: https://arxiv.org/



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