Morse Inequalities for Orbifold Cohomology

Abstract

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.

References in corpus (4)

• A New Cohomology Theory for Orbifold
• Orbifolds as Groupoids: an Introduction
• Foundations of Topological Stacks I
• Differentiable Stacks and Gerbes

Cited by in corpus (6)

• Riemannian metrics on Lie groupoids
• Vector Fields and Flows on Differentiable Stacks
• Gauge-fixing on the Lattice via Orbifolding
• Proper Orbifold Cohomology
• The index of a vector field on an orbifold with boundary
• Approximating orbifold spectra using collapsing connected sums