The Development Of Morse Theory On Orbifold

Morse theory and orbifold are two different concepts in the study of geometric topology and analysis. Classical Morse theory is a geometric way to understand the homology of manifolds. Orbifolds are spaces that locally look like the quotient of a manifold by a finite group. Richard Hepworth link up the two concepts and beginsthe study of Morse theory for orbifolds, or more precisely for differentiableDeligne-Mumford stacks. This paper reviewed the results, first introduced the classical Morse theory, and then the introduction of orbifold Morse theory, at the last is some results of Morse theory on the discrete space.