Morse Theory on Meshes

In this report, we discuss two papers that deal with computing Morse function on triangulated manifolds. Axen [1] gives an algorithm for computing Morse function on a triangulated manifold of arbitrary dimension but it not practical because of its space requirement. Hence, he describes an algorithm for computing critical points and their Morse indices for a 2-manifold. Edelsbrunner et al. [2] deals with compact 2-manifolds without any boundary. The paper describes how to derive a Morse complex for such a manifold and also talks about how to simply the complex by canceling pairs of critical points in order of increasing persistence.