Persistence Simplifiation of Discrete Morse Functions on Surfaces

Abstract

We combine the concept of persistent homology with Forman's discrete Morse theory on regular 2-manifold CW complexes to solve the problem of minimizing the number of critical points among all functions within a prescribed distance from a given input function. We give a constructive proof of the tightness of the lower bound on the number of critical points provided by the Stability Theorem of persistent homology.