**Optimal discrete Morse functions for 2-manifolds**

*Thomas Lewiner, Hélio Lopes, Geovan Tavares*

## Abstract:

Morse theory was originally formulated for smooth manifolds. Recently, Robin Forman formulated a version of this theory for discrete structures such as cell complexes. It opens up several categories of interesting objects (particularly meshes) to applications of Morse theory. Once a Morse function has been defined on a manifold, then information about its topology can be deduced from its critical elements. This paper introduces a linear algorithm to define optimal discrete Morse functions on discrete 2-manifolds, where optimality entails having the least number of critical elements. The algorithm presented is also extended to general finite cell complexes of dimension at most 2, with no guarantee of optimality.## Downloads:

PDF paper (1 MB)## BibTeX:

@article{optimal_morse_cgta,author = {Thomas Lewiner and Hélio Lopes and Geovan Tavares},

title = {Optimal discrete Morse functions for 2-manifolds},

year = {2003},

month = {november},

journal = {Computational Geometry: Theory and Applications},

volume = {26},

number = {3},

pages = {221--233},

publisher = {Elsevier},

doi = {10.1016/S0925-7721(03)00014-2},

url = {\url{http://thomas.lewiner.org/pdfs/optimal_morse_cgta.pdf}}

}