H. Edelsbrunner, J. Harer, A. Zomorodian, Hierarchical Morse-Smale Complexes for Piecewise Linear 2-Manifolds, Discrete Comp. Geom., 30 (2003), 87-107.

Abstract:

We present algorithms for constructing a hierarchy of increasingly coarse Morse complexes that decompose a piecewise linear 2-manifold. While Morse complexes are defined only in the smooth category, we extend the construction to the piecewise linear category by ensuring structural integrity and simulating differentiability. We then simplify Morse complexes by cancelling pairs of critical points in order of increasing persistence.

Bibtex: 

@article{ehz-hmscpl2m-03,
  author = "Edelsbrunner, H. and Harer, J. and Zomorodian, A.",
  title = "Hierarchical {M}orse-{S}male Complexes for Piecewise 
           Linear 2-Manifolds",
  journal = "Discrete Comput. Geom.",
  year = 2003,
  volume = 30,
  pages = "87--107",
}