Morse-smale complexes for piecewise linear 3-manifolds

We define the Morse-Smale complex of a Morse function over a 3-manifold as the overlay of the descending and ascending manifolds of all critical points. In the generic case, its 3-dimensional cells are shaped like crystals and are separated by quadrangular faces. In this paper, we give a combinatorial algorithm for constructing such complexes for piecewise linear data. Keywords. Computational geometry and topology, Morse theory, densities, triangulations, combinatorial algorithms.

• Type: Conference
• Year: 2003
• Where: COMPGEOM
• Authors: Herbert Edelsbrunner, John Harer, Vijay Natarajan, Valerio Pascucci
• Keywords: Combinatorial Algorithms, COMPGEOM 2003, Morse Function, Piecewise Linear Data