Morse-smale complexes for piecewise linear 3-manifolds

Authors:
Herbert Edelsbrunner;John Harer;Vijay Natarajan;Valerio Pascucci
Affiliations:
Duke University, Durham, North Carolina;Duke University, Durham, North Carolina;Duke University, Durham, North Carolina;Lawrence Livermore Natl. Lab, Livermore, California
Venue:
Proceedings of the nineteenth annual symposium on Computational geometry
Year:
2003

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Abstract

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.