Morse Complexes for Piecewise Linear 3-Manifolds

We define the Morse complex of a Morse function over a 3manifold as the overlay of the stable and unstable 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.

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