2010/08/22 by Ethan D. Bloch, Bloch, Ethan D.
Computer Science · Mathematics · #Digital Image Processing Techniques #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.CO #math.GT
paper · pdf · doi:10.48550/arxiv.1008.3724
arxiv created 2010/08/22 · arxiv updated 2010/08/24
It is proved that every discrete Morse function in the sense of Forman on a finite regular CW complex can be represented by a polyhedral Morse function in the sense of Banchoff on an appropriate embedding in Euclidean space of the barycentric subdivision of the CW complex; such a representation preserves critical points. The proof is stated in terms of discrete Morse functions on a class of posets that is slightly broader than the class of face posets of finite regular CW complexes.