Polyhedral Representation of Discrete Morse Functions on Regular CW Complexes and Posets

Details Polyhedral Representation of Discrete Morse Functions on Regular CW Complexes and Posets Polyhedral Representation of Discrete Morse Functions on Regular CW Complexes and Posets

2010-08-22

arxiv.org/abs/1008.3724v1

Mathematics

Combinatorics

Scientific paper

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.

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