Reducing Complexes with Discrete Morse Theory

Abstract: Simplicial decompositions of spaces often introduce large number of simplices which can become a nuisance especially in computational settings. Inspired by smooth Morse theory, Forman introduced discrete Morse theory which, among its many applications, offers an approach to reduce many kinds of cell complexes. In this talk we first introduce an abstract cell complex that unifies various combinatorial spaces—such as simplicial and CW complexes. We then show how discrete Morse theory allows us to reduce a finite cell complex to a Morse complex which contains less cells while preserving the homology.

algebraic topologycategory theory

Audience: researchers in the topic

Bilkent Topology Seminar

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Recordings of talks available at www.youtube.com/channel/UCLrmyGpqxyeVpTcA1b5HcMw/videos