Discrete Morse Theory from A Graph Matching Perspective

Thursday, October 30, 2014 - 2:00pm - 3:00pm
Lind 305
Patricia Hersh (North Carolina State University)
Robin Forman introduced a discrete version of Morse theory as a way of studying topological structure (e.g. Betti numbers and homotopy type) of simplicial complexes and of more general finite CW complexes. Chari observed that to construct a discrete Morse function, it suffices to find a certain type of graph theoretic matching on the Hasse diagram of the face poset of the complex of interest. Soon thereafter, numerous applications began to be found by an assortment of people, most (if not all) of which boiled down to finding suitable graph theoretic matchings. I will give an overview of this area, including joint work with Eric Babson regarding order complexes of partially ordered sets. Background in topological combinatorics will not be assumed.