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Applied Topology Seminar

Thursday, April 19, 2018 - 3:00pm

Kevin Knudsen

University of Florida

Location

University of Pennsylvania

4E19 DRL

Inspired by the work of Forman on discrete Morse theory, which is a
combinatorial adaptation to cell complexes of classical Morse theory
on manifolds, we introduce a discrete analogue of the stratified Morse
theory of Goresky and MacPherson. We describe the basics of this
theory and prove fundamental theorems relating the topology of a
general simplicial complex with the critical simplices of a discrete
stratified Morse function on the complex. We also provide an algorithm
that constructs a discrete stratified Morse function out of an
arbitrary function defined on a finite simplicial complex; this is
different from simply  constructing a discrete Morse function on such
a complex. We give simple examples to convey the utility of our
theory. This is joint work with Bei Wang (U. Utah).