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).
Applied Topology Seminar
Thursday, April 19, 2018 - 3:00pm
Kevin Knudsen
University of Florida