Title: An alternative to Novikov-Morse theory from the perspective of topological persistence
Speaker: Dan Burghelea (Ohio State University)
Abstract: A large class of flows of interest have trajectories minimizing “actions.” Novikov theory extends Morse theory to relate the dynamics of such a generic smooth flow (vector field with a Lyapunov closed one form with Morse zeros) on a closed smooth manifold to the underlying topology of the manifold.
I have proposed an alternative to such theory which weakens the hypothesis (closed manifold, closed Morse one form) to compact ANR, topological closed one form, and is computer friendly based on ‘`topological persistence.’' In this talk I will explain the topology behind this approach and the new invariants involved in.
Seminar URL: https://research.math.osu.edu/topology/
