Using Morse homology to understand persistence modules II

Geometry Topology Working Seminar
Friday, December 2, 2022 - 2:00pm for 1.5 hours (actually 80 minutes)
Skiles 006
Daniel Irvine – Georgia Tech –
John Etnyre

Morse theory and Morse homology together give a method for understanding how the topology of a smooth manifold changes with respect to a filtration of the manifold given by sub-level sets. The Morse homology of a smooth manifold can be expressed using an algebraic object called a persistence module. A persistence module is a module graded by real numbers, and in this setup the grading on the module corresponds to the aforementioned filtration on the smooth manifold.

This is the second of a series of talks that aims to explain the relationship between Morse homology and persistence modules. In this second talk, I will define persistence modules, explain how to compute Morse homology using persistence modules, and explain how the K√ľnneth theorem and the cup product work with persistence modules. The material from the first part of this series will be assumed.