Title: Persistent homology and its fibre

Abstract:

Persistent homology is a main tool in topological data analysis. So it is natural to ask how strong this invariant is and how much information is lost. There are many ways to ask this question. Here we will concentrate on the case of level set filtrations on simplicial sets. Already the example of a triangle yields a rich structure with the Möbius band showing up as one of the fibres. Our analysis forces us to look at the persistence map with fresh eyes.

The talk will be based on joint work with Jacob Leygonie: https://arxiv.org/pdf/2104.01372.pdf