Computing persistent homology: A Morse theory perspective. Recording 44 min, password Morse1928
In this talk, we will see how algebraic Morse theory can be used to obtain filtered chain equivalences between chain complexes described by intermediate matrices in persistence computations. This connection enables us to cast some of the commonly encountered persistence algorithms in terms of algebraic Morse theory. As an application of this framework, we will describe a new algorithm for computing persistence that fully exploits this structure resulting in improved output sensitive complexity bounds. The talk is based on joint work with Ulrich Bauer and Talha bin Masood.