The Generalized Persistence Diagram Encodes the Bigraded Betti Numbers

Explore the relationship between generalized persistence diagrams and bigraded Betti numbers in this 39-minute lecture from the Applied Algebraic Topology Network. Discover how the generalized persistence diagram, introduced by Kim and Mémoli, encodes the bigraded Betti numbers of finite 2-parameter persistence modules. Learn to visually interpret bigraded Betti numbers from the generalized persistence diagram, similar to the extraction method used for interval decomposable modules. Understand the implications of these findings, which reveal that all invariants of 2-parameter persistence modules computed by RIVET software are encoded within the generalized persistence diagram.