One graph to rule them all

Let P be a finite poset. We will show that for any P-persistent object X in the category of finite topological spaces there is a P- weighted graph, whose weighted clique complex has the same P-persistent homology as X. Joint work with A. Patania (ISI-PoliTO), M. Scolamiero (KTH) and G. Petri (ISI). Work done within the EU funded FET Open Project "TOPDRIM".