$P$-persistent homology of finite topological spaces

Abstract

Let $P$ be a finite poset. We will show that for any reasonable $P$-persistent object $X$ in the category of finite topological spaces, there is a $P-$ weighted graph, whose clique complex has the same $P$-persistent homology as $X$.

References in corpus (2)

• On Derived Equivalences of Categories of Sheaves Over Finite Posets
• Persistent homology analysis of brain artery trees