Positivity of Multiparameter Persistence Diagrams and Bottleneck Stability

Abstract

Persistent homology studies the birth and death of cycles in a parameterized family of spaces. In this paper, we study the birth and death of cycles in a multifiltration of a chain complex with the goal of producing a persistence diagram that satisfies bottleneck stability.

The claim that Dgm(S^n) is finite is not true. Our second paper "Edit Distance and Persistence Diagrams over Lattice" on multiparameter persistent homology also using the Mobius inversion formula is more to our liking