Wasserstein distance for generalized persistence modules and abelian categories

In persistence theory and practice, measuring distances between modules is central. The Wasserstein distances are the standard family of $L^p$ distances (with $1 \leq p \leq \infty$) for persistence modules. We give an algebraic formulation of these distances. For $p=1$ it generalizes to abelian categories and for arbitrary $p$ it generalizes to Krull-Schmidt categories. These distances may be useful for the computation of distance between generalized persistence modules. This is joint work with Peter Bubenik and Donald Stanley.Non UBCUnreviewedAuthor affiliation: Cleveland State UniversityFacult