Computing homology robustly: from persistence to the geometry of normed chain complexes

Abstract: Topological Data Analysis uses homology as a feature for large data sets. It has successfully addressed the issue of the robustness of computing homology. Nevertheless, the conditioning number suggests an alternative approach. When computing the cohomology of a graph (or a simplicial complex), it has geometric significance: it is known as Cheeger's constant or spectral gap. This indicates that (co-)chain complexes contain more information than their mere (co-)homology. We turn the set of normed chain complexes into a metric space and study a compactness criterion.

algebraic topologyfunctional analysisgroup theorygeometric topologyoperator algebras

Audience: researchers in the topic

Vienna Geometry and Analysis on Groups Seminar