Higher Interpolation and Extension for Persistence Modules

Peter Bubenik (May 20, 2016)

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Abstract

Persistence modules are the central algebraic object in topological data analysis. This
motivates the study of the geometry of the space of persistence modules. We isolate an elegant
coherence condition that guarantees the interpolation and extension of sets of persistence
modules. This "higher interpolation" is a consequence of the existence of certain universal
constructions. As an application, it allows one to compare Vietoris-Rips and Cech complexes
built within the space of persistence modules. This is joint work with Vin de Silva and Vidit
Nanda.