Higher interpolation and extension for persistence modules

Peter Bubenik, Vin de Silva, Vidit Nanda

Published 2016-03-24Version 1

The use of topological persistence in contemporary data analysis has provided considerable impetus for investigations into the geometric and functional-analytic structure of the space of persistence modules. In this paper, we isolate a coherence criterion which guarantees the extensibility of non-expansive maps into this space across embeddings of the domain to larger ambient metric spaces. Our coherence criterion is category-theoretic, allowing Kan extensions to provide the desired extensions. As a consequence of such "higher-interpolation", it becomes possible to compare Vietoris-Rips and Cech complexes built within the space of persistence modules.