# Geometry in the space of persistence modules

@inproceedings{Silva2013GeometryIT, title={Geometry in the space of persistence modules}, author={Vin de Silva and Vidit Nanda}, booktitle={SoCG '13}, year={2013} }

Topological persistence is, by now, an established paradigm for constructing robust topological invariants from point cloud data: the data are converted into a filtered simplicial complex, the complex gives rise to a persistence module, and the module is described by a persistence diagram. In this paper, we study the geometry of the spaces of persistence modules and diagrams, with special attention to Cech and Rips complexes. The metric structures are determined in terms of interleaving maps…

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