Persistent Homology of Filtered Covers

Details Persistent Homology of Filtered Covers Persistent Homology of Filtered Covers

2012-02-28

arxiv.org/abs/1202.6132v1

Mathematics

Algebraic Topology

12 pages, no figures

Scientific paper

We prove an extension to the simplicial Nerve Lemma which establishes isomorphism of persistent homology groups, in the case where the covering spaces are filtered. While persistent homology is now widely used in topological data analysis, the usual Nerve Lemma does not provide isomorphism of persistent homology groups. Our argument involves some homological algebra: the key point being that although the maps produced in the standard proof of the Nerve Lemma do not commute as maps of chain complexes, the maps they induce on homology do.

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