A Multicover Nerve for Geometric Inference

CCCG: The Canadian Conference in Computational Geometry
2012

We show that filtering the barycentric decomposition of a \v Cech complex by the cardinality of the vertices captures precisely the topology of $k$-covered regions among a collection of balls for all values of $k$.
Moreover, we relate this result to the Vietoris-Rips complex to get an approximation in terms of the persistent homology.

@inproceedings{sheehy12multicover, Title = {A Multicover Nerve for Geometric Inference}, Author = {Donald R. Sheehy}, Booktitle = {CCCG: Canadian Conference in Computational Geometry}, Year = {2012}}