A Multicover Nerve for Geometric Inference
Donald R. Sheehy · 2012
We show that filtering the barycentric decomposition of a Čech 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. 1