Abstract:Recovering homological features of spaces from samples has become one of the central themes of topological data analysis, leading to many successful applications. Many of the results in this area focus on global homological features of a subset of a Euclidean space. In this case, homology recovery predicates on imposing well understood geometric conditions on the underlying set. Typically, these conditions guarantee that small enough neighborhoods of the set have the same homology as the set itself. Existing w… Show more
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