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math.AT2006★ 123 cited
A statistical approach to persistent homology
Peter Bubenik, Peter T. Kim
Assume that a finite set of points is randomly sampled from a subspace of a metric space. Recent advances in computational topology have provided several approaches to recovering t…
math.AT2003★ 4 cited
Closed Model Categories for Presheaves of Simplicial Groupoids and Presheaves of 2-Groupoids
Zhi-Ming Luo, Peter Bubenik, Peter T. Kim
It is shown that the category of presheaves of simplicial groupoids and the category of presheaves of 2-groupoids have Quillen closed model structures. Furthermore, their homotopy…