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math.AT2026
Limit Computation Over Posets via Minimal Initial Functors
Tamal K. Dey, Michael Lesnick
It is well known that limits can be computed by restricting along an initial functor, and that this often simplifies limit computation. We systematically study the algorithmic impl…
math.AT2024
Sparse Approximation of the Subdivision-Rips Bifiltration for Doubling Metrics
Michael Lesnick, Kenneth McCabe
The Vietoris-Rips filtration, the standard filtration on metric data in topological data analysis, is notoriously sensitive to outliers. Sheehy's subdivision-Rips bifiltration $\ma…
math.AT2024
Nerve Models of Subdivision Bifiltrations
Michael Lesnick, Kenneth McCabe
We study the size of Sheehy's subdivision bifiltrations, up to homotopy. We focus in particular on the subdivision-Rips bifiltration of a metric space , the on…