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math.AT2026
Function-Rips complexes in persistent homotopy theory: Stability and persistent Latschev theorems
Steve Oudot, Lukas Waas
Classical results of Hausmann and Latschev show that Vietoris-Rips complexes can recover the homotopy type of a manifold, even from finite metric spaces that are nearby in Gromov-H…
math.AT2024
Differential Calculus and Optimization in Persistence Module Categories
Steve Oudot
Persistence modules are representations of products of totally ordered sets in the category of vector spaces. They appear naturally in the representation theory of algebras, but in…