2 papers
math.MG2025
Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips complexes
Henry Adams, Johnathan Bush, Nate Clause +13
We explore emerging relationships between the Gromov--Hausdorff distance, Borsuk--Ulam theorems, and Vietoris--Rips simplicial complexes. The Gromov--Hausdorff distance between two…
math.AT2024
The Generalized Rank Invariant: Möbius invertibility, Discriminating Power, and Connection to Other Invariants
Nathaniel Clause, Woojin Kim, Facundo Mémoli
In addition to inherent computational challenges, the absence of a canonical method for quantifying `persistence' in multi-parameter persistent homology remains a hurdle in its app…