21 citations · 43 across the 11 of their papers we have counts for
3 papers · 2 filters
Gromov Hyperbolicity, Geodesic Defect, and Apparent Pairs in Vietoris-Rips Filtrations
Ulrich Bauer, Fabian Roll
Motivated by computational aspects of persistent homology for Vietoris-Rips filtrations, we generalize a result of Eliyahu Rips on the contractibility of Vietoris-Rips complexes of…
Structure and Interleavings of Relative Interlevel Set Cohomology
Ulrich Bauer, Magnus Bakke Botnan, Benedikt Fluhr
The relative interlevel set cohomology (RISC) is an invariant of real-valued continuous functions closely related to the Mayer--Vietoris pyramid introduced by Carlsson, de Silva, a…
Persistent homology for functionals
Ulrich Bauer, Anibal M. Medina-Mardones, Maximilian Schmahl
We introduce topological conditions on a broad class of functionals that ensure that the persistent homology modules of their associated sublevel set filtration admit persistence d…