Persistent homology for functionals
Algebraic Topology
2024-01-08 v3 Functional Analysis
Abstract
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 diagrams, which, in particular, implies that they satisfy generalized Morse inequalities. We illustrate the applicability of these results by recasting the original proof of the Unstable Minimal Surface Theorem given by Morse and Tompkins in a modern and rigorous framework.
Cite
@article{arxiv.2107.14247,
title = {Persistent homology for functionals},
author = {Ulrich Bauer and Anibal M. Medina-Mardones and Maximilian Schmahl},
journal= {arXiv preprint arXiv:2107.14247},
year = {2024}
}
Comments
29 pages, 1 figure