Strong relations between discrete surfaces, poset-based connected manifolds, and normal pseudomanifolds
Algebraic Topology
2025-08-05 v1
Abstract
In this paper, we study some relationships existing between some particular mathematical structures: discrete surfaces coming from discrete topology and mathematical morphology, poset-based connected manifolds coming from discrete topology, and normal pseudomanifolds which are much used in discrete geometry and topological data analysis. We will also show that, even when poset-based connected manifolds are assumed to be simplicial complexes, and then supplied with many additional topological properties, they are not necessarily smooth. A set of sufficient conditions to ensure that poset-based connected manifolds are smooth will be provided.
Cite
@article{arxiv.2508.01792,
title = {Strong relations between discrete surfaces, poset-based connected manifolds, and normal pseudomanifolds},
author = {Nicolas Boutry},
journal= {arXiv preprint arXiv:2508.01792},
year = {2025}
}