On the weak homotopy types of small finite spaces
Algebraic Topology
2024-06-05 v2 Combinatorics
Abstract
We show that a connected finite topological space with or less points has a weak homotopy type of a wedge of spheres. In other words, we show that the order complex of a connected finite poset with or less points has a homotopy type of a wedge of spheres.
Cite
@article{arxiv.2404.12564,
title = {On the weak homotopy types of small finite spaces},
author = {Kango Matsushima and Shuichi Tsukuda},
journal= {arXiv preprint arXiv:2404.12564},
year = {2024}
}
Comments
48 pages. Corrected typos. Added a reference