paper

On the weak homotopy types of small finite spaces

arXiv:2404.12564

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.

48 pages. Corrected typos. Added a reference