Realizing wedges of Moore spaces as classifying spaces of finite semigroups
Group Theory
2025-11-18 v1 Algebraic Topology
Rings and Algebras
Abstract
Fiedorowicz suggested that it was likely that every finite simply connected CW complex is homotopy equivalent to the classifying space of a finite semigroup. We prove that every finite wedge of simply connected Moore spaces of finitely generated abelian groups is homotopy equivalent to the classifying space of a finite semigroup. Consequently, homology groups alone cannot preclude a finite simply connected CW complex from being homotopy equivalent to the classifying space of a finite semigroup.
Keywords
Cite
@article{arxiv.2511.12657,
title = {Realizing wedges of Moore spaces as classifying spaces of finite semigroups},
author = {Aris Martinian and Benjamin Steinberg},
journal= {arXiv preprint arXiv:2511.12657},
year = {2025}
}