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arXiv · 2511.12657

Realizing wedges of Moore spaces as classifying spaces of finite semigroups

Aris Martinian·Benjamin Steinberg
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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.

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Aris Martinian, Benjamin Steinberg. 2025-11-16. Realizing wedges of Moore spaces as classifying spaces of finite semigroups. https://arxiv.org/abs/2511.12657

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