The homology of completely simple semigroups

TL;DR

This paper explicitly computes the Eilenberg-Mac Lane homology of completely simple semigroups using topological methods and explores their homological and topological finiteness properties, extending prior investigations.

Contribution

It provides a topological computation of homology for completely simple semigroups and completes previous work on their finiteness properties, including a proof of Pride's homological lower bound.

Findings

Explicit homology computations for completely simple semigroups

Extension of finiteness property investigations

Topological proof of Pride's homological lower bound

Abstract

I explicitly compute the Eilenberg-Mac Lane homology of a completely simple semigroup using topological means. I also complete Gray and Pride's investigation into the homological finiteness properties of completely simple semigroups, as well as studying their topological finiteness properties. I give a topological proof of Pride's unpublished homological lower bound for the deficiency of a monoid or semigroup.