Semigroup Actions, Covering Spaces and Schutzenberger Groups
Group Theory
2009-06-01 v1
Abstract
We associate a 2-complex to the following data: a presentation of a semigroup and a transitive action of on a set by partial transformations. The automorphism group of the action acts properly discontinuously on this 2-complex. A sufficient condition is given for the 2-complex to be simply connected. As a consequence we obtain simple topological proofs of results on presentations of Sch\"utzenberger groups. We also give a geometric proof that a finitely generated regular semigroup with finitely many idempotents has polynomial growth if and only if all its maximal subgroups are virtually nilpotent.
Cite
@article{arxiv.0905.4888,
title = {Semigroup Actions, Covering Spaces and Schutzenberger Groups},
author = {Benjamin Steinberg},
journal= {arXiv preprint arXiv:0905.4888},
year = {2009}
}