 
Summary: arXiv:1104.2301v1[math.GR]12Apr2011
GEOMETRIC SEMIGROUP THEORY
JON MCCAMMOND, JOHN RHODES, AND BENJAMIN STEINBERG
Abstract. Geometric semigroup theory is the systematic investigation
of finitelygenerated semigroups using the topology and geometry of
their associated automata. In this article we show how a number of
easilydefined expansions on finite semigroups and automata lead to sim
plifications of the graphs on which the corresponding finite semigroups
act. We show in particular that every finite semigroup can be finitely
expanded so that the expansion acts on a labeled directed graph which
resembles the right Cayley graph of a free Burnside semigroup in many
respects.
Contents
1. Introduction 2
2. The topology of directed graphs 2
2.1. Directed graphs 3
2.2. Morphisms of directed graphs 6
2.3. Semigroups and automata 7
2.4. Rooted graphs 9
2.5. The unique simple path property 14
