  Geometric semigroup theory is the systematic investigation of
finitely-generated semigroups using the topology and geometry of their
associated automata. In this article we show how a number of easily-defined
expansions on finite semigroups and automata lead to simplifications 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.
