Semigroups in Geometry and Topology
by
Jimmie Lawson
Louisiana State University

We consider ``homogeneous topological geometries, " topological spaces X endowed with a geometric structure for which the group G of homeomorphisms preserving the geometric structure acts transitively. Suppose that H is a subgroup of G which has an open orbit Hx in X. Then there is good motivation for studying the ``compression semigroup" S of Hx, which consists of all g in G which carry the orbit Hx into itself. It turns out that two natural questions to ask about S is whether it is a maximal subsemigroup of the group G, and whether each of its elements admit an appropriate type of ``polar decomposition, " where one factor comes from H. Typically one expects positive answers to these questions. The theory is considered in more detail for the important cases of hyperbolic, Möbius, and Lorentzian geometry.

Date received: March 21, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caan-09.