REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: A partial group is a set containing an identity and inverses, but with a composition that is only sometimes defined. The set of local homeomorphisms of a topological space is such a set. If the partial group is associative, in a general sense, then it realizes as a subspace of the standard Eilenberg-Maclane Space of type (G, 1) where G is the universal group of the partial group. So a partial group structure allows the homology of the universal group to be computed from a subcomplex constructed just from relations induced by the composition. In this talk we present some general and some specific aspects of partial groups and homology. Partial groups arise naturally in the theory of the Euler Class for circle bundles with discrete structure group, and in the classification of codimension-one real analytic pseudogroup structures on surfaces, and we will describe the role they play in these contexts.