Configuration Spaces.

Abstract

A knowledge of the space of configurations of η points in a manifold leads to information about the topological and non-homotopy properties of the manifold, as well as the identity components of the spaces of autohomeomorphisms and diffeomorphisms of the manifold. In the first part of this paper we give the fundamental sequence of fibrations for the study of configuration spaces, and localize the problem of computing the homotopy groups of these spaces to finding a cross section of a particular fibration.