A classification of fibre bundles over 2-dimensional spaces

Abstract

The classification problem for principal fibre bundles over two-dimensional CW-complexes is considered. Using the Postnikov factorization for the base space of a universal bundle a Puppe sequence that gives an implicit solution for the classification problem is constructed. In cases, when the structure group $G$ is path-connected or ${\pi }_1(G)=0$, the classification can be given in terms of cohomology groups.

28 pages, Latex, to be published in the Proceedings of the Meeting "New Developments in Algebraic Topology" (July 13-14, 1998, Faro, Portugal)