Continuous Alexander-Spanier Cohomology Classifies Principal Bundles with Abelian Structure Group
by
Bernd Günther
Coauthors: L. Mdzinarishvili

We prove that Alexander-Spanier cohomology Hⁿ(X;G) of a CW-complex X with continuous coefficients in a topological Abelian group G equals the set k_\Gamman(X) of isomorphism classes of principal \Gamma_n-bundles over X, n >= 2. The structure groups \Gamma_n are inductively defined by \Gamma₂ : = S(G) / S₀(G), the quotient of the singular complex of G by the subgroup of singular 0-simplexes, and \Gamma_n : = B\Gamma_n-1 for n >= 3.

Date received: June 24, 1996

Copyright © 1996 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 # caah-30.