Continuous Alexander-Spanier cohomology classifies principal bundles with Abelian structure group. (English) Zbl 0891.55004
The authors prove that Alexander-Spanier cohomology \(H^n(X;G)\) with coefficients in a topological Abelian group \(G\) is isomorphic to the group of isomorphism classes of principal bundles with certain Abelian structure groups. The result holds if either \(X\) is a CW-space and \(G\) arbitrary or if \(X\) is metrizable or compact Hausdorff and \(G\) an ANR.
Reviewer: M.Anastasiei (Iaşi)
MSC:
55N05 | Čech types |
55R15 | Classification of fiber spaces or bundles in algebraic topology |
55U10 | Simplicial sets and complexes in algebraic topology |