On covering spaces and Galois extensions

Lindsay Nathan Childs

Vol. 37 (1971), No. 1, 29–33

DOI: 10.2140/pjm.1971.37.29

Abstract

Let X be a connected compact Hausdorff space, and G a finite abelian group. In this note we obtain a short exact sequence (Theorem 1) which describes the group of isomorphism classes of regular covering spaces of X with group G. The sequence is derived as an immediate translation of a similar sequence involving the group of commutative Galois extensions with group G of C(X), the ring of complex-valued continuous functions on X.

Mathematical Subject Classification 2000

Primary: 54C40

Secondary: 16A74

Milestones

Received: 19 February 1970

Published: 1 April 1971