Homology, Homotopy and Applications

Volume 6 (2004)

Number 1

Equivariant covering spaces and homotopy covering spaces

Pages: 473 – 500

DOI: https://dx.doi.org/10.4310/HHA.2004.v6.n1.a23

Authors

Steven R. Costenoble (Department of Mathematics, Hofstra University, Hempstead, New York, U.S.A.)

Stefan Waner (Department of Mathematics, Hofstra University, Hempstead, New York, U.S.A.)

Abstract

Nonequivariantly, covering spaces over a connected (locally nice) space $X$ are in one-to-one correspondence with actions of the fundamental group of $X$ on discrete sets. For nonconnected spaces we consider instead actions of the fundamental groupoid. In this paper we generalize to the equivariant case, showing that we can use either of two possible notions of action of the equivariant fundamental groupoid. We consider both equivariant covering spaces and the more general notion of equivariant homotopy covering spaces.

Keywords

covering spaces, equivariant homotopy theory

2010 Mathematics Subject Classification

Primary 55R91. Secondary 18B40, 22A30, 55N25, 55N91, 55R15.

Published 1 January 2004