# Acyclic covers

### John J. Millson

University of Maryland, College Park, USA

## Abstract

The following question, which is directly related to the Whitehead problem of subcomplexes of acyclic 2-complexes, is studied: If $\frak P$ is a class of groups, X is a 2-dimensional CW-complex and X' is an acyclic, infinite cyclic cover of X with $\pi_1(X')$ in $\frak P$ , must X' be contractible? A positive answer is given if X is finite and $\frak P$ is the class of amenable groups.

## Cite this article

John J. Millson, Acyclic covers. Comment. Math. Helv. 74 (1999), no. 2, pp. 173–178

DOI 10.1007/S000140050084