Commentarii Mathematici Helvetici

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Volume 74, Issue 2, 1999, pp. 173–178
DOI: 10.1007/s000140050084

Published online: 1999-06-30

Acyclic covers

John J. Millson[1]

(1) University of Maryland, College Park, USA

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.

Keywords: 2-complexes, covering space, amenable

Millson John: Acyclic covers. Comment. Math. Helv. 74 (1999), 173-178. doi: 10.1007/s000140050084