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The Quarterly Journal of Mathematics 2004 55(4):421-440; doi:10.1093/qmath/hah011
© 2004 by Oxford University Press
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Acyclic groups and wild arcs

A. J. Berrick * and Yan-Loi Wong §

Department of Mathematics, National University of Singapore, Kent Ridge 117543, Singapore  *

We discuss two classes of acyclic groups that are commutator subgroups of finitely presented groups with infinite cyclic abelianization. The first is algebraic and includes groups first exhibited by Baumslag and Gruenberg, of which it is shown that Epstein's acyclic group is a special case. The second class is geometric, and is shown to include a number of wild arc groups in the literature.

Received 21 November 2003.

* E-mail: berrick{at}math.nus.edu.sg

§ E-mail: matwyl{at}nus.edu.sg


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