New York Journal of Mathematics
Volume 22 (2016) 755-774


J. O. Button and R. P. Kropholler

Nonhyperbolic free-by-cyclic and one-relator groups

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Published: August 1, 2016
Keywords: Free-by-cyclic, 1-relator, CAT(0)
Subject: 20F05, 57M20

We show that the free-by-cyclic groups of the form F2Z act properly cocompactly on CAT(0) square complexes. We also show using generalized Baumslag-Solitar groups that all known groups defined by a 2-generator 1-relator presentation are either SQ-universal or are cyclic or isomorphic to a soluble Baumslag-Solitar group.

Author information

J. O. Button:
Selwyn College, University of Cambridge, Cambridge CB3 9DQ, UK

R. P. Kropholler:
Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK