Nonhyperbolic free-by-cyclic and one-relator groups

Abstract

We show that the free-by-cyclic groups of the form $F_2$ $\rtimes$ $\Bbb Z$ 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.