Nonhyperbolic free-by-cyclic and one-relator groups

摘要

We show that the free-by-cyclic groups of the form F2⋊ Z act properly cocompactly on CAT(0) square complexes. We also show using generalized Baumslag-Solitar groups that all known groups defined bya 2-generator 1-relator presentation are either SQ-universal or arecyclic or isomorphic to a soluble Baumslag-Solitar group.