Some new CAT(0) free-by-cyclic groups

Abstract

We show the existence of several new infinite families of polynomially-growing automorphisms of free groups whose mapping tori are CAT(0) free-by-cyclic groups. Such mapping tori are thick, and thus not relatively hyperbolic. These are the first families comprising infinitely many examples for each rank of the nonabelian free group; they contrast strongly with Gersten's example of a thick free-by-cyclic group which cannot be a subgroup of a CAT(0) group.

7 pages, 2 figures; v2: the original paper has been split in two, with the other half (containing construction of train track maps on graphs of groups) to appear; v3: minor revisions according to referee comments

References in corpus (4)

• The mapping-torus of a free group automorphism is hyperbolic relative to the canonical subgroups of polynomial growth
• A remark on thickness of free-by-cyclic groups
• Non Hyperbolic Free-By-Cyclic and One-Relator Groups
• Train Tracks on Graphs of Groups and Outer Automorphisms of Hyperbolic Groups

Cited by in corpus (1)

• Train Tracks on Graphs of Groups and Outer Automorphisms of Hyperbolic Groups