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

TL;DR

This paper constructs new infinite families of free-by-cyclic groups with polynomially-growing automorphisms, which are CAT(0), thick, and not relatively hyperbolic, expanding the known examples in geometric group theory.

Contribution

It introduces the first infinite families of CAT(0) free-by-cyclic groups for each rank, contrasting previous examples and advancing understanding of their geometric properties.

Findings

Existence of infinitely many CAT(0) free-by-cyclic groups for each rank

These groups are thick and not relatively hyperbolic

Contrast with Gersten's example of non-CAT(0) thick free-by-cyclic group

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.