English

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

Group Theory 2022-09-13 v3

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.

Keywords

Cite

@article{arxiv.1909.03097,
  title  = {Some new CAT(0) free-by-cyclic groups},
  author = {Rylee Alanza Lyman},
  journal= {arXiv preprint arXiv:1909.03097},
  year   = {2022}
}

Comments

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

R2 v1 2026-06-23T11:08:11.818Z