Large mapping tori of free group endomorphisms
Abstract
Description
We present an algorithm which, given any finite presentation of a group as input, will terminate with answer yes if and only if the group is large. We use this to prove that a mapping torus of a finitely generated free group automorphism is large if it contains the integers times the integers as a subgroup of infinite index. We then extend this result to mapping tori of finitely generated free group endomorphisms, as well as showing that such a group is large if it contains a Baumslag-Solitar group of infinite index and has a finite index subgroup with first Betti number at least 2. We also show that if a group possesses a deficiency 1 presentation where one of the relators is a commutator then it is the integers times the integers, or it is large, or it is as far as possible from being residually finite.
41 pages with no figures
41 pages with no figures