Free products from spinning and rotating families

Abstract

The far-reaching work of Dahmani-Guirardel-Osin and recent work of Clay-Mangahas-Margalit provide geometric approaches to the study of the normal closure of a subgroup (or a collection of subgroups)in an ambient group $G$. Their work gives conditions under which the normal closure in $G$ is a free product. In this paper we unify their results and simplify and significantly shorten the proof of the Dahmani-Guirardel-Osin theorem.

22 pages, 8 figures. Further simplified and shortened main proofs. Also added proofs that elements in the group generated by a spinning/rotating family either act loxodromically or are contained in a point stabilizer á la DGO and CMM. Added referee comments. Accepted to l`Enseignement Mathématique