English

Free products from spinning and rotating families

Geometric Topology 2022-01-05 v3 Group Theory

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 GG. Their work gives conditions under which the normal closure in GG is a free product. In this paper we unify their results and simplify and significantly shorten the proof of the Dahmani-Guirardel-Osin theorem.

Keywords

Cite

@article{arxiv.2010.10735,
  title  = {Free products from spinning and rotating families},
  author = {Mladen Bestvina and Ryan Dickmann and George Domat and Sanghoon Kwak and Priyam Patel and Emily Stark},
  journal= {arXiv preprint arXiv:2010.10735},
  year   = {2022}
}

Comments

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 \'a la DGO and CMM. Added referee comments. Accepted to l`Enseignement Math\'{e}matique