Free products from spinning and rotating families
Mladen Bestvina, Ryan Dickmann, George Domat, Sanghoon Kwak, Priyam, Patel, Emily Stark

TL;DR
This paper unifies and simplifies existing geometric approaches to understanding when the normal closure of subgroups in a group forms a free product, building on the work of Dahmani-Guirardel-Osin and others.
Contribution
It provides a unified framework that simplifies and shortens the proofs of key theorems regarding free products from spinning and rotating families.
Findings
Unified existing results into a single framework.
Simplified the proof of the Dahmani-Guirardel-Osin theorem.
Extended geometric conditions for free products.
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 . Their work gives conditions under which the normal closure in is a free product. In this paper we unify their results and simplify and significantly shorten the proof of the Dahmani-Guirardel-Osin theorem.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology
