2020/10/21 by Mladen Bestvina, Bestvina, Mladen, Ryan Dickmann +9
Mathematics · #Advanced Algebra and Geometry #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GR #math.GT #msc:20E08 #msc:20F65 #msc:51M09 #msc:57M07 #msc:57M60
paper · pdf · doi:10.48550/arxiv.2010.10735
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
arxiv created 2022/01/03 · arxiv updated 2022/01/05
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.