Farrell–Jones via Dehn fillings

2015/10/27 by Yago Antolín, Rémi Coulon, Giovanni Gandini
Mathematics · #Advanced Operator Algebra Research #Conjecture #Dehn surgery #Finite Group Theory Research #Finite group #Geometric and Algebraic Topology #Group (periodic table) #Order (exchange) #Relatively hyperbolic group #Structured program theorem #math.GR #math.GT #msc:18F25 #msc:20F65 #msc:20F67

paper · pdf · doi:10.1142/s1793525318500292

published as J. Topol. Anal. 10 (2018), no. 4, 873-895 · 19 pages

arxiv created 2015/10/27 · openalex created_date 2016/06/24 · openalex publication_date 2017/06/01 · arxiv updated 2019/09/02 · openalex updated_date 2026/08/05

Abstract

Following the approach of Dahmani, Guirardel and Osin, we extend the group theoretical Dehn filling theorem to show that the pre-images of infinite order subgroups have a certain structure of a free product. We then apply this result to establish the Farrell–Jones conjecture for groups hyperbolic relative to a family of residually finite subgroups satisfying the Farrell–Jones conjecture, partially recovering a result of Bartels.

Citations

• Géométrie et théorie des groupes
• Sur les Groupes Hyperboliques d’après Mikhael Gromov
• Three dimensional manifolds, Kleinian groups and hyperbolic geometry
• Peripheral fillings of relatively hyperbolic groups
• Dehn filling in relatively hyperbolic groups
• The virtual Haken conjecture (with an appendix by Ian Agol, Daniel Groves and Jason Manning)