Fillings, finite generation and direct limits of relatively hyperbolic groups

2006/06/02 by Daniel Groves, Jason Fox Manning, Groves, Daniel +1
Mathematics · #19K56 #20F65 #20F67 #Advanced Operator Algebra Research #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:19K56 #msc:20F65 #msc:20F67

paper · pdf · doi:10.48550/arxiv.math/0606070

(v1)10 pages. (v2) 11 pages, to appear in Groups, Geometry and Dynamics

openalex publication_date 2006/06/02 · arxiv created 2007/02/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We examine the relationship between finitely and infinitely generated relatively hyperbolic groups, in two different contexts. First, we elaborate on a remark from math.GR/0601311, which states that the version of Dehn filling in relatively hyperbolic groups proved in math.GR/0510195, allowing infinitely generated parabolic subgroups, follows from the version with finitely generated parabolics. Second, we observe that direct limits of relatively hyperbolic groups are in fact direct limits of finitely generated relatively hyperbolic groups. We use this (and known results) to derive some consequences about the Strong Novikov Conjecture for groups as constructed in math.GR/0411039.

Citations

• Tree-graded spaces and asymptotic cones of groups
• A topological characterisation of relatively hyperbolic groups
• The coarse Baum–Connes conjecture and groupoids
• Small cancellations over relatively hyperbolic groups and embedding theorems

Related

• Small cancellations over relatively hyperbolic groups and embedding theorems
• Dehn filling in semisimple Lie groups
• Specializing cubulated relatively hyperbolic groups
• Finite non-parabolic subgroups of relatively hyperbolic groups
• Bi-exactness of relatively hyperbolic groups