2014/11/26 by Uri Bader, Alex Furman, Roman Sauer
Computer Science · Mathematics · #Betti number #Closure (psychology) #Combinatorics #Countable set #Finite Group Theory Research #Geometric and Algebraic Topology #Lattice (music) #Mathematics #Pure mathematics #math.GR #msc:20F65 #msc:22D99 #semigroups and automata theory
paper · pdf · doi:10.1215/00127094-2019-0042
published as Duke Math. J. 169, no. 2 (2020), 213-278 · 7 pages
arxiv created 2014/11/26 · openalex created_date 2016/06/24 · openalex publication_date 2019/12/12 · arxiv updated 2020/02/12 · openalex updated_date 2026/08/05
We introduce a class of countable groups by some abstract group-theoretic conditions. This class includes linear groups with finite amenable radical and finitely generated residually finite groups with some nonvanishing ℓ2-Betti numbers that are not virtually a product of two infinite groups. Further, it includes acylindrically hyperbolic groups. For any group Γ in this class, we determine the general structure of the possible lattice embeddings of Γ, that is, of all compactly generated, locally compact groups that contain Γ as a lattice. This leads to a precise description of possible nonuniform lattice embeddings of groups in this class. Further applications include the determination of possible lattice embeddings of fundamental groups of closed manifolds with pinched negative curvature.