Lattice envelopes
| Autor: | Uri Bader, Alex Furman, Roman Sauer |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Class (set theory)
geometric group theory General Mathematics 22D05 Closure (topology) Structure (category theory) locally compact groups Group Theory (math.GR) Lattice (discrete subgroup) Combinatorics quasi-isometries rigidity lattices Simple (abstract algebra) Convergence (routing) FOS: Mathematics Countable set 20F65 Mathematics - Group Theory Word (group theory) Mathematics |
| Zdroj: | Duke Math. J. 169, no. 2 (2020), 213-278 |
| Popis: | We introduce a class of countable groups by some abstract group-theoretic conditions. It includes linear groups with finite amenable radical and finitely generated residually finite groups with some non-vanishing $\ell^2$-Betti numbers that are not virtually a product of two infinite groups. Further, it includes acylindrically hyperbolic groups. For any group $\Gamma$ in this class we determine the general structure of its possible lattice embeddings, i.e. of all compactly generated, locally compact groups that contain $\Gamma$ as a lattice. This leads to a precise description of possible non-uniform 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. Comment: incorporated suggestions and corrections from referee report; fixed an issue in proof of thm B and generalized Thm 5.11 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|