[Papers]
[Alex Furman]

Lattice envelopes

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.

Authors:
U. Bader,
A. Furman,
R. Sauer

Bibliographical: Duke Math. J., **169** (2020), no. 2, 213 -– 278.

Download: pdf | published-pdf |
arxiv:1711.08410

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[Papers]
[Alex Furman]