Envelopes of certain solvable groups

  • Tullia Dymarz

    University of Wisconsin, Madison, USA


A discrete subgroup of a locally compact group is called a uniform lattice if the quotient is compact. Such an is called an envelope of . In this paper we study the problem of classifying envelopes of various solvable groups including the solvable Baumslag-Solitar groups, lamplighter groups and certain abelian-by-cyclic groups. Our techniques are geometric and quasi-isometric in nature. In particular we show that for every we consider there is a finite family of preferred model spaces such that, up to compact groups, is a cocompact subgroup of . We also answer problem 10.4 in [8] for a large class of abelian-by-cyclic groups.

Cite this article

Tullia Dymarz, Envelopes of certain solvable groups. Comment. Math. Helv. 90 (2015), no. 1, pp. 195–224

DOI 10.4171/CMH/351