183 research outputs found
Envelopes of certain solvable groups
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 .Comment: To appear in Commentarii Mathematici Helvetici, 30 page
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