JournalscmhVol. 90, No. 1pp. 195–224

Envelopes of certain solvable groups

  • Tullia Dymarz

    University of Wisconsin, Madison, USA
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A discrete subgroup Γ\Gamma of a locally compact group HH is called a uniform lattice if the quotient H/ΓH/\Gamma is compact. Such an HH is called an envelope of Γ\Gamma. 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 Γ\Gamma we consider there is a finite family of preferred model spacesXX such that, up to compact groups, HH is a cocompact subgroup of Isom(X)Isom(X). We also answer problem 10.4 in \cite{FM3} for a large class of abelian-by-cyclic groups.

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

DOI 10.4171/CMH/351