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Creators/Authors contains: "D. B. McReynolds, Mark Pengitore"

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  1. (, Preprint)
    For finitely generated groups G and H equipped with word metrics, a translation-like action of H on G is a free action where each element of H moves elements of G a bounded distance. Translation-like actions provide a geometric generalization of subgroup containment. Extending work of Cohen, we show that cocompact lattices in a general semisimple Lie group G that is not isogenous to SL(2,ℝ) admit translation-like actions by ℤ2. This result follows from a more general result. Namely, we prove that any cocompact lattice in the unipotent radical N of the Borel subgroup AN of G acts translation-like on any cocompact lattice in G. We also prove that for noncompact simple Lie groups G,H with H 
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