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arXiv · 1608.08572

Separated Nets in Nilpotent Groups

Tullia Dymarz·Michael Kelly·Sean Li·Anton Lukyanenko
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Abstract

In this paper we generalize several results on separated nets in Euclidean space to separated nets in connected simply connected nilpotent Lie groups. We show that every such group $G$ contains separated nets that are not biLipschitz equivalent. We define a class of separated nets in these groups arising from a generalization of the cut-and-project quasi-crystal construction and show that generically any such separated net is bounded displacement equivalent to a separated net of constant covolume. In addition, we use a generalization of the Laczkovich criterion to provide `exotic' perturbations of such separated nets.

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Tullia Dymarz, Michael Kelly, Sean Li, Anton Lukyanenko. 2016-08-30. Separated Nets in Nilpotent Groups. https://arxiv.org/abs/1608.08572

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