most recent 30 from http://mathoverflow.net 2013-05-25T17:40:57Z http://mathoverflow.net/feeds/question/84279 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/84279/quasi-isometry-classes-of-elementary-amenable-groups Denis Osin 2011-12-25T20:00:32Z 2011-12-25T20:35:51Z

<p>Is there any elementary argument showing that there exist uncountably many distinct quasi-isometry classes of elementary amenable groups? How about solvable groups? </p> <p>For amenable groups it follows from the result of Grigorchuk (proved in the 80's) stating that there are uncountably many groups of intermediate growth with pairwise incomparable growth functions.</p>

http://mathoverflow.net/questions/84279/quasi-isometry-classes-of-elementary-amenable-groups/84281#84281 Mark Sapir 2011-12-25T20:35:51Z 2011-12-25T20:35:51Z

<p>Doesn't it follows from our paper on lacunary hyperbolic groups? The elementary amenable lacunary hyperbolic groups corresponding to sufficiently different sequences of parameters will be not quasi-isometric because their asymptotic cones corresponding to certain sequences of parameters will not be bi-Lipschitz equivalent (one cone will be a tree while another one won't). </p>