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Iterated asymptotic cones (1108.1146v1)
Published 4 Aug 2011 in math.MG and math.GR
Abstract: Iterated asymptotic cones have been used by Dru\c{t}u and Sapir to construct a group with uncountably many pairwise non-homeomorphic asymptotic cones. In this paper we define a class of metric spaces which display a wide range of behaviors with respect to iterated asymptotic cones, and we use those to construct examples within the class of groups. Namely, we will show that there exists a group whose iterated cones are pairwise non-homeomorphic, or periodically homeomorphic.