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Iterated asymptotic cones

Iterated asymptotic cones have been used by Druţu 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.

preprint2011arXivOpen access
Lars ScheeleAlessandro Sisto
math.MGmath.GR
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Lars ScheeleAlessandro Sisto

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