Groups, Geometry, and Dynamics

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Volume 10, Issue 1, 2016, pp. 279–317
DOI: 10.4171/GGD/350

Published online: 2016-02-09

Some properties of median metric spaces

Brian H. Bowditch[1]

(1) University of Warwick, Coventry, United Kingdom

We describe a number of properties of a median metric space. In particular, we show that a complete connected median metric space of finite rank admits a canonical bi-lipschitz equivalent CAT(0) metric. Metric spaces of this sort arise, up to bi-lipschitz equivalence, as asymptotic cones of certain classes of finitely generated groups, and the existence of such a structure has various consequences for the large scale geometry of the group.

Keywords: Median metric space, median algebra, CAT(0), cube complex

Bowditch Brian: Some properties of median metric spaces. Groups Geom. Dyn. 10 (2016), 279-317. doi: 10.4171/GGD/350