Bowditch, B. H. (Brian Hayward), 1961- . (2011) Coarse median spaces and groups. Geometriae Dedicata . ISSN 0046-5755 (In Press)

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Abstract

We introduce the notion of a coarse median on a metric space. This satisfies the axioms of a median algebra up to bounded distance. The existence of such a median on a geodesic space is quasi-isometry invariant, and so it applies to finitely generated groups via their Cayley graphs. We show that asymptotic cones of such spaces are topological median algebras. We define a notion of rank for a coarse median and show that this bounds the dimension of a quasi-isometrically embedded euclidean plane in the space. Using the centroid construction of Behrstock and Minsky, we show that the mapping class group has this property, and recover the rank theorem of Behrstock and Minsky and of Hamenst¨adt. We explore various other properties of such spaces, and develop some of the background material regarding median algebras.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Geometriae Dedicata
Publisher:	Springer
Place of Publication:	Coventry
ISSN:	0046-5755
Date:	2011
Status:	Peer Reviewed
Publication Status:	In Press
Access rights to Published version:	Restricted or Subscription Access
Description:	Preprint
Related URLs:	Author
URI:	http://wrap.warwick.ac.uk/id/eprint/48816

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