Bowditch, B. H. (2014) Embedding median algebras in products of trees. Geometriae Dedicata, 170 (1). pp. 157-176. doi:10.1007/s10711-013-9874-x ISSN 0046-5755.

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Abstract

We show that a metric median algebra satisfying certain conditions admits a bilipschitz embedding into a finite product of R-trees. This gives rise to a characterisation of closed connected subalgebras of finite products of complete R-trees up to bilipschitz equivalence. Spaces of this sort arise as asymptotic cones of coarse median spaces. This applies to a large class of finitely generated groups, via their Cayley graphs. We show that such groups satisfy the rapid decay property. We also recover the result of Behrstock, Drut¸u and Sapir, that the asymptotic cone of the mapping class group embeds in a finite product of R-trees.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Data structures (Computer science)
Journal or Publication Title:	Geometriae Dedicata
Publisher:	Springer
ISSN:	0046-5755
Official Date:	June 2014
Dates:	Date Event June 2014 Published
Volume:	170
Number:	1
Number of Pages:	20
Page Range:	pp. 157-176
DOI:	10.1007/s10711-013-9874-x
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	7 June 2016
Date of first compliant Open Access:	7 June 2016

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