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Embedding median algebras in products of trees

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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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Official URL: http://dx.doi.org/10.1007/s10711-013-9874-x

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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:
DateEvent
June 2014Published
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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