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