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Embedding median algebras in products of trees
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Bowditch, B. H. (Brian Hayward), 1961- (2011) Embedding median algebras in products of trees. Coventry: University of Warwick. (Unpublished)
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Official URL: http://homepages.warwick.ac.uk/~masgak/papers/medi...
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: | Scholarly Text |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Publisher: | University of Warwick |
| Place of Publication: | Coventry |
| Date: | 2011 |
| Number of Pages: | 27 |
| Status: | Not Peer Reviewed |
| Publication Status: | Unpublished |
| Access rights to Published version: | Open Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/48818 |
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