Embedding median algebras in products of trees

作者：Bowditch Brian H^*

来源：Geometriae Dedicata, 2014, 170(1): 157-176.

DOI：10.1007/s10711-013-9874-x

• Median algebra
• R-Tree
• Embedding
• Rapid decay

We show that a metric median algebra satisfying certain conditions admits a bilipschitz embedding into a finite product of -trees. This gives rise to a characterisation of closed connected subalgebras of finite products of complete -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, DruA u pound and Sapir, that the asymptotic cone of the mapping class group embeds in a finite product of -trees.

• 出版日期2014-6