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Journal of the London Mathematical Society 2006 73(1):84-108; doi:10.1112/S0024610705022738
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© The London Mathematical Society

Quasi-Actions on Trees and Property (QFA)

J. F. Manning

Mathematics Department, MC253-37, California Institute of Technology Pasadena, CA 91125, USA manning{at}caltech.edu

Received 27 February 2004. Revision received 11 August 2004.

We prove some general results about quasi-actions on trees and define Property (QFA), which is analogous to Serre's Property (FA), but in the coarse setting. This property is shown to hold for a class of groups, including SL(n, Z) for n ≥ 3. We also give a way of thinking about Property (QFA) by breaking it down into statements about particular classes of trees.


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