Ja n 20 06 QUASI - ACTIONS ON TREES AND PROPERTY ( QFA )
نویسنده
چکیده
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. Contents 1. Introduction 1 1.1. Acknowledgements 2 2. Preliminaries 2 2.1. Coarse geometry 2 2.2. Quasi-trees and other hyperbolic spaces 3 2.3. Bounded cohomology, amenability, and Trauber's Theorem 7 3. Lemmata 7 3.1. Getting some action 8 3.2. Cayley graphs of Z 9 3.3. Extracting a pseudocharacter 11 4. A class of groups with Property (QFA) 17 5. (QFA)-type properties for particular kinds of trees 19 References 20 Appendix A. Boundedly generated groups with pseudocharacter(s) by Nicolas Monod and Bertrand Rémy Appendicular references 24
منابع مشابه
5 Quasi - Actions on Trees and Property ( Qfa )
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. Contents 1. Introduction 1 1.1. ...
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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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