Simple locally compact groups acting on trees and their germs of automorphisms |
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| Authors: | Pierre-Emmanuel Caprace Tom De Medts |
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| Affiliation: | (1) School of Mathematics and Statistics, The University of Sydney, Sydney, NSW, 2006, Australia;(2) Present address: Mathematisches Seminar der Universit?t Hamburg, Bundesstr. 55, 20146 Hamburg, Germany;(3) Science Institute, University of Iceland, Dunhaga 3, 107 Reykjav?k, Iceland |
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| Abstract: | Automorphism groups of locally finite trees provide a large class of examples of simple totally disconnected locally compact groups. It is desirable to understand the connections between the global and local structure of such a group. Topologically, the local structure is given by the commensurability class of a vertex stabiliser; on the other hand, the action on the tree suggests that the local structure should correspond to the local action of a stabiliser of a vertex on its neighbours. |
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