- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:04:58
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
3
2009
2
Local similarities and the Haagerup property (with an appendix by Daniel S. Farley)
Bruce
Hughes
Vanderbilt University, NASHVILLE, UNITED STATES
Local similarity, ultrametric space, Haagerup property
A new class of groups, the locally finitely determined groups of local similarities on compact ultrametric spaces, is introduced and it is proved that these groups have the Haagerup property (that is, they are a-T-menable in the sense of Gromov). The class includes Thompson's groups, which have already been shown to have the Haagerup property by D. S. Farley, as well as many other groups acting on boundaries of trees. A sufficient condition, used in this article, for the Haagerup property is shown in the appendix by D. S. Farley to be equivalent to the well-known property of having a proper action on a space with walls.
Group theory and generalizations
Topological groups, Lie groups
General topology
General
299
315
10.4171/GGD/58
http://www.ems-ph.org/doi/10.4171/GGD/58