Rigidity at infinity of trees and Euclidean buildings

K Struyve - Transformation Groups, 2016 - Springer
Transformation Groups, 2016Springer
We show that if a group G acts isometrically on a locally finite leafless ℝ-tree inducing a two-
transitive action on its ends, then this tree is determined by the action of G on the boundary.
As a corollary we obtain that locally finite irreducible Euclidean buildings of dimension at
least two are determined by their complete building at infinity.
Abstract
We show that if a group G acts isometrically on a locally finite leafless ℝ-tree inducing a two-transitive action on its ends, then this tree is determined by the action of G on the boundary. As a corollary we obtain that locally finite irreducible Euclidean buildings of dimension at least two are determined by their complete building at infinity.
Springer
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