The cone topology on masures
Abstract
Masures are generalizations of Bruhat–Tits buildings and the main examples are associated with almost split Kac–Moody groups G over non-Archimedean local fields. In this case, G acts strongly transitively on its corresponding masure ∆ as well as on the building at infinity of ∆, which is the twin building associated with G. The aim of this article is twofold: firstly, to introduce and study the cone topology on the twin building at infinity of a masure. It turns out that this topology has various favorable properties that are required in the literature as axioms for a topological twin building. Secondly, by making use of the cone topology, we study strongly transitive actions of a group G on a masure ∆. Under some hypotheses, with respect to the masure and the group action of G, we prove that G acts strongly transitively on ∆ if and only if it acts strongly transitively on the twin building at infinity ∂∆. Along the way a criterion for strong transitivity is given and the existence and good dynamical properties of strongly regular hyperbolic automorphisms of the masure are proven.
Domains
Group Theory [math.GR]
Origin : Files produced by the author(s)
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