Amenability of actions on the boundary of a building

TL;DR

This paper proves that automorphism groups of buildings act topologically amenably on their boundaries, implying they have property (A) and satisfy the Novikov conjecture, with potential applications in rigidity theory.

Contribution

It establishes the topological amenability of automorphism group actions on building boundaries, linking to property (A) and the Novikov conjecture.

Findings

Automorphism groups act topologically amenably on boundary

Groups have property (A)

Satisfy the Novikov conjecture

Abstract

We prove that the action of the automorphism group of a building on its boundary is topologically amenable. The notion of boundary we use was defined in a previous paper \cite{CL}. It follows from this result that such groups have property (A), and thus satisfy the Novikov conjecture. It may also lead to applications in rigidity theory.