JournalsggdVol. 5, No. 1pp. 177–188

(Non)-completeness of ℝ-buildings and fixed point theorems

  • Koen Struyve

    Universiteit Gent, Belgium
(Non)-completeness of ℝ-buildings and fixed point theorems cover

Abstract

We prove two generalizations of results of Bruhat and Tits involving metrical completeness and R\mathbb{R}-buildings. Firstly, we give a generalization of the Bruhat–Tits fixed point theorem also valid for non-complete R\mathbb{R}-buildings with the added condition that the group is finitely generated. Secondly, we generalize a criterion which reduces the problem of completeness to the wall trees of the R\mathbb{R}-building. This criterion was proved by Bruhat and Tits for R\mathbb{R}-buildings arising from root group data with valuation.

Cite this article

Koen Struyve, (Non)-completeness of ℝ-buildings and fixed point theorems. Groups Geom. Dyn. 5 (2011), no. 1, pp. 177–188

DOI 10.4171/GGD/121