Receding polar regions of a spherical building and the center conjecture. (Q2391385)

The goal of this paper is to developp further ideas of Chapter 6 of [\textit{R. M. Weiss}, The structure of spherical buildings. Princeton: Princeton University Press (2004; Zbl 1061.51011)], and apply them to get new results. First, in a very simple way, the authors obtain various simple properties of root groups. Moreover using results of Timmesfeld, Balser and Lytchak, they give a new proof of Tits's center conjecture for convex chamber subcomplexes of thick spherical buildings. The main ingredient of the paper is the introduction by the authors of the notion of a (receding) polar region of a spherical building.