Roots in 2-spherical apartments (Q2882931)

A key element of the geometry of higher rank spherical buildings, which can be used to classify them, is that they have the Moufang property. This property follows from an extension result, which roughly asserts that the global geometry of the building is determined by its local structure.NEWLINENEWLINEThe latter property is known to hold in the much broader context of \(2\)-spherical buildings: their Weyl group has the property that the order of the composition of two simple reflections is always finite. The object of this paper is to develop the tools leading to a possible proof that this implies that these buildings are Moufang. The main result is a connectivity property of the \(2\)-interior of a root \(\alpha\) (i.e. the set of \(2\)-residues stricly contained in \(\alpha\)).