Abstract

Chamber systems over a type set I were defined by J. Tits as a family of partitions of a set of vertices called chambers. An equivalent representation as certain classes of graphs with edges labeled by non-empty subsets of I allows one to describe morphisms, truncations, and residues graph-theoretically. Residual connectedness is defined for chamber systems. For a residually connected chamber system, each edge is labeled by exactly one type, while chamber systems in which each chamber lies on infinitely many distinct panels are not residually connected at all. Generalized polygons are presented as both chamber systems and point-line geometries in order to introduce chamber systems of type M. Buildings are plucked out of the sea of all chamber systems of type M by any one of six equivalent conditions involving strong-gatedness of residues, or galleries of reduced type.

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