A class of automorphism groups of polygonal complexes (Q2730929)

The author constructs groups acting on certain 2-dimensional polyhedral cell-complexes which he calls polygonal complexes, and he gives a complete description of the class of groups which act by automorphisms simply transitively on the oriented edges of non-positively curved polygonal complexes. Here, the non-positivity of the curvature is a property which non-trivial circuits at each link must satisfy (as in Gromov's theory). Such an action is a higher-dimensional analogue of the action of groups on their Cayley graphs. The construction here is based on the notion of a positively curved orbihedron and its fundamental group, and it generalizes ideas contained in a previous paper of \textit{W. Ballmann} and the author [Geom. Funct. Anal. 7, No. 4, 615-645 (1997; Zbl 0897.22007)]. The class of groups contains rotation groups of regular tesselations, some special 2-dimensional Coxeter groups and some finite extensions of Coxeter groups. The author relates the construction he presents here to Kazhdan's property (T).