Covers of simplicial complexes and applications to geometry (Q802138)

This paper makes the techniques of 1-cohomology available for the study of covers of simplicial complexes and their fundamental groups, with the aim of applications in combinatorial geometry, e.g. in the theory of buildings. The strength of these techniques is demonstrated by a number of such applications, among them a generalization of the theorem of J. Tits that buildings are 2-simply connected. The setting of the paper is purely geometric and combinatorial, without reference to parallel techniques in topology, the author adressing himself explicitly to geometers as his intended audience. Incidentally, the transposition from topology to combinatorics which he achieves results in a much more direct approach for simplicial complexes and is of great elegance and simplicity. [A detailed version of this review is available on request.]