Tautological characteristic classes, I

We discuss the formalism of tautological characteristic classes of flat bundles.Applied to PSL.2; K/, it yields the Witt class of Nekovář.Applied to PGL C .2n;K/, the general linear groups with positive determinant over an arbitrary ordered field, it yields (a generalization of) the Euler class. 20G10; 20J06This algebraic construction needs an input.For us such an input comes from a geometry (or, as some will undoubtedly insist, algebra), namely from the complex of geometric configurations.One takes a homogeneous space G=H (for example a projective space over an arbitrary field K) and builds a simplicial complex whose simplices are n-tuples of points "in general position".The notion of general position that we use depends on the situation, and is discussed separately in each case, but the underlying idea is