Combinatorial Thom-Hirzebruch characteristic classes

With any flat combinatorial metric on an arbitrary oriented combinatorial manifold, one associates a family of signature operators S-t depending on a small real parameter t. These operators have support on a Const. t-neighborhood of the diagonal and inherit the local symmetry of the combinatorial structure. One shows that when tSE arrow0, the measures tau(d), introduced by Connes, Sullivan and the author, applied onto the operators S-t, converge toward a simplicial chain representing the Thom-Hirzebruch homology class of corresponding degree.