2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100925The groups of differential characters of Cheeger and Simons admit a natural multiplicative structure. The map given by the squares of degree 2k differential characters reduces to a homomorphism of ordinary cohomology groups. We prove that the homomorphism factors through the Steenrod squaring operation of degree 2k. A simple application shows that five-dimensional Chern-Simons theory for pairs of B-fields is SL(2, Z)-invariant on spin manifolds.10 pages, LaTeX 2e, Introduction revisedAlgebraic TopologyDifferential Geometrytext