A T ] 1 7 M ar 2 00 5 Differential characters and the Steenrod squares

The groups of differential characters of Cheeger and Simons admit a natural multiplicative structure. The quadratic map given by the square of a differential character of degree 2k reduces to a homomorphism of the ordinary cohomology groups. We prove that the homomorphism factors through the Steenrod squaring operation of degree 2k on the cohomology of degree 2k + 1. We also realize the other Steenrod squaring operations of even degree in a context of differential characters.