2004/11/02 by Kiyonori Gomi, Gomi, Kiyonori · 1 citation
Mathematics · #History and Theory of Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematics and Applications #math.AT #math.DG
paper · pdf · doi:10.48550/arxiv.math/0411043
10 pages, LaTeX 2e, Introduction revised
arxiv created 2006/10/16 · arxiv updated 2009/12/01
The 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.