Differential characters and the Steenrod squares

Details Differential characters and the Steenrod squares Differential characters and the Steenrod squares

2004-11-02

arxiv.org/abs/math/0411043v3

Mathematics

Algebraic Topology

10 pages, LaTeX 2e, Introduction revised

Scientific paper

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.

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