Differential characters and the Steenrod squares

Kiyonori Gomi

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arXiv · math/0411043

Differential characters and the Steenrod squares

Kiyonori Gomi

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Abstract

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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Kiyonori Gomi. 2006-10-16. Differential characters and the Steenrod squares. https://arxiv.org/abs/math/0411043

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