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VOL. 52 | 2008 Differential characters and the Steenrod squares
Kiyonori Gomi

Editor(s) Robert Penner, Dieter Kotschick, Takashi Tsuboi, Nariya Kawazumi, Teruaki Kitano, Yoshihiko Mitsumatsu

## 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 $SL(2, \mathbb{Z})$-invariant on spin manifolds.

## Information

Published: 1 January 2008
First available in Project Euclid: 28 November 2018

zbMATH: 1162.55012
MathSciNet: MR2509714

Digital Object Identifier: 10.2969/aspm/05210297