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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

Rights: Copyright © 2008 Mathematical Society of Japan

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