Communications in Analysis and Geometry

Volume 29 (2021)

Number 4

Relative differential cohomology and generalized Cheeger–Simons characters

Pages: 921 – 1005

DOI: https://dx.doi.org/10.4310/CAG.2021.v29.n4.a4

Authors

Fabio Ferrari Ruffino (Departamento de Matemática, Universidade Federal de São Carlos, SP, Brasil)

Juan Carlos Rocha Barriga (Departamento de Matemática, Universidade Federal de São Carlos, SP, Brasil)

Abstract

We provide a suitable axiomatic framework for differential cohomology in the relative case and we deduce the corresponding long exact sequences. We also construct the relative version of the generalized Cheeger–Simons characters and we define the integration map when the fibre has a boundary, generalizing to any cohomology theory the results of [13] (F. Ferrari Ruffino, “Relative Deligne cohomology and Cheeger–Simons character”, Comm. Anal. Geom. 22 (2014), no. 3, 573–593).

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Fabio Ferrari Ruffino was supported by FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo), processo 2014/03721-3.

Juan Carlos Rocha Barriga was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.

Received 1 January 2018

Accepted 14 November 2018

Published 22 July 2021