Communications in Analysis and Geometry
Volume 29 (2021)
Relative differential cohomology and generalized Cheeger–Simons characters
Pages: 921 – 1005
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  (F. Ferrari Ruffino, “Relative Deligne cohomology and Cheeger–Simons character”, Comm. Anal. Geom. 22 (2014), no. 3, 573–593).
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