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).

中文翻译：

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相对微分上同调和广义 Cheeger-Simons 特征

我们为相对情况下的微分上同调提供了一个合适的公理框架，并推导出相应的长精确序列。我们还构建了广义 Cheeger-Simons 特征的相对版本，并在纤维具有边界时定义了积分图，将 [13] 的结果推广到任何上同调理论（F. Ferrari Ruffino，“Relative Deligne cohomology and Cheeger– Simons character”，Comm. Anal. Geom. 22 (2014), no. 3, 573–593)。