2013/10/10 by Christian Becker, Becker, Christian
Mathematics · #53C08 #55N20 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1310.2851
openalex publication_date 2013/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study two notions of relative differential cohomology, using the model of differential characters. The two notions arise from the two options to construct relative homology, either by cycles of a quotient complex or of a mapping cone complex. We discuss the relation of the two notions of relative differential cohomology to each other. We discuss long exact sequences for both notions, thereby clarifying their relation to absolute differential cohomology. We construct the external and internal product of relative and absolute characters and show that relative differential cohomology is a right module over the absolute differential cohomology ring. Finally we construct fiber integration and transgression for relative differential characters.