Cheeger-Simons differential characters with compact support and Pontryagin duality

Becker, Christian, Benini, Marco, Schenkel, Alexander and Szabo, Richard J. (2017) Cheeger-Simons differential characters with compact support and Pontryagin duality. Communications in Analysis and Geometry . ISSN 1944-9992 (In Press)

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By adapting the Cheeger-Simons approach to differential cohomology, we establish a notion of differential cohomology with compact support. We show that it is functorial with respect to open embeddings and that it fits into a natural diagram of exact sequences which compare it to compactly supported singular cohomology and differential forms with compact support, in full analogy to ordinary differential cohomology. We prove an excision theorem for differential cohomology using a suitable relative version. Furthermore, we use our model to give an independent proof of Pontryagin duality for differential cohomology recovering a result of [Harvey, Lawson, Zweck -- Amer. J. Math. 125 (2003) 791]: On any oriented manifold, ordinary differential cohomology is isomorphic to the smooth Pontryagin dual of compactly supported differential cohomology. For manifolds of finite-type, a similar result is obtained interchanging ordinary with compactly supported differential cohomology.

Item Type: Article
Keywords: Cheeger-Simons differential characters, differential cohomology, relative differential cohomology, differential cohomology with compact support, smooth Pontryagin duality
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
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Depositing User: Schenkel, Dr Alexander
Date Deposited: 04 Oct 2017 09:27
Last Modified: 04 May 2020 18:58

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