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Cheeger-Simons differential characters with compact support and Pontryagin duality

Becker, Christian; Benini, Marco; Schenkel, Alexander; Szabo, Richard J.

Authors

Christian Becker

Marco Benini

Alexander Schenkel

Richard J. Szabo



Abstract

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.

Journal Article Type Article
Publication Date Dec 30, 2019
Journal Communications in Analysis and Geometry
Print ISSN 1019-8385
Electronic ISSN 1944-9992
Publisher International Press
Peer Reviewed Peer Reviewed
Volume 27
Issue 7
Pages 1473–1522
APA6 Citation Becker, C., Benini, M., Schenkel, A., & Szabo, R. J. (2019). Cheeger-Simons differential characters with compact support and Pontryagin duality. Communications in Analysis and Geometry, 27(7), 1473–1522
Keywords Cheeger-Simons differential characters, differential cohomology, relative differentialcohomology, differential cohomology with compact support, smooth Pontryagin duality
Related Public URLs https://arxiv.org/abs/1511.00324
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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