Cheeger-Simons differential characters with compact support and Pontryagin duality

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

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.

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

• Journal Article Type: Article
• Acceptance Date: Jul 30, 2017
• Online Publication Date: Dec 30, 2019
• Publication Date: Dec 30, 2019
• Deposit Date: Oct 4, 2017
• Publicly Available 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
• Keywords: Cheeger-Simons differential characters, differential cohomology, relative differentialcohomology, differential cohomology with compact support, smooth Pontryagin duality
• Public URL: https://nottingham-repository.worktribe.com/output/875217
• Related Public URLs: https://arxiv.org/abs/1511.00324