Cheeger-Simons differential characters with compact support and Pontryagin duality
- 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.
Author details: | Christian BeckerORCiDGND, Marco BeniniORCiDGND, Alexander Schenkel, Richard J. Szabo |
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DOI: | https://doi.org/10.4310/CAG.2019.v27.n7.a2 |
ISSN: | 1019-8385 |
ISSN: | 1944-9992 |
Title of parent work (English): | Communications in analysis and geometry |
Publisher: | International Press of Boston |
Place of publishing: | Somerville |
Publication type: | Article |
Language: | English |
Date of first publication: | 2019/12/30 |
Publication year: | 2019 |
Release date: | 2021/04/26 |
Volume: | 27 |
Issue: | 7 |
Number of pages: | 50 |
First page: | 1473 |
Last Page: | 1522 |
Funding institution: | European Cooperation in Science and Technology (COST)European Cooperation in Science and Technology (COST) [MP1405 QSPACE]; Collaborative Research Center (SFB) "Raum Zeit Materie" - Deutsche Forschungsgemeinschaft (DFG, Germany)German Research Foundation (DFG); Della Riccia Foundation (Italy); Alexander von Humboldt Foundation (Germany)Alexander von Humboldt Foundation; Deutsche Forschungsgemeinschaft (DFG, Germany)German Research Foundation (DFG); UK Science and Technology Facilities CouncilScience & Technology Facilities Council (STFC) [ST/L000334/1] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |
Publishing method: | Open Access / Green Open-Access |