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.
Verfasserangaben: | 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 |
Titel des übergeordneten Werks (Englisch): | Communications in analysis and geometry |
Verlag: | International Press of Boston |
Verlagsort: | Somerville |
Publikationstyp: | Wissenschaftlicher Artikel |
Sprache: | Englisch |
Datum der Erstveröffentlichung: | 30.12.2019 |
Erscheinungsjahr: | 2019 |
Datum der Freischaltung: | 26.04.2021 |
Band: | 27 |
Ausgabe: | 7 |
Seitenanzahl: | 50 |
Erste Seite: | 1473 |
Letzte Seite: | 1522 |
Fördernde 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] |
Organisationseinheiten: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC-Klassifikation: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer Review: | Referiert |
Publikationsweg: | Open Access / Green Open-Access |