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...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Published: |
International Press
2017
|
| Subjects: | |
| Online Access: | https://eprints.nottingham.ac.uk/46865/ |
| _version_ | 1848797414814646272 |
|---|---|
| author | Becker, Christian Benini, Marco Schenkel, Alexander Szabo, Richard J. |
| author_facet | Becker, Christian Benini, Marco Schenkel, Alexander Szabo, Richard J. |
| author_sort | Becker, Christian |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:03:30Z |
| format | Article |
| id | nottingham-46865 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:03:30Z |
| publishDate | 2017 |
| publisher | International Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-468652020-05-04T18:58:04Z https://eprints.nottingham.ac.uk/46865/ Cheeger-Simons differential characters with compact support and Pontryagin duality Becker, Christian Benini, Marco Schenkel, Alexander Szabo, Richard J. 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. International Press 2017-07-30 Article PeerReviewed 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) Cheeger-Simons differential characters differential cohomology relative differential cohomology differential cohomology with compact support smooth Pontryagin duality |
| spellingShingle | Cheeger-Simons differential characters differential cohomology relative differential cohomology differential cohomology with compact support smooth Pontryagin duality Becker, Christian Benini, Marco Schenkel, Alexander Szabo, Richard J. Cheeger-Simons differential characters with compact support and Pontryagin duality |
| title | Cheeger-Simons differential characters with compact support and Pontryagin duality |
| title_full | Cheeger-Simons differential characters with compact support and Pontryagin duality |
| title_fullStr | Cheeger-Simons differential characters with compact support and Pontryagin duality |
| title_full_unstemmed | Cheeger-Simons differential characters with compact support and Pontryagin duality |
| title_short | Cheeger-Simons differential characters with compact support and Pontryagin duality |
| title_sort | cheeger-simons differential characters with compact support and pontryagin duality |
| topic | Cheeger-Simons differential characters differential cohomology relative differential cohomology differential cohomology with compact support smooth Pontryagin duality |
| url | https://eprints.nottingham.ac.uk/46865/ |