TY - JOUR
T1 - Cheeger-Simons differential characters with compact support and Pontryagin duality
AU - Becker, Christian
AU - Benini, Marco
AU - Schenkel, Alexander
AU - Szabo, Richard J.
N1 - Funding Information:
It is a pleasure to thank Christian Bär for very helpful discussions and Ulrich Bunke for his valuable comments on the first version of this paper. We are grateful to the anonymous referees for their useful suggestions, that contributed to improve the quality of the paper. This work was supported in part by the Action MP1405 QSPACE from the European Cooperation in Science and Technology (COST). The work of C.B. is partially supported by the Collaborative Research Center (SFB) “Raum Zeit Materie”, funded by the Deutsche Forschungsgemeinschaft (DFG, Germany). The work of M.B. is supported partly by a Research Fellowship of the Della Riccia Foundation (Italy) and partly by a Postdoctoral Fellowship of the Alexander von Humboldt Foundation (Germany). The work of A.S. is supported by a Research Fellowship of the Deutsche Forschungsgemeinschaft (DFG, Germany). The work of R.J.S. is partially supported by the Consolidated Grant ST/L000334/1 from the UK Science and Technology Facilities Council.
Publisher Copyright:
© 2019 International Press of Boston, Inc.. All rights reserved.
PY - 2019/12/30
Y1 - 2019/12/30
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85079647728&partnerID=8YFLogxK
U2 - 10.4310/cag.2019.v27.n7.a2
DO - 10.4310/cag.2019.v27.n7.a2
M3 - Article
AN - SCOPUS:85079647728
SN - 1019-8385
VL - 27
SP - 1473
EP - 1522
JO - Communications in Analysis and Geometry
JF - Communications in Analysis and Geometry
IS - 7
ER -