Cheeger-Simons differential characters with compact support and Pontryagin duality

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

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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.

Original languageEnglish
Pages (from-to)1473-1522
Number of pages50
JournalCommunications in Analysis and Geometry
Volume27
Issue number7
DOIs
Publication statusPublished - 30 Dec 2019

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Geometry and Topology
  • Statistics, Probability and Uncertainty

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