Differential cohomology theories as sheaves of spectra
By U. Bunke, T. Nikolaus, M. Völkl. 2013
77 citations recorded by the source corpus.
We show that every sheaf on the site of smooth manifolds with values in a stable $$(\infty ,1)$$(∞,1)-category (like spectra or chain complexes) gives rise to a “differential cohomology diagram” and a homotopy formula, which are common features of all classical examples of differential cohomology theories. These structures are naturally derived from a canonical decomposition of a sheaf into a homotopy invariant part and a piece which has a trivial evaluation on a point. In the classical examples the latter is the contribution of differential forms. This decomposition suggests a natural scheme to analyse new sheaves by determining these pieces and the gluing data. We perform this analysis for a variety of classical and not so classical examples.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2d27051d949170100d9d3cd855bcf0173b7cb4f7
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In Computational Theory and Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Anomalies in the space of coupling constants and their dynamical applications II (2019, background): “We remark that some of the earliest appearances of differential cohomology in physics, implicitly and explicitly, are [44, 45]; the mathematical theory is now highly developed; see [46–49] and the references therein.”
- Notes on generalized global symmetries in QFT (2015, background): “’ Ultimately because the space of connections on a fixed bundle is contractible, the geometric realization of BG is homotopic to that of BGconn, despite the fact that the 2-groups are not equivalent [30].”