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2019 Twisted differential generalized cohomology theories and their Atiyah–Hirzebruch spectral sequence
Daniel Grady, Hisham Sati
Algebr. Geom. Topol. 19(6): 2899-2960 (2019). DOI: 10.2140/agt.2019.19.2899


We construct the Atiyah–Hirzebruch spectral sequence (AHSS) for twisted differential generalized cohomology theories. This generalizes to the twisted setting the authors’ corresponding earlier construction for differential cohomology theories, as well as to the differential setting the AHSS for twisted generalized cohomology theories, including that of twisted K–theory by Rosenberg and by Atiyah and Segal. In describing twisted differential spectra we build on the work of Bunke and Nikolaus, but we find it useful for our purposes to take an approach that highlights direct analogies with classical bundles and that is at the same time amenable for calculations. We will, in particular, establish that twisted differential spectra are bundles of spectra equipped with a flat connection. Our prominent case will be twisted differential K–theory, for which we work out the differentials in detail. This involves differential refinements of primary and secondary cohomology operations the authors developed in earlier papers. We illustrate our constructions and computational tools with examples.


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Daniel Grady. Hisham Sati. "Twisted differential generalized cohomology theories and their Atiyah–Hirzebruch spectral sequence." Algebr. Geom. Topol. 19 (6) 2899 - 2960, 2019.


Received: 29 November 2017; Revised: 6 December 2018; Accepted: 7 January 2019; Published: 2019
First available in Project Euclid: 29 October 2019

zbMATH: 07142622
MathSciNet: MR4023332
Digital Object Identifier: 10.2140/agt.2019.19.2899

Primary: 19L50, 53C05, 55R20, 55T25, 57R19
Secondary: 14A20, 55S05, 55S20

Rights: Copyright © 2019 Mathematical Sciences Publishers


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Vol.19 • No. 6 • 2019
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