Twisted differential cohomology

Abstract

The main goal of the present paper is the construction of twisted generalized differential cohomology theories and the comprehensive statement of its basic functorial properties. Technically it combines the homotopy theoretic approach to (untwisted) generalized differential cohomology developed by Hopkins-Singer and later by the first author and D. Gepner with the oo-categorical treatement of twisted cohomology by Ando-Blumberg-Gepner. We introduce the notion of a differential twist for a given generalized cohomology theory and construct twisted differential cohomology groups (resp. spectra). The main technical results of the paper are existence and uniqueness statements for differential twists. These results will be applied in a variety of examples, including K-theory, topological modular forms and other cohomology theories.

70 pages

References in corpus (3)

• Higher Topos Theory
• Affineness and chromatic homotopy theory
• On a generalized Connes-Hochschild-Kostant-Rosenberg theorem

Cited by in corpus (9)

• Twistorial Cohomotopy implies Green-Schwarz anomaly cancellation
• The character map in (twisted differential) non-abelian cohomology
• The intersection motive of the moduli stack of shtukas
• Ramond-Ramond fields and twisted differential K-theory
• Spectral sequences in smooth generalized cohomology
• Flux Quantization
• Twisted differential generalized cohomology theories and their Atiyah-Hirzebruch spectral sequence
• Combinatorial parametrised spectra
• Twisted differential KO-theory