Primary operations in differential cohomology

Daniel Grady, Hisham Sati

    Research output: Contribution to journalArticle

    Abstract

    We characterize primary operations in differential cohomology via stacks, and illustrate by differentially refining Steenrod squares and Steenrod powers explicitly. This requires a delicate interplay between integral, rational, and mod p cohomology, as well as cohomology with U(1) coefficients and differential forms. Along the way we develop computational techniques in differential cohomology, including a Künneth decomposition, that should also be useful in their own right, and point to applications to higher geometry and mathematical physics.

    Original languageEnglish (US)
    Pages (from-to)519-562
    Number of pages44
    JournalAdvances in Mathematics
    Volume335
    DOIs
    StatePublished - Sep 7 2018

    Fingerprint

    Cohomology
    Higher geometry
    Computational Techniques
    Differential Forms
    Physics
    Decompose
    Coefficient

    Keywords

    • Cohomology operations
    • Deligne cohomology
    • Differential cohomology
    • Gerbes
    • Stacks
    • Steenrod squares

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Primary operations in differential cohomology. / Grady, Daniel; Sati, Hisham.

    In: Advances in Mathematics, Vol. 335, 07.09.2018, p. 519-562.

    Research output: Contribution to journalArticle

    Grady, Daniel ; Sati, Hisham. / Primary operations in differential cohomology. In: Advances in Mathematics. 2018 ; Vol. 335. pp. 519-562.
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