Higher-twisted periodic smooth deligne cohomology

Daniel Grady, Hisham Sati

    Research output: Contribution to journalArticle

    Abstract

    Generalizing degree one twisting of Deligne cohomology, as a differential refinement of integral cohomology, from previous work, here we consider higher degree twists. The Rham complex, hence de Rham cohomology, admits twists of any odd degree. However, in order to consider twists of integral cohomology we need a periodic version. Combining the periodic versions of both ingredients leads us to introduce a periodic form of Deligne cohomology. We demonstrate that this theory indeed admits a twist by a gerbe of any odd degree.We present the main properties of the new theory and illustrate its use with examples and computations, mainly via a corresponding twisted differential Atiyah-Hirzebruch spectral sequence.

    Original languageEnglish (US)
    Pages (from-to)129-159
    Number of pages31
    JournalHomology, Homotopy and Applications
    Volume21
    Issue number1
    DOIs
    StatePublished - Jan 1 2019

    Fingerprint

    Twist
    Cohomology
    Odd
    Gerbe
    De Rham Cohomology
    Michael Francis Atiyah
    Spectral Sequence
    Refinement
    Demonstrate

    Keywords

    • Atiyah-Hirzebruch spectral sequence
    • Deligne cohomology
    • Differential cohomology
    • Gerbe
    • Stack
    • Twisted cohomology

    ASJC Scopus subject areas

    • Mathematics (miscellaneous)

    Cite this

    Higher-twisted periodic smooth deligne cohomology. / Grady, Daniel; Sati, Hisham.

    In: Homology, Homotopy and Applications, Vol. 21, No. 1, 01.01.2019, p. 129-159.

    Research output: Contribution to journalArticle

    Grady, Daniel ; Sati, Hisham. / Higher-twisted periodic smooth deligne cohomology. In: Homology, Homotopy and Applications. 2019 ; Vol. 21, No. 1. pp. 129-159.
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