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HIGHER-TWISTED PERIODIC SMOOTH DELIGNE COHOMOLOGY.

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Τίτλος: HIGHER-TWISTED PERIODIC SMOOTH DELIGNE COHOMOLOGY.
Συγγραφείς: GRADY, DANIEL1 djg9@nyu.edu, SATI, HISHAM1 hsati@nyu.edu
Πηγή: Homology, Homotopy & Applications. 2019, Vol. 21 Issue 1, p129-159. 31p.
Θεματικοί όροι: *Cohomology theory, *Spectral sequences (Mathematics), *Automorphisms, *Differential forms, *Homotopy theory
Περίληψη: 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. [ABSTRACT FROM AUTHOR]
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  Data: 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. [ABSTRACT FROM AUTHOR]
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      – Code: eng
        Text: English
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      – SubjectFull: Spectral sequences (Mathematics)
        Type: general
      – SubjectFull: Automorphisms
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              Text: 2019
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