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A Note on Real Line Bundles with Connection and Real Smooth Deligne Cohomology

Peter Marius Flydal , $icon-email$ Gereon Quick , Eirik Eik Svanes

Abstract

We define a Real version of smooth Deligne cohomology for manifolds with involution which interpolates between equivariant sheaf cohomology and smooth imaginary-valued forms. Our main result is a classification of Real line bundles with Real connection on manifolds with involution.

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A Note on Real Line Bundles with Connection and Real Smooth Deligne Cohomology

Abstract