A note on Real line bundles with connection and Real smooth Deligne cohomology

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.

arXiv comment13 pages, minor revision, final version, accepted for publication in AMV