A Note on Real Line Bundles with Connection and Real Smooth Deligne Cohomology
Peter Marius Flydal
,
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.