Real bundle gerbes, orientifolds and twisted $KR$-homology
Real bundle gerbes, orientifolds and twisted $KR$-homology
We consider Real bundle gerbes on manifolds equipped with an involution and prove that they are classified by their Real Dixmier-Douady class in Grothendieck's equivariant sheaf cohomology.We show that the Grothendieck group of Real bundle gerbe modules is isomorphic to twisted KR-theory for a torsion Real Dixmier-Douady class.Using these modules …