### Séminaire Topologies

Le jeudi 24 mai 2018 à 11:15 - salle 430

Richard Szabo
Real bundle gerbes and twisted KR-homology

We consider Real bundle gerbes on manifolds equipped with an involution, which are classified by their Real Dixmier-Douady class in Grothendieck's equivariant sheaf cohomology. The Grothendieck group of Real bundle gerbe modules is isomorphic to twisted KR-theory for a torsion Real Dixmier-Douady class. Using these modules as building blocks, we introduce geometric cycles for twisted KR-homology which generate a real-oriented generalised homology theory dual to twisted KR-theory for Real closed manifolds, and for arbitrary Real Dixmier-Douady class.

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