A geometric model of twisted differential Ktheory
A geometric model of twisted differential Ktheory

Byungdo Park, CUNY, Graduate Center
Fine Hall 322
A twisted vector bundle is a weaker notion of an ordinary vector bundle whose cocycle condition is off by a U(1)valued Cech 2cocycle (the cycle data of a U(1)gerbe) called a topological twist. We will introduce a geometric model of a differential extension of twisted complex Ktheory using twisted vector bundles with connection as cycles and U(1)gerbes with connection as differential twists. Here a U(1)gerbe with connection is a total degree 2 cocycle in the Cechde Rham double complex. We will give an introduction to the ChernWeil theory of twisted vector bundles, define a twisted differential Ktheory, and introduce a hexagon diagram of twisted differential Ktheory.