An index theorem in differential K-theory
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We construct a geometric model for differential K-theory, and prove it is isomorphic to the model proposed in . We construct differential K-orientations for families and elucidate the pushforward map given in  in detail. We prove a geometric index theorem for odd dimensional manifolds. Finally, using this index theorem and the holonomy theorem of Bismut and Freed from , we prove what may be considered a special case of a geometric refinement of the Aityah-Singer index theorem.