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KT (K-theory)
http://ncatlab.org/nlab/show/differential+K-theory
arXiv:1209.6451 Regulators and cycle maps in higher-dimensional differential algebraic K-theory fra arXiv Front: math.KT av Ulrich Bunke, Georg Tamme We develop differential algebraic K-theory of regular and separated schemes of finite type over Spec(Z). Our approach is based on a new construction of a functorial, spectrum level Beilinson regulator using differential forms. We construct a cycle map which represents differential algebraic K-theory classes by geometric vector bundles. As an application we derive Lott’s relation between short exact sequences of geometric bundles with a higher analytic torsion form.
[arXiv:0907.3508] An index theorem in differential K-theory from arXiv Front: math.AT by Daniel S. Freed, John Lott. Let X –> B be a proper submersion with a Riemannian structure. Given a differential K-theory class on X, we define its analytic and topological indices as differential K-theory classes on B. We prove that the two indices are the same.
arXiv:1110.0151 Explict isomorphisms between differential K-theories from arXiv Front: math.KT by Man-Ho Ho We construct explicit isomorphisms between Freed-Lott differential K-theory and Simons-Sullivan differential K-theory. We also discuss the differential index theorem in Simons-Sullivan differential K-theory.
nLab page on Differential K-theory