Differential Ktheory

General Introduction
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Search results
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Online References
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Paper References
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
arXiv:1209.6451 Regulators and cycle maps in higherdimensional differential algebraic Ktheory fra arXiv Front: math.KT av Ulrich Bunke, Georg Tamme We develop differential algebraic Ktheory 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 Ktheory 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 Ktheory 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 Ktheory class on X, we define its analytic and topological indices as differential Ktheory classes on B. We prove that the two indices are the same.
arXiv:1110.0151 Explict isomorphisms between differential Ktheories from arXiv Front: math.KT by ManHo Ho We construct explicit isomorphisms between FreedLott differential Ktheory and SimonsSullivan differential Ktheory. We also discuss the differential index theorem in SimonsSullivan differential Ktheory.
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