Structured vector bundles define differential K-theory

Abstract

A equivalence relation, preserving the Chern-Weil form, is defined between connections on a complex vector bundle. Bundles equipped with such an equivalence class are called Structured Bundles, and their isomorphism classes form an abelian semi-ring. By applying the Grothedieck construction one obtains the ring K, elements of which, modulo a complex torus of dimension the sum of the odd Betti numbers of the base, are uniquely determined by the corresponding element of ordinary K and the Chern-Weil form. This construction provides a simple model of differential K-theory, c.f.Hopkins-Singer (2005), as well as a useful codification of vector bundles with connection.

23 pages

References in corpus (2)

• Setting the quantum integrand of M-theory
• Dirac Charge Quantization and Generalized Differential Cohomology

Cited by in corpus (10)

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• The Mayer-Vietoris Property in Differential Cohomology
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• Differential cohomology (encyclopedia article)
• The flat Grothendieck-Riemann-Roch theorem without adiabatic techniques
• Differential K-theory as equivalence classes of maps to Grassmannians and unitary groups