Structured vector bundles define differential K-theory

James Simons; Dennis Sullivan

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arXiv · 0810.4935

Structured vector bundles define differential K-theory

James Simons·Dennis Sullivan

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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.

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James Simons, Dennis Sullivan. 2008-10-28. Structured vector bundles define differential K-theory. https://arxiv.org/abs/0810.4935

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