Structured vector bundles define differential K-theory

Details Structured vector bundles define differential K-theory Structured vector bundles define differential K-theory

2008-10-28

arxiv.org/abs/0810.4935v1

Mathematics

Algebraic Topology

23 pages

Scientific paper

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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