Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structured vector bundles define differential K-theory   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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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg