Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chern-Weil Constructions on $\Psi$DO Bundles   We construct Chern-Weil classes on infinite dimensional vector bundles with
structure group contained in the algebra $\cl[\leq 0](M, E)$ of non-positive
order classical pseudo-differential operators acting on a finite rank vector
bundle $E$ over a closed manifold $M$. Mimicking the finite dimensional
Chern-Weil construction, we replace the ordinary trace on matrices by linear
functionals on $\cl[\leq 0] (M, E)$ built from the leading symbols of the
operators. The corresponding Chern classes vanish for loop groups, but a
weighted trace construction yields a non-zero class perviously constructed by
Freed. For loop spaces, the structure group reduces to a gauge group of bundle
automorphisms, and we produce non-vanishing universal Chern classes in all
degrees, using a universal connection theorem for these bundles.

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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex