Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integration over the u-plane in Donaldson theory   We analyze the u-plane contribution to Donaldson invariants of a
four-manifold X. For $b_2^+(X)>1$, this contribution vanishes, but for
$b_2^+=1$, the Donaldson invariants must be written as the sum of a u-plane
integral and an SW contribution. The u-plane integrals are quite intricate, but
can be analyzed in great detail and even calculated. By analyzing the u-plane
integrals, the relation of Donaldson theory to N=2 supersymmetric Yang-Mills
theory can be described much more fully, the relation of Donaldson invariants
to SW theory can be generalized to four-manifolds not of simple type, and
interesting formulas can be obtained for the class numbers of imaginary
quadratic fields. We also show how the results generalize to extensions of
Donaldson theory obtained by including hypermultiplet matter fields.

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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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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: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg