Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: What to expect from $U(n)$ Seiberg-Witten monopoles for $n > 1$   We study generalisations to the structure groups U(n) of the familiar
(abelian) Seiberg-Witten monopole equations on a four-manifold $X$ and their
moduli spaces. For $n=1$ one obtains the classical monopole equations. For $n >
1$ our results indicate that there should not be any non-trivial
gauge-theoretical invariants which are obtained by the scheme `evaluation of
cohomology classes on the fundamental cycle of the moduli space'. For, if
$b_2^+$ is positive the moduli space should be `cobordant' to the empty space
because we can deform the equations so as the moduli space of the deformed
equations is generically empty. Furthermore, on K\"ahler surfaces with $b_2^+ >
1$, the moduli spaces become empty as soon as we perturb with a non-vanishing
holomorphic 2-form.

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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an