Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Surface group representations in PU(p,q) and Higgs bundles   Using the L^2 norm of the Higgs field as a Morse function, we study the
moduli spaces of U(p,q)-Higgs bundles over a Riemann surface. We require that
the genus of the surface be at least two, but place no constraints on (p,q). A
key step is the identification of the function's local minima as moduli spaces
of holomorphic triples. In a companion paper "Moduli spaces of holomorphic
triples over compact Riemann surfaces" (math.AG/0211428) we prove that these
moduli spaces of triples are non-empty and irreducible.
  Because of the relation between flat bundles and fundamental group
representations, we can interpret our conclusions as results about the number
of connected components in the moduli space of semisimple
PU(p,q)-representations. The topological invariants of the flat bundles are
used to label subspaces. These invariants are bounded by a Milnor-Wood type
inequality. For each allowed value of the invariants satisfying a certain
coprimality condition, we prove that the corresponding subspace is non-empty
and connected. If the coprimality condition does not hold, our results apply to
the closure of the moduli space of irreducible representations.
  This paper, and its companion mentioned above, form a substantially revised
version of math.AG/0206012.

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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: eess