Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symplectic and Poisson structures of certain moduli spaces. II.
  Projective representations of cocompact discrete planar groups   Let $G$ be a Lie group with a biinvariant metric, not necessarily positive
definite. It is shown that a certain construction carried out in an earlier
paper for the fundamental group of a closed surface may be extended to an
arbitrary infinite orientation preserving cocompact planar discrete group of
euclidean or non-euclidean motions $\pi$ and yields (i) a symplectic structure
on a certain smooth manifold $\Cal M$ containing the space $\roman{Hom}(\pi,G)$
of homomorphisms and, furthermore, (ii) a hamiltonian $G$-action on $\Cal M$
preserving the symplectic structure together with a momentum mapping in such a
way that the reduced space equals the space $\roman{Rep}(\pi,G)$ of
representations. More generally, the construction also applies to certain
spaces of projective representations. For $G$ compact, the resulting spaces of
representations inherit structures of {\it stratified symplectic space\/} in
such a way that the strata have finite symplectic volume . For example, {\smc
Mehta-Seshadri} moduli spaces of semistable holomorphic parabolic bundles with
rational weights or spaces closely related to them arise in this way by {\it
symplectic reduction in finite dimensions\/}.

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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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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: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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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: cs