Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symplectic geometry of the moduli space of projective structures in
  homological coordinates   We introduce a natural symplectic structure on the moduli space of quadratic
differentials with simple zeros and describe its Darboux coordinate systems in
terms of so-called homological coordinates. We then show that this structure
coincides with the canonical Poisson structure on the cotangent bundle of the
moduli space of Riemann surfaces, and therefore the homological coordinates
provide a new system of Darboux coordinates. We define a natural family of
commuting "homological flows" on the moduli space of quadratic differentials
and find the corresponding action-angle variables.
  The space of projective structures over the moduli space can be identified
with the cotangent bundle upon selection of a reference projective connection
that varies holomorphically and thus can be naturally endowed with a symplectic
structure. Different choices of projective connections of this kind (Bergman,
Schottky, Wirtinger) give rise to equivalent symplectic structures on the space
of projective connections but different symplectic polarizations: the
corresponding generating functions are found. We also study the monodromy
representation of the Schwarzian equation associated with a projective
connection, and we show that the natural symplectic structure on the the space
of projective connections induces the Goldman Poisson structure on the
character variety. Combined with results of Kawai, this result shows the
symplectic equivalence between the embeddings of the cotangent bundle into the
space of projective structures given by the Bers and Bergman projective
connections.

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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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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: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat