Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on collapse, entropy, and vanishing of the Yamabe invariant of
  symplectic 4-manifolds   We make use of $\mathcal{F}$-structures and technology developed by Paternain
- Petean to compute minimal entropy, minimal volume, and Yamabe invariant of
symplectic 4-manifolds, as well as to study their collapse with sectional
curvature bounded from below. \`A la Gompf, we show that these invariants
vanish on symplectic 4-manifolds that realize any given finitely presented
group as their fundamental group. We extend to the symplectic realm a result of
LeBrun which relates the Kodaira dimension with the Yamabe invariant of compact
complex surfaces.

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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
3
The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
1
The categories of this paper are: cs
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The categories of this paper are: plasm-ph