Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Do uniruled six-manifolds contain Sol Lagrangian submanifolds?   We prove using symplectic field theory that if the suspension of a hyperbolic
diffeomorphism of the two-torus Lagrangian embeds in a closed uniruled
symplectic six-manifold, then its image contains the boundary of a symplectic
disc with vanishing Maslov index. This prevents such a Lagrangian submanifold
to be monotone, for instance the real locus of a smooth real Fano manifold. It
also prevents any Sol manifold to be in the real locus of an orientable real
Del Pezzo fibration over a curve, confirming an expectation of J. Koll\'ar.
Finally, it constraints Hamiltonian diffeomorphisms of uniruled symplectic
four-manifolds.

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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-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: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an