Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Comultiplicativity of the Ozsvath-Szabo contact invariant   Suppose that S is a surface with boundary and that g and h are
diffeomorphisms of S which restrict to the identity on the boundary. Let Y_g,
Y_h, and Y_{hg} be the three-manifolds with open book decompositions given by
(S,g), (S,h), and (S,hg), respectively. We show that the Ozsvath-Szabo contact
invariant is natural under a comultiplication map on Heegaard Floer homology.
It follows that if the contact invariants associated to the open books (S, g)
and (S, h) are non-zero then the contact invariant associated to the open book
(S, hg) is also non-zero. We extend this comultiplication to a map on HF^+, and
as a result we obtain obstructions to the three-manifold Y_{hg} being an
L-space. We also use this to find restrictions on contact structures which are
compatible with planar open books.

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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol