Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On 3-manifolds that are boundaries of exotic 4-manifolds   We give several criteria on a closed, oriented 3-manifold that will imply
that it is the boundary of a (simply connected) 4-manifold that admits
infinitely many distinct smooth structures. We also show that any weakly
fillable contact 3-manifold, or contact 3-manifolds with non-vanishing Heegaard
Floer invariant, is the boundary of a simply connected 4-manifolds that admits
infinitely many distinct smooth structures each of which supports a symplectic
structure with concave boundary, that is there are infinitely many exotic caps
for any such contact manifold.

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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph