Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exotic non-leaves with infinitely many ends   We show that any simply connected topological closed $4$-manifold punctured
along any compact, totally disconnected tame subset $\Lambda$ admits a
continuum of smoothings which are not diffeomorphic to any leaf of a $C^{1,0}$
codimension one foliation on a compact manifold. This includes the remarkable
case of $S^4$ punctured along a tame Cantor set. This is the lowest reasonable
regularity for this realization problem. These results come from a new
criterion for nonleaves in $C^{1,0}$ regularity. We also include a new
criterion for nonleaves in the $C^2$-category.
  Some of our smooth nonleaves are "exotic", i.e., homeomorphic but not
diffeomorphic to leaves of codimension one foliations on a compact manifold.

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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: econ