Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Basic cohomology of canonical holomorphic foliations on complex
  moment-angle manifolds   We describe the basic cohomology ring of the canonical holomorphic foliation
on a moment-angle manifold, LVMB-manifold or any complex manifold with a
maximal holomorphic torus action. Namely, we show that the basic cohomology has
a description similar to the cohomology ring of a complete simplicial toric
variety due to Danilov and Jurkiewicz. This settles a question of Battaglia and
Zaffran, who previously computed the basic Betti numbers for the canonical
holomorphic foliation in the case of a shellable fan. Our proof uses an
Eilenberg-Moore spectral sequence argument; the key ingredient is the formality
of the Cartan model for the torus action on a moment-angle manifold. We develop
the concept of transverse equivalence as an important tool for studying smooth
and holomorphic foliated manifolds. For an arbitrary complex manifold with a
maximal torus action, we show that it is transverse equivalent to a
moment-angle manifold and therefore has the same basic cohomology.

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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn