Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A correspondence between a class of cone structures and contact forms   In the spirit of Sullivan's paper "Cycles for the Dynamical Study of Foliated
Manifolds and Complex Manifolds", existence of a contact structure on a closed
manifold $M$ is shown to be equivalent to existence of an ample $S^1$-invariant
cone structure with no nontrivial exact structure cycles on the manifold $S^1
\times M$.

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The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex