Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Losik classes for codimension-one foliations   Following Losik's approach to Gelfand's formal geometry, certain
characteristic classes for codimension-one foliations coming from the
Gelfand-Fuchs cohomology are considered. Sufficient conditions for
non-triviality in terms of dynamical properties of generators of the holonomy
groups are found. The non-triviality for the Reeb foliations is shown; this is
in contrast with some classical theorems on the Godbillon-Vey class, e.g, the
Mizutani-Morita-Tsuboi Theorem about triviality of the Godbillon-Vey class of
foliations almost without holonomy is not true for the classes under
consideration. It is shown that the considered classes are trivial for a large
class of foliations without holonomy. The question of triviality is related to
ergodic theory of dynamical systems on the circle and to the problem of smooth
conjugacy of local diffeomorphisms. Certain classes are obstructions for the
existence of transverse affine and projective connections.

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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex