| BAZAIKIN, Yaroslav V and Anton GALAEV. Losik classes for codimension one foliations. Journal of the Institute of Mathematics of Jussieu. Cambridge (United Kingdom): Cambridge University Press, 2022, vol. 21, No 4, p. 1391-1419. ISSN 1474-7480. Available from: https://dx.doi.org/10.1017/S1474748020000596. |
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@article{2362218,
author = {Bazaikin, Yaroslav V and Galaev, Anton},
article_location = {Cambridge (United Kingdom)},
article_number = {4},
doi = {http://dx.doi.org/10.1017/S1474748020000596},
keywords = {foliation; leaf space of foliation; characteristic classes of foliation; Gelfand-Fuchs cohomology; Godbillon-Vey-Losik class; Chern-Losik class; Duminy-Losik class; transverse connection; foliation almost without holonomy; dynamical systems; ergodic theory; conjugacy of diffeomorphisms},
language = {eng},
issn = {1474-7480},
journal = {Journal of the Institute of Mathematics of Jussieu},
title = {Losik classes for codimension one foliations},
volume = {21},
year = {2022}
}
TY - JOUR
ID - 2362218
AU - Bazaikin, Yaroslav V - Galaev, Anton
PY - 2022
TI - Losik classes for codimension one foliations
JF - Journal of the Institute of Mathematics of Jussieu
VL - 21
IS - 4
SP - 1391-1419
EP - 1391-1419
PB - Cambridge University Press
SN - 14747480
KW - foliation
KW - leaf space of foliation
KW - characteristic classes of foliation
KW - Gelfand-Fuchs cohomology
KW - Godbillon-Vey-Losik class
KW - Chern-Losik class
KW - Duminy-Losik class
KW - transverse connection
KW - foliation almost without holonomy
KW - dynamical systems
KW - ergodic theory
KW - conjugacy of diffeomorphisms
N2 - 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 nontriviality in terms of dynamical properties of generators of the holonomy groups are found. The nontriviality for the Reeb foliations is shown; this is in contrast with some classical theorems on the Godbillon-Vey class; for example, 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.
ER -
BAZAIKIN, Yaroslav V and Anton GALAEV. Losik classes for codimension one foliations. \textit{Journal of the Institute of Mathematics of Jussieu}. Cambridge (United Kingdom): Cambridge University Press, 2022, vol.~21, No~4, p.~1391-1419. ISSN~1474-7480. Available from: https://dx.doi.org/10.1017/S1474748020000596.
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