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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