LOSIK CLASSES FOR CODIMENSION-ONE FOLIATIONS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F22%3A50019315" target="_blank" >RIV/62690094:18470/22:50019315 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.cambridge.org/core/journals/journal-of-the-institute-of-mathematics-of-jussieu/article/abs/losik-classes-for-codimensionone-foliations/5013B99C49A88A7CC38EBFF67D7ABE1E" target="_blank" >https://www.cambridge.org/core/journals/journal-of-the-institute-of-mathematics-of-jussieu/article/abs/losik-classes-for-codimensionone-foliations/5013B99C49A88A7CC38EBFF67D7ABE1E</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/S1474748020000596" target="_blank" >10.1017/S1474748020000596</a>

Jazyk výsledku

angličtina

Název v původním jazyce

LOSIK CLASSES FOR CODIMENSION-ONE FOLIATIONS

Popis výsledku v původním jazyce

Following Losik&apos;s approach to Gelfand&apos;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.

Název v anglickém jazyce

LOSIK CLASSES FOR CODIMENSION-ONE FOLIATIONS

Popis výsledku anglicky

Following Losik&apos;s approach to Gelfand&apos;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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-00496S" target="_blank" >GA18-00496S: Singulární prostory ze speciální holonomie a foliací</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU

ISSN

1474-7480

e-ISSN

1475-3030

Svazek periodika

21

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

29

Strana od-do

1391-1419

Kód UT WoS článku

000776435900001

EID výsledku v databázi Scopus

2-s2.0-85099144485