Cosimplicial cohomology of restricted meromorphic functions on foliated manifolds

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00636775" target="_blank" >RIV/67985840:_____/25:00636775 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.indag.2024.10.003" target="_blank" >https://doi.org/10.1016/j.indag.2024.10.003</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.indag.2024.10.003" target="_blank" >10.1016/j.indag.2024.10.003</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Cosimplicial cohomology of restricted meromorphic functions on foliated manifolds

Popis výsledku v původním jazyce

Starting from the axiomatic description of meromorphic functions with prescribed analytic properties, we introduce the cosimplicial cohomology of restricted meromorphic functions defined on foliations of smooth complex manifolds. Spaces for double chain-cochain complexes and coboundary operators are constructed. Multiplications of several restricted meromorphic functions with non-commutative parameters, as well as for elements of double complex spaces are introduced and their properties are discussed. In particular, we prove that the construction of invariants of cosimplicial cohomology of restricted meromorphic functions is non-vanishing, independent of the choice of the transversal basis for a foliation, and invariant with respect to changes of coordinates on a smooth manifold and on transversal sections. As an application, we provide an example of general cohomological invariants, in particular, generalizing the Godbillon–Vey invariant for codimension one foliations.

Název v anglickém jazyce

Cosimplicial cohomology of restricted meromorphic functions on foliated manifolds

Popis výsledku anglicky

Starting from the axiomatic description of meromorphic functions with prescribed analytic properties, we introduce the cosimplicial cohomology of restricted meromorphic functions defined on foliations of smooth complex manifolds. Spaces for double chain-cochain complexes and coboundary operators are constructed. Multiplications of several restricted meromorphic functions with non-commutative parameters, as well as for elements of double complex spaces are introduced and their properties are discussed. In particular, we prove that the construction of invariants of cosimplicial cohomology of restricted meromorphic functions is non-vanishing, independent of the choice of the transversal basis for a foliation, and invariant with respect to changes of coordinates on a smooth manifold and on transversal sections. As an application, we provide an example of general cohomological invariants, in particular, generalizing the Godbillon–Vey invariant for codimension one foliations.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Indagationes Mathematicae-New Series

ISSN

0019-3577

e-ISSN

1872-6100

Svazek periodika

36

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

16

Strana od-do

961-976

Kód UT WoS článku

001511668900003

EID výsledku v databázi Scopus

2-s2.0-85207285035