Cosimplicial meromorphic functions cohomology on complex manifolds

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00573349" target="_blank" >RIV/67985840:_____/23:00573349 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1142/S0129055X23300029" target="_blank" >https://doi.org/10.1142/S0129055X23300029</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0129055X23300029" target="_blank" >10.1142/S0129055X23300029</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Cosimplicial meromorphic functions cohomology on complex manifolds

Popis výsledku v původním jazyce

Developing ideas of [B. L. Feigin, Conformal field theory and cohomologies of the Lie algebra of holomorphic vector fields on a complex curve, in Proc. Int. Congress of Mathematicians (Kyoto, 1990 ), Vols. 1 and 2 (Mathematical Society of Japan, Tokyo, 1991), pp. 71-85], we introduce canonical cosimplicial cohomology of meromorphic functions for infinite-dimensional Lie algebra formal series with prescribed analytic behavior on domains of a complex manifold M. Graded differential cohomology of a sheaf of Lie algebras via the cosimplicial cohomology of -formal series for any covering by Stein spaces on M is computed. A relation between cosimplicial cohomology (on a special set of open domains of M) of formal series of an infinite-dimensional Lie algebra and singular cohomology of auxiliary manifold associated to a -module is found. Finally, multiple applications in conformal field theory, deformation theory, and in the theory of foliations are proposed.

Název v anglickém jazyce

Cosimplicial meromorphic functions cohomology on complex manifolds

Popis výsledku anglicky

Developing ideas of [B. L. Feigin, Conformal field theory and cohomologies of the Lie algebra of holomorphic vector fields on a complex curve, in Proc. Int. Congress of Mathematicians (Kyoto, 1990 ), Vols. 1 and 2 (Mathematical Society of Japan, Tokyo, 1991), pp. 71-85], we introduce canonical cosimplicial cohomology of meromorphic functions for infinite-dimensional Lie algebra formal series with prescribed analytic behavior on domains of a complex manifold M. Graded differential cohomology of a sheaf of Lie algebras via the cosimplicial cohomology of -formal series for any covering by Stein spaces on M is computed. A relation between cosimplicial cohomology (on a special set of open domains of M) of formal series of an infinite-dimensional Lie algebra and singular cohomology of auxiliary manifold associated to a -module is found. Finally, multiple applications in conformal field theory, deformation theory, and in the theory of foliations are proposed.

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

2023

Kód důvěrnosti údajů

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

Název periodika

Reviews in Mathematical Physics

ISSN

0129-055X

e-ISSN

1793-6659

Svazek periodika

35

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

22

Strana od-do

2330002

Kód UT WoS článku

000931519500001

EID výsledku v databázi Scopus

2-s2.0-85148749764