Cosimplicial meromorphic functions cohomology on complex manifolds
Result description
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.
Keywords
complex manifoldscosimplicial cohomologymeromorphic functions
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Cosimplicial meromorphic functions cohomology on complex manifolds
Original language description
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.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Reviews in Mathematical Physics
ISSN
0129-055X
e-ISSN
1793-6659
Volume of the periodical
35
Issue of the periodical within the volume
5
Country of publishing house
SG - SINGAPORE
Number of pages
22
Pages from-to
2330002
UT code for WoS article
000931519500001
EID of the result in the Scopus database
2-s2.0-85148749764
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Pure mathematics
Year of implementation
2023