Cosimplicial meromorphic functions cohomology on complex manifolds

0573349 - MÚ 2024 RIV SG eng J - Článek v odborném periodiku
Zuevsky, Alexander
Cosimplicial meromorphic functions cohomology on complex manifolds.
Reviews in Mathematical Physics. Roč. 35, č. 5 (2023), č. článku 2330002. ISSN 0129-055X. E-ISSN 1793-6659
Institucionální podpora: RVO:67985840
Klíčová slova: complex manifolds * cosimplicial cohomology * meromorphic functions
Obor OECD: Pure mathematics
Impakt faktor: 1.8, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1142/S0129055X23300029

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.
Trvalý link: https://hdl.handle.net/11104/0343811