Cosimplicial meromorphic functions cohomology on complex manifolds

Abstract

Developing ideas of \cite{Fei}, 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 $\mathcal{G}$ via the cosimplicial cohomology of $\mathcal{G}$-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 $\mathcal{G}$ and singular cohomology of auxiliary manifold associated to a $\mathcal{G}$-module is found. Finally, multiple applications in conformal field theory, deformation theory, and in the theory of foliations are proposed.

arXiv admin note: text overlap with arXiv:math-ph/9806015 by other authors

References in corpus (2)

• Vertex Algebras and Algebraic Curves
• Deformation theory and rational homotopy type