2021/06/11 by Alexander Zuevsky, Zuevsky, A. · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2106.07746
Developing ideas of \citeFei, 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.