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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2021
- DOI:
- 10.48550/arXiv.2106.07746
- arXiv:
- arXiv:2106.07746
- Bibcode:
- 2021arXiv210607746Z
- Keywords:
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- Mathematics - Functional Analysis
- E-Print:
- arXiv admin note: text overlap with arXiv:math-ph/9806015 by other authors