Canonical torsor bundles of prescribed rational functions on complex curves

TL;DR

This paper constructs a bundle of prescribed rational functions over complex curves, providing an intrinsic formulation that aids in advanced studies in Lie algebras, conformal field theory, and deformation theory.

Contribution

It explicitly defines and constructs a coordinate-independent prescribed rational functions-valued bundle on complex curves, linking it to various mathematical and physical theories.

Findings

Explicit construction of the bundle $\\mathcal{W}_M$

Coordinate-independent formulation of the bundle

Applications to Lie algebra cohomology and conformal field theory

Abstract

Prescribed rational functions constitute a subset of rational functions satisfying certain symmetry and analyticity conditions. We define and construct explicitly prescribed rational functions-valued bundle $\mathcal{W}_M$ over a smooth complex curve $M$. An intrinsic coordinate-independent formulation for such bundle is is given. The construction presented in this paper is useful for studies of the canonical cosimplicial cohomology of infinite-dimensional Lie algebras on smooth manifolds, as well as for purposed of conformal field theory, deformation theory, and the theory of foliations.