On holonomy groupoid of vertex operator algebra bundles on foliations

TL;DR

This paper introduces a new category of vertex operator algebra bundles on foliated complex manifolds, providing an intrinsic formulation and linking their cohomology to the holonomy groupoid.

Contribution

It develops a coordinate-independent framework for vertex operator algebra bundles on foliations and connects their cohomology to the holonomy groupoid cohomology.

Findings

Defined vertex operator algebra bundles on foliations.

Provided an intrinsic, coordinate-free formulation.

Linked bundle cohomology to holonomy groupoid cohomology.

Abstract

For a foliation $\F$ defined on a smooth complex manifold $M$ we introduce the category of vertex operator algebra $V$ bundles with sections provided by vectors of elements of the space of algebraically extended $V$-module $W$-valued differentials. An intrinsic coordinate-independent formulation for such bundles is given. Finally, we identify the cohomology of the spaces of sections for a vertex operator algebra $V$ bundle with vertex operator algebra cohomology of the holonomy groupoid $Hol(M, \F)$.