Characterization of codimension one foliations on complex curves by connections

TL;DR

This paper proposes a method to characterize the space of leaves of codimension one foliations on complex curves using connections, and explores an example involving vertex algebra cohomology.

Contribution

It introduces a novel approach to describe foliations via connections and analyzes a specific case with vertex algebra cohomology.

Findings

Characterization of leaf spaces using connections

Application to vertex algebra cohomology of foliations on complex curves

New insights into the structure of codimension one foliations

Abstract

A way to characterize the space of leaves of a foliation in terms of connections is proposed. A particular example of vertex algebra cohomology of codimension one foliations on complex curves is considered.