Leray Residues and Abel's Theorem in CR codimension k

TL;DR

This paper extends Leray's residue calculus to smooth CR manifolds of general type, broadening the mathematical framework for analyzing complex structures in higher codimensions.

Contribution

It introduces a generalized Leray residue calculus applicable to CR manifolds of arbitrary type, expanding the tools available for complex geometric analysis.

Findings

Developed a new residue calculus framework for CR manifolds

Extended classical residue theory to higher codimension CR structures

Provided foundational results for further research in complex geometry

Abstract

In this paper we generalize Leray's calculus of residues in several complex variables, to the situation of an abstract smooth CR manifold M of general type (n,k).