Obstructions to finite dimensional cohomology of abstract Cauchy-Riemann complexes

TL;DR

This paper investigates conditions under which certain global cohomology groups of compact abstract CR manifolds are infinite dimensional, highlighting obstructions related to the Levi form.

Contribution

It establishes new conditions on the Levi form that lead to infinite dimensionality of cohomology groups in abstract CR manifolds.

Findings

Certain Levi form conditions imply infinite dimensional cohomology groups

Obstructions to finite dimensionality are characterized by Levi form properties

Results apply to CR manifolds of arbitrary codimension

Abstract

Let $M$ be a compact abstract $CR$ manifold of arbitrary $CR$ codimension. Under certain conditions on the Levi form we prove the infinite dimensionality of some global cohomology groups of $M$.