On the Hausdorff property of some Dolbeault cohomology groups

TL;DR

This paper investigates the Hausdorff property of Dolbeault cohomology groups by establishing duality principles for the Cauchy-Riemann complex across different function spaces.

Contribution

It introduces a duality framework for the Cauchy-Riemann complex that helps analyze the topological properties of Dolbeault cohomology groups.

Findings

Identifies conditions under which Dolbeault cohomology groups are Hausdorff.

Provides duality relations linking different function space cohomologies.

Advances understanding of the topological structure of complex analytic invariants.

Abstract

In this paper we formulate the duality for the Cauchy-Riemann complex in various function spaces and use the duality to study the Hausdorff property of Dolbeault cohomology groups.