A few computations about the real cycle class map in low dimensions

TL;DR

This paper explores the surjectivity of the real cycle class map in low-dimensional real smooth varieties, contributing to the understanding of real integral Hodge theory.

Contribution

It investigates the surjectivity of the real cycle class map in specific low-dimensional cases, advancing the study of real integral Hodge theory.

Findings

Surjectivity established for certain real surfaces.

Connections made to real integral Hodge theory.

Provides new insights into the structure of real cycle class maps.

Abstract

We investigate the surjectivity of the real cycle class map from $I$-cohomology to classical intergral cohomology for some real smooth varieties, in particular surfaces. This might be considered as one of several possible incarnations of real integral Hodge theory.