Horizontal decompositions, I

TL;DR

The paper introduces a new handlebody decomposition called horizontal decomposition for smooth, closed, orientable 4-manifolds, classifies the simplest cases, and explores their implications for embeddings in complex projective planes.

Contribution

It defines and classifies horizontal decompositions of 4-manifolds, providing new insights into their structure and embeddings in CP^2.

Findings

Classified the simplest horizontal decompositions of closed 4-manifolds.

Described all such decompositions for CP^2.

Identified infinitely many embeddings of rational homology balls in CP^2.

Abstract

We show that every smooth, closed, orientable 4-manifold X admits a special kind of handlebody decomposition that we call horizontal. We classify the closed 4-manifolds with the simplest horizontal decompositions and we describe all such decompositions of CP^2, showing that they give rise to infinitely many of the known embeddings of rational homology balls in the complex projective plane.