On Stein rational balls smoothly but not symplectically embedded in CP^2

TL;DR

This paper constructs an infinite family of Stein rational homology balls that can be smoothly embedded into CP^2 but cannot be embedded in a symplectic manner, highlighting differences between smooth and symplectic topology.

Contribution

It introduces a new family of Stein rational homology balls with smooth but not symplectic embeddings into CP^2, extending previous work by Brendan Owens.

Findings

Constructed an infinite family of Stein rational homology balls.

Demonstrated these balls can be smoothly embedded into CP^2.

Proved these embeddings cannot be symplectically realized.

Abstract

We extend recent work of Brendan Owens by constructing a doubly infinite family of Stein rational homology balls which can be smoothly but not symplectically embedded in CP^2.