Mazur manifolds and symplectic structures

TL;DR

This paper employs Heegaard Floer homology to obstruct symplectic structures on certain Mazur manifolds and explores implications for exotic 4-manifolds with specific boundary conditions.

Contribution

It introduces a method to obstruct symplectic structures on Mazur manifolds using Floer homology and links these results to the existence of exotic 4-manifold pairs.

Findings

Obstructions to symplectic structures on Akbulut-Kirby Mazur manifolds with specific boundary spheres.

Implications for the existence of exotic pairs of simply connected 4-manifolds.

Connections between Floer homology invariants and 4-manifold topology.

Abstract

We use the Heegaard Floer homology cobordism maps to obstruct the existence of a symplectic structure on the Akbulut-Kirby Mazur manifolds whose boundary is a Brieskorn sphere $Y$ among $\Sigma(2,3,13),$ $\Sigma(2,5,7)$ and $\Sigma(3,4,5)$. Furthermore, we describe how our results imply the existence of exotic pairs of simply connected 4-manifolds, with definite intersection form, whose boundary is $Y$.