Lefschetz fibrations and symplectic homology

TL;DR

This paper demonstrates the existence of infinitely many distinct symplectic structures on Euclidean spaces of dimension greater than 6, using Lefschetz fibrations and symplectic homology techniques.

Contribution

It constructs infinitely many pairwise distinct symplectic structures on Euclidean spaces via Lefschetz fibrations, expanding understanding of symplectic topology in high dimensions.

Findings

Existence of infinitely many distinct symplectic structures on R^{2k} for k>3

Construction of these structures using Lefschetz fibrations

Application of symplectic homology to distinguish the structures

Abstract

We show that for each k > 3 there are infinitely many finite type Stein manifolds diffeomorphic to Euclidean space R^{2k} which are pairwise distinct as symplectic manifolds.