Leafwise Symplectic Structures on Lawson's Foliation (3rd revised)

TL;DR

This paper demonstrates that Lawson's foliation on the 5-sphere can be equipped with a smooth leafwise symplectic structure, achieved by constructing an end-periodic symplectic structure on Fermat type cubic surfaces.

Contribution

It introduces a novel construction of leafwise symplectic structures on Lawson's foliation, utilizing end-periodic symplectic structures on specific cubic surfaces.

Findings

Lawson's foliation admits a smooth leafwise symplectic structure

Fermat type cubic surfaces can be endowed with end-periodic symplectic structures

The construction bridges complex algebraic geometry and symplectic topology

Abstract

The aim of this paper is to show that Lawson's foliation on the 5-sphere admits a smooth leafwise symplectic structure. The main part of the construction is to show that the Fermat type cubic surface admits an end-periodic symplectic structure.