A note on infinite number of exact Lagrangian fillings for spherical spuns

TL;DR

This paper presents high-dimensional examples of Legendrian submanifolds with infinitely many exact Lagrangian fillings, constructed via spherical spinning of known examples, expanding understanding of their geometric properties.

Contribution

It introduces a method to generate infinite families of Lagrangian fillings for Legendrian submanifolds using spherical spinning, extending previous examples to higher dimensions.

Findings

Existence of infinitely many exact Lagrangian fillings for certain Legendrian submanifolds.

Application of spherical spinning to produce new high-dimensional examples.

Extension of known low-dimensional phenomena to higher dimensions.

Abstract

In this short note we discuss high-dimensional examples of Legendrian submanifolds of the standard contact Euclidean space with an infinite number of exact Lagrangian fillings up to Hamiltonian isotopy. They are obtained from the examples of Casals and Ng by applying to them the spherical spinning construction.