Lagrangian slice disks with symplectomorphic exteriors

TL;DR

This paper constructs large families of Lagrangian slice disks with Weinstein deformation equivalent exteriors, addressing a key question in symplectic topology and expanding understanding of Lagrangian embeddings.

Contribution

It introduces a method to produce arbitrarily large families of Lagrangian slice disks with Weinstein deformation equivalent exteriors, modifying previous constructions by Abe and Tange.

Findings

Existence of large families of Lagrangian slice disks with identical exteriors

Answer to a Lagrangian version of Hitt and Sumners' question

Raises new open questions in the study of Lagrangian slice disks

Abstract

By modifying a construction of Abe and Tange, we exhibit arbitrarily large families of Lagrangian slice disks with Weinstein deformation equivalent exteriors. This answers a Lagrangian version of a question of Hitt and Sumners. We raise other open questions related to Lagrangian slice disks and their exteriors.