On the topology of Lagrangian fillings of the standard Legendrian sphere

In this paper we study the uniqueness of Lagrangian fillings of the standard Legendrian sphere \(\mathcal{L}_0\) in the standard contact sphere \((S^{2n-1}, \xi_{\text st})\). We show that every exact Maslov zero Lagrangian filling \(L\) of \(\mathcal{L}_0\) in a Liouville filling of \((S^{2n-1}, \x...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2023-09
Main Authors: Kim, Joontae, Kwon, Myeonggi
Format: Article
Language:English
Subjects:
Homology
Uniqueness
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we study the uniqueness of Lagrangian fillings of the standard Legendrian sphere \(\mathcal{L}_0\) in the standard contact sphere \((S^{2n-1}, \xi_{\text st})\). We show that every exact Maslov zero Lagrangian filling \(L\) of \(\mathcal{L}_0\) in a Liouville filling of \((S^{2n-1}, \xi_{\text st})\) is a homology ball. If we restrict ourselves to real Lagrangian fillings, then \(L\) is diffeomorphic to the \(n\)-ball for \(n \geq 6\).
ISSN:2331-8422
DOI:10.48550/arxiv.2112.11984