On the topology of Lagrangian fillings of the standard Legendrian sphere

Abstract

In this paper we study the uniqueness of Lagrangian fillings of the standard Legendrian sphere ${\mathcal{L}}_0$ in the standard contact sphere $(S^{2n-1},{\xi }_{\text{s}t})$. We show that every exact Maslov zero Lagrangian filling $L$ of ${\mathcal{L}}_0$ in a Liouville filling of $(S^{2n-1},{\xi }_{\text{s}t})$ is a homology ball. If we restrict ourselves to real Lagrangian fillings, then $L$ is diffeomorphic to the $n$-ball for $n\ge 6$.

arXiv comment15 pages, 2 figures. Title changed. Accepted for publication in J. Symplectic Geom