On the topology of Lagrangian fillings of the standard Legendrian sphere

초록

In this paper we study the uniqueness of Lagrangian fillings of the standard Legendrian sphere L<inf>0</inf> in the standard contact sphere (S2n−1, ξ<inf>st</inf> ). We show that every exact Maslov zero Lagrangian filling L of L<inf>0</inf> in a Liouville filling of (S2n−1, ξ<inf>st</inf> ) is a homology ball. If we restrict ourselves to real Lagrangian fillings, then L is diffeomorphic to the n-ball for n ≥ 6. © 2024, International Press, Inc.. All rights reserved.