Rigidity and uniruling for Lagrangian submanifolds

TL;DR

This paper investigates the topological properties of monotone Lagrangian submanifolds within symplectic manifolds by examining their quantum homology and related quantum structures.

Contribution

It introduces new methods linking quantum homology of the ambient manifold to the topology of Lagrangian submanifolds, revealing rigidity and uniruling properties.

Findings

Establishes conditions for rigidity of Lagrangian submanifolds.

Provides criteria for uniruling based on quantum homology.

Connects quantum structures to topological invariants.

Abstract

This paper explores the topology of monotone Lagrangian submanifolds $L$ inside a symplectic manifold $M$ by exploiting the relationships between the quantum homology of $M$ and various quantum structures associated to the Lagrangian $L$.