Tight Lagrangian homology spheres in compact homogeneous K\"ahler manifolds

TL;DR

This paper classifies certain Lagrangian submanifolds in compact homogeneous Kähler manifolds that are topologically spheres and have minimal intersection properties, advancing understanding of symplectic topology.

Contribution

It provides a complete classification of tight Lagrangian homology spheres in irreducible compact homogeneous Kähler manifolds, a previously unexplored area.

Findings

Classification of tight Lagrangian homology spheres achieved

Identification of specific topological and geometric properties

Extension of known results in symplectic and Kähler geometry

Abstract

For any irreducible compact homogeneous K\"ahler manifold, we classify the compact tight Lagrangian submanifolds which have the Z_2-homology of a sphere.