Families of monotone symplectic manifolds constructed via symplectic cut and their Lagrangian submanifolds

TL;DR

This paper constructs families of monotone symplectic manifolds using symplectic cutting from cotangent bundles with circle actions and explores obstructions to embedding certain Lagrangian submanifolds.

Contribution

It introduces new families of monotone symplectic manifolds via symplectic cutting and identifies obstructions to monotone Lagrangian embeddings within them.

Findings

Construction of new monotone symplectic manifolds via symplectic cut

Identification of obstructions to Lagrangian embeddings

Analysis of Lagrangian submanifold properties in these manifolds

Abstract

We describe families of monotone symplectic manifolds constructed via the symplectic cutting procedure of Lerman from the cotangent bundle of manifolds endowed with a free circle action. We also give obstructions to the monotone Lagrangian embedding of some compact manifolds in these symplectic manifolds.