Obstructions to the existence of monotone Lagrangian embeddings into cotangent bundles of manifolds fibered over the circle

TL;DR

This paper investigates topological barriers preventing certain monotone Lagrangian embeddings in cotangent bundles of manifolds fibered over the circle, extending previous work to broader classes of spaces.

Contribution

It generalizes Damian's constructions to identify new topological obstructions for monotone Lagrangian embeddings in cotangent bundles of fibered manifolds.

Findings

Identifies specific topological obstructions to monotone Lagrangian embeddings.

Extends previous results to manifolds fibered over the circle.

Provides new criteria for the non-existence of such embeddings.

Abstract

We extend constructions and results of Damian to get topological obstructions to the existence of closed monotone Lagrangian embeddings into the cotangent bundle of a space which is the total space of a fibration over the circle.