Legendrian barriers in prequantization bundles

TL;DR

This paper demonstrates that prequantization bundles contain explicit Legendrian barriers that prevent the embedding of extended cylinders over Legendrian submanifolds, revealing new geometric obstructions.

Contribution

It introduces explicit Legendrian barriers in prequantization bundles and shows their role in obstructing certain embeddings, a novel geometric insight.

Findings

Legendrian barriers are explicitly constructed in prequantization bundles

These barriers obstruct the embedding of long cylinders over Legendrian submanifolds

The results provide new geometric obstructions in contact topology

Abstract

We show that prequantization bundles have explicit Legendrian barriers, whose removal obstruct the embedding of long cylinders over Legendrian submanifolds.