# The Legendrian Whitney trick

## TL;DR

This paper introduces a Legendrian Whitney trick that enables the removal of intersections between certain contact and Legendrian submanifolds, facilitating the proof of an h-principle for codimension-two contact embeddings.

## Contribution

It presents a novel Legendrian Whitney trick and applies it to establish the h-principle for codimension-two contact embeddings with prescribed contact structures.

## Key findings

- The Legendrian Whitney trick allows intersection removal under smooth cancellation conditions.
- The technique proves the existence of certain contact embeddings.
- It advances understanding of contact topology and Legendrian submanifold interactions.

## Abstract

In this article, we prove a Legendrian Whitney trick which allows for the removal of intersections between codimension-two contact submanifolds and Legendrian submanifolds, assuming such a smooth cancellation is possible. This technique is applied to show the existence h-principle for codimension-two contact embeddings with a prescribed contact structure.