Braided embeddings of contact 3-manifolds in the standard contact 5-sphere

TL;DR

This paper explores how to embed contact 3-manifolds into the standard contact 5-sphere using braiding techniques and investigates obstructions to such braidings through contact geometric methods.

Contribution

It introduces a method for embedding contact 3-manifolds into the standard contact 5-sphere via braidings and identifies obstructions to braiding using contact geometry.

Findings

Many contact 3-manifolds can be embedded into the standard contact 5-sphere.

Obstructions to braiding are characterized using contact geometric techniques.

Abstract

In this paper we study embeddings of contact manifolds using braidings of one manifold about another. In particular we show how to embed many contact 3-manifolds into the standard contact 5-sphere. We also show how to obstruct braidings of one manifold about another using contact geometry.