Stabilization of divisors in high-dimensional contact manifolds

TL;DR

This paper introduces a stabilization operation for codimension 2 contact submanifolds in high-dimensional contact manifolds, linking stabilization to overtwistedness and invariance of contact structures, and demonstrates the non-simplicity of many transverse links.

Contribution

It defines a new stabilization process for contact submanifolds in high dimensions, connecting it to overtwistedness and invariance properties, and shows many transverse links are non-simple.

Findings

Stabilization characterizes overtwisted contact structures.

Transverse stabilization preserves formal contact isotopy classes.

Many transverse links are proven to be non-simple.

Abstract

A stabilization operation is defined for codimension $2$ contact submanifolds in $\dim \geq 5$ contact manifolds $(M, \xi)$. The definition is such that (1) a given $(M, \xi)$ is overtwisted iff its standard transverse unknot is stabilized and (2) transverse stabilization preserves the formal contact isotopy class and intrinsic contact structure of a link. We prove that many transverse links are non-simple.