Braiding Knots in Contact 3-Manifolds

TL;DR

This paper demonstrates that transverse links in contact 3-manifolds can be braided and extends Markov's theorem to classify when two braids represent the same transverse link.

Contribution

It introduces a method to braid transverse links in contact 3-manifolds and generalizes Markov's theorem for transverse isotopy classification.

Findings

Transverse links can be braided in contact 3-manifolds.

Generalization of Markov's theorem for transverse links.

Provides criteria for isotopy of transverse braids.

Abstract

We show that a transverse link in a contact structure supported by an open book decomposition can be transversely braided. We also generalize Markov's theorem on when the closures of two braids represent (transversely) isotopic links.