A bypass in the middle

TL;DR

This paper offers a topological characterization of certain bypasses in contact 3-manifolds, leading to new proofs of h-principles in overtwisted contact structures.

Contribution

It introduces a novel topological criterion for contractibility of bypasses and applies it to establish new proofs of fundamental h-principles.

Findings

Characterization of bypasses via disjointness conditions

New proofs of h-principles in overtwisted contact 3-manifolds

Topological methods for bypass analysis

Abstract

We provide a topological characterization for a family of bypasses with a fixed attaching arc to be contractible. This characterization is formulated in terms of the existence of a bypass that is disjoint from the given family away from the attaching region. As an application, we provide new proofs of several h-principles in overtwisted contact 3-manifolds.