On the Gabai-Eliashberg-Thurston theorem

TL;DR

This paper provides a new three-dimensional proof of the Gabai-Eliashberg-Thurston theorem, establishing that certain 3-manifolds admit universally tight contact structures, enhancing understanding of contact topology.

Contribution

It offers a novel, purely three-dimensional proof of a fundamental theorem linking 3-manifold topology and contact geometry, previously proved using different methods.

Findings

Every closed, oriented, irreducible 3-manifold with nonzero second homology admits a universally tight contact structure.

The proof simplifies and clarifies the understanding of the existence of tight contact structures in 3-manifolds.

The result strengthens the connection between 3-manifold topology and contact geometry.

Abstract

We present a new, completely three-dimensional proof of the fact, due to Gabai-Eliashberg-Thurston, that every closed, oriented, irreducible 3-manifold with nonzero second homology carries a universally tight contact structure.