The vanishing of the contact invariant in the presence of torsion

TL;DR

This paper proves that the Ozsvath-Szabo contact invariant becomes zero for closed contact 3-manifolds exhibiting positive Giroux torsion, highlighting a significant property in contact topology.

Contribution

It establishes a vanishing result for the contact invariant in the presence of positive Giroux torsion, advancing understanding of contact invariants in topology.

Findings

Contact invariant vanishes with positive Giroux torsion

Provides a new criterion for contact invariant behavior

Enhances understanding of contact topology and torsion effects

Abstract

We prove that the Ozsvath-Szabo contact invariant of a closed contact 3-manifold with positive Giroux torsion vanishes.