Tight contact structures on the Brieskorn spheres -\Sigma(2,3,6n-1) and contact invariants

TL;DR

This paper computes Ozsváth–Szabó contact invariants for all tight contact structures on a family of Brieskorn spheres, advancing understanding of contact topology in these manifolds.

Contribution

It provides a complete calculation of contact invariants for tight contact structures on -Σ(2,3,6n-1), a previously uncharted class of manifolds.

Findings

Explicit contact invariants for all tight structures on -Σ(2,3,6n-1)

Classification of tight contact structures on these Brieskorn spheres

Enhanced understanding of contact topology in complex 3-manifolds

Abstract

We compute the Ozsv\'ath--Szab\'o contact invariants for all tight contact structures on the manifolds -\Sigma(2,3,6n-1).