Tight small Seifert fibered manifolds with $e_0=-2$

Abstract

In this paper we provide the classification of tight contact structures on some small Seifert fibered manifolds. As an application of this classification, combined with work of Lekili in \cite{L2010}, we obtain infinitely many counterexamples to a question of Honda-Kazez-Matić that asks whether a right-veering, non-destabilizable open book necessarily supports a tight contact structure.

Corrected main result, and typos. A new section is added

References in corpus (3)

• Right-veering diffeomorphisms of compact surfaces with boundary II
• Four-dimensional symplectic cobordisms containing three-handles
• The vanishing of the contact invariant in the presence of torsion

Cited by in corpus (5)

• Classification of tight contact structures on surgeries on the figure-eight knot
• Fillability of small Seifert fibered spaces
• Seiberg-Witten Floer homotopy contact invariant
• A simple class of infinitely many absolutely exotic manifolds
• Classification of tight contact structures on a solid torus