On tight contact structures with negative maximal twisting number on small Seifert manifolds

TL;DR

This paper investigates the properties of transverse contact structures on small Seifert manifolds and uses these properties to classify tight contact structures within a specific family of such manifolds.

Contribution

It introduces new methods for analyzing transverse contact structures and provides a classification of tight contact structures on certain small Seifert manifolds.

Findings

Characterization of transverse contact structures on small Seifert manifolds

Classification results for tight contact structures on a family of small Seifert manifolds

Insights into the maximal twisting number in the context of tight contact structures

Abstract

We study some properties of transverse contact structures on small Seifert manifolds, and we apply them to the classification of tight contact structures on a family of small Seifert manifolds.