A note on Mazur type Stein fillings of planar contact manifolds

TL;DR

This paper constructs a family of Stein fillable contact 3-spheres with planar open book supports, where each Stein filling is of Mazur type, advancing understanding of contact topology and Stein fillings.

Contribution

It introduces a new family of Stein fillable contact 3-spheres with Mazur type Stein fillings supported by planar open books.

Findings

Constructed a family of contact 3-spheres with specific Stein fillings.

Demonstrated that each contact structure is supported by a planar open book.

Provided examples of Stein fillings of Mazur type for these contact manifolds.

Abstract

We construct a family of Stein fillable contact homology 3-spheres such that each contact structure of the family is supported by an open book with planar page, and a Stein filling of the contact manifold is of Mazur type.