Partial twists and exotic Stein fillings

TL;DR

The paper introduces an algorithm to generate infinitely many pairwise exotic Stein fillings for the same contact 3-manifolds using positive allowable Lefschetz fibrations, revealing new topological diversity.

Contribution

It provides a novel algorithmic method to produce and analyze infinitely many exotic Stein fillings with specified topological invariants.

Findings

Infinite exotic Stein fillings for the same contact manifold

Realization of topological invariants across fillings

Existence of contact 3-manifolds with infinitely many exotic fillings

Abstract

We give an algorithm which produces infinitely many pairwise exotic Stein fillings of the same contact 3-manifolds, applying positive allowable Lefschetz fibrations over the disk. As a corollary, for a large class of Stein fillings, we realize the topological invariants (i.e. fundamental group, homology group, homology group of the boundary, and intersection form) of each filling as those of infinitely many pairwise exotic Stein fillings. Furthermore, applying the algorithm, we produce various contact 3-manifolds of support genus one each of which admits infinitely many pairwise exotic Stein fillings.