Exotic Stein fillings with arbitrary fundamental group

TL;DR

This paper constructs complex surface singularity links with infinitely many exotic Stein fillings and smooth four-manifolds, all sharing a specified fundamental group, advancing understanding of 4-manifold topology and Stein fillings.

Contribution

It demonstrates the existence of isolated complex surface singularity links with infinitely many exotic Stein fillings for any finitely presentable group, and constructs exotic smooth four-manifolds with prescribed fundamental groups.

Findings

Existence of singularity links with infinitely many Stein fillings

Construction of exotic smooth four-manifolds with given fundamental group

Presence of non-holomorphic Lefschetz fibrations in constructed manifolds

Abstract

For any finitely presentable group $G$, we show the existence of an isolated complex surface singularity link which admits infinitely many exotic Stein fillings such that the fundamental group of each filling is isomorphic to $G$. We also provide an infinite family of closed exotic smooth four-manifolds with the fundamental group $G$ such that each member of the family admits a non-holomorphic Lefschetz fibration over the two-sphere.