Higher-dimensional contact manifolds with infinitely many Stein fillings

TL;DR

This paper constructs higher-dimensional contact manifolds that are Stein fillable and demonstrates that each admits infinitely many Stein fillings that are pairwise homotopy inequivalent, revealing complex filling structures in high dimensions.

Contribution

It introduces a method to produce infinite families of high-dimensional contact manifolds with infinitely many distinct Stein fillings, expanding understanding of contact topology.

Findings

Existence of infinite families of Stein fillable contact manifolds in dimensions 4n-1.

Each manifold admits infinitely many pairwise homotopy inequivalent Stein fillings.

Advances the classification of Stein fillings in higher dimensions.

Abstract

For any integer $n\geq 2$, we construct an infinite family of Stein fillable contact $(4n-1)$-manifolds each of which admits infinitely many pairwise homotopy inequivalent Stein fillings.