On subcritically Stein fillable 5-manifolds

TL;DR

This paper studies subcritical Stein fillability of contact structures on 5-manifolds, classifying their types based on fundamental group and almost contact structures, and establishing uniqueness results on the 5-sphere.

Contribution

It provides classification results for subcritically Stein fillable contact structures on 5-manifolds, especially for those with finite cyclic fundamental groups and on the 5-sphere.

Findings

Diffeomorphism classification for manifolds with finite cyclic fundamental group.

Uniqueness of the standard contact structure on the 5-sphere.

Subcritical fillability determined by underlying almost contact structure.

Abstract

We make some elementary observations concerning subcritically Stein fillable contact structures on 5-manifolds. Specifically, we determine the diffeomorphism type of such contact manifolds in the case the fundamental group is finite cyclic, and we show that on the 5-sphere the standard contact structure is the unique subcritically fillable one. More generally, it is shown that subcritically fillable contact structures on simply connected 5-manifolds are determined by their underlying almost contact structure. Along the way, we discuss the homotopy classification of almost contact structures.