On generalizing Lutz twists

TL;DR

This paper generalizes Lutz twists to all dimensions, demonstrating the flexibility of contact structures and showing that Euclidean space admits multiple distinct contact structures.

Contribution

It introduces a higher-dimensional generalization of Lutz twists, expanding the understanding of contact structures and their classifications.

Findings

Every contact manifold can be given a non-fillable contact structure

$\mathbb{R}^{2n+1}$ admits at least three distinct contact structures

The generalization shows great flexibility in overtwisted families

Abstract

We give a possible generalization of Lutz twist to all dimensions. This reproves the fact that every contact manifold can be given a non-fillable contact structure and also shows great flexibility in the manifolds that can be realized as cores of overtwisted families. We moreover show that $R^{2n+1}$ has at least three distinct contact structures. This version of the paper contains both the texts of the published version of the paper together with an Erratum to the published version appended to the end.