The fundamental group of the space of contact structures on the 3-torus

TL;DR

This paper proves that the fundamental group of the space of contact structures on the 3-torus is isomorphic to the integers, revealing its topological complexity.

Contribution

It establishes the fundamental group's structure for the space of contact structures on the 3-torus, a previously unknown topological property.

Findings

Fundamental group is isomorphic to the integers.

Space of contact structures has a nontrivial topological structure.

Provides new insights into contact topology of the 3-torus.

Abstract

We show that the fundamental group of the space of contact structures on the 3-torus (based at the standard contact structure) is isomorphic to the integers.