Odd-dimensional solvmanifolds are contact

TL;DR

This paper proves that all odd-dimensional parallelisable closed manifolds, including certain solvmanifolds, admit contact structures, extending known results about odd-dimensional tori.

Contribution

It generalizes Bourgeois's result by showing all odd-dimensional parallelisable closed manifolds are contact, including solvmanifolds from solvable Lie groups.

Findings

Any odd-dimensional parallelisable closed manifold admits a contact structure.

Solvmanifolds from lattices in solvable Lie groups are contact.

Extends contact structure existence beyond tori to broader classes.

Abstract

Bourgeois proved in [5] that odd-dimensional tori admit a contact structure. We shall prove a more general result: Any odd-dimensional parallelisable closed manifold admits a contact structure. This implies that a solvmanifold $\Gamma \backslash G$ is contact, where $\Gamma$ is a lattice in a connected and simply-connected solvable Lie group G of odd dimension.