Odd dimensional tori are contact manifolds

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Existence and classification of overtwisted contact structures in all dimensions (2014, methodology): “Bourgeois [5] proved that for any closed contact manifold M and any surface Σ with genus at least one, the product M × Σ admits a contact structure, using work of E.”
Weak and strong fillability of higher dimensional contact manifolds (2011, background): “1 Starting from a closed contact manifold (V , ξ) and a supporting open book decomposition [32], Frédéric Bourgeois constructed in [4] a”
Reeb vector fields and open book decompositions (2008, methodology): “ysocki-Zehnder [HWZ1]. Compactness was explainedin [BEHWZ]. The Fredholm theory and transversality (for non-multiply-covered curves)were treated by Dragnev [Dr]. For the Morse-Bott approach, refer to [Bo1]. Examples of contact homology calculations were done by Bourgeois-Colin [BC], Ustilovsky [U] a”
Geometric criteria for overtwistedness (2015, background): “Bourgeois’ construction [5] of contact structures in Y × T 2 and the observation [42, Example 1.”
Taubes’s proof of the Weinstein conjecture in dimension three (2009, background): “For example it was only in 2002 that odd-dimensional tori were shown to admit contact structures, by Bourgeois [8].”
Twisted supersymmetric 5D Yang-Mills theory and contact geometry (2012, background): “This manifold admits a T (2)-invariant contact structure [21].”