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We exhibit examples of closed Riemannian 7-manifolds with holonomy G_2 suchthat the underlying manifolds are diffeomorphic but whose associatedG_2-structures are not homotopic. This is achieved by defining two invariantsof certain U(3)-structures. We show that these agree with the invariants ofG_2-structures defined by Crowley and Nordstr\"om. We construct a suitablecoboundary for G_2 manifolds obtained via the Twisted Connected Sum method thatallows the invariants to be computed in terms of the input data of theconstruction. We find explicit examples where the invariants detect differentconnected components of the moduli of G_2-metrics.

Disconnecting the moduli space of G_2-metrics via U(4)-coboundary defects