Asymptotically cylindrical 7-manifolds of holonomy G₂ with applications to compact irreducible G₂-manifolds

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We construct examples of exponentially asymptotically cylindrical Riemannian 7-manifolds with holonomy group equal to G₂. To our knowledge, these are the first such examples. We also obtain exponentially asymptotically cylindrical coassociative calibrated submanifolds. Finally, we apply our results to show that one of the compact G₂-manifolds constructed by Joyce by desingularisation of a flat orbifold T⁷/Γcan be deformed to one of the compact G₂-manifolds obtainable as a generalized connected sum of two exponentially asymptotically cylindrical SU(3)-manifolds via the method given by the first author (math.DG/0012189).