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

We construct examples of exponentially asymptotically cylindrical (EAC) Riemannian 7-manifolds with holonomy group equal to G2. To our knowledge, these are the first such examples. We also obtain EAC 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/Γ can be deformed to give one of the compact G2-manifolds obtainable as a generalized connected sum of two EAC SU(3)-manifolds via the method of Kovalev (J Reine Angew Math 565:125–160, 2003).