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

摘要

We construct examples of exponentially asymptotically cylindrical (EAC) Riemannian 7-manifolds with holonomy group equal to G ₂. 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 G ₂-manifolds constructed by Joyce by desingularisation of a flat orbifold T 7/Γ can be deformed to give one of the compact G ₂-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).