Asymptotically cylindrical 7-manifolds of holonomy G_2 with applications to compact irreducible G_2-manifolds

摘要

We construct examples of exponentially asymptotically cylindrical Riemannian7-manifolds with holonomy group equal to G_2. To our knowledge, these are thefirst such examples. We also obtain exponentially asymptotically cylindricalcoassociative calibrated submanifolds. Finally, we apply our results to showthat one of the compact G_2-manifolds constructed by Joyce by desingularisationof a flat orbifold T^7/\Gamma can be deformed to one of the compactG_2-manifolds obtainable as a generalized connected sum of two exponentiallyasymptotically cylindrical SU(3)-manifolds via the method given by the firstauthor (math.DG/0012189).