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

TL;DR

This paper constructs the first known examples of asymptotically cylindrical G_2-manifolds, explores their properties, and applies these results to deform certain compact G_2-manifolds, advancing understanding in special holonomy geometry.

Contribution

It provides the first examples of asymptotically cylindrical G_2-manifolds and demonstrates their application in deforming Joyce's compact G_2-manifolds.

Findings

First examples of asymptotically cylindrical G_2-manifolds

Existence of asymptotically cylindrical coassociative submanifolds

Deformation of Joyce's G_2-manifolds using these constructions

Abstract

We construct examples of exponentially asymptotically cylindrical Riemannian 7-manifolds with holonomy group equal to G_2. 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 G_2-manifolds constructed by Joyce by desingularisation of a flat orbifold T^7/\Gamma can be deformed to one of the compact G_2-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).