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

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/Γcan 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).

36 pages; v2: corrected trivial typos; v3: some arguments corrected and improved; v4: a number of improvements on presentation, paritularly in sections 4 and 6, including an added picture.

References in corpus (1)

• Deformations of asymptotically cylindrical G_2 manifolds

Cited by in corpus (6)

• K3 surfaces with non-symplectic involution and compact irreducible G_2-manifolds
• New invariants of G_2-structures
• Spin(7)-Manifolds as Generalized Connected Sums and 3d N=1 Theories
• Towards Generalized Mirror Symmetry for Twisted Connected Sum $G_2$ Manifolds
• Evidence for an Algebra of ${\mathbf{G}}_2$ Instantons
• Superconformal algebras for generalized Spin(7) and G${}_2$ connected sums