Deformations of asymptotically cylindrical G_2 manifolds

Abstract

We prove that for a 7-dimensional manifold M with cylindrical ends the moduli space of exponentially asymptotically cylindrical torsion-free G_2 structures is a smooth manifold (if non-empty), and study some of its local properties. We also show that the holonomy of the induced metric of an exponentially asymptotically cylindrical G_2 manifold M is exactly G_2 if and only if its fundamental group is finite and neither M nor any double cover of M is homeomorphic to a cylinder.

31 pages, corrected proof of proposition 6.23

References in corpus (1)

• Ricci-flat deformations of asymptotically cylindrical Calabi--Yau manifolds

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• Desingularization of G_2 manifolds with isolated conical singularities
• Asymptotically cylindrical 7-manifolds of holonomy G_2 with applications to compact irreducible G_2-manifolds
• Complete non-compact Spin(7) manifolds from self-dual Einstein 4-orbifolds
• Asymptotically cylindrical Calabi-Yau manifolds
• Asymptotically cylindrical manifolds with holonomy Spin(7). I
• Superconformal algebras for generalized Spin(7) and G${}_2$ connected sums
• Complete Calabi-Yau metrics from P^2 # 9 \bar P^2
• Manifolds with analytic corners
• Analysis and spectral theory of neck-stretching problems
• Gluing and deformation of asymptotically cylindrical Calabi-Yau manifolds in complex dimension three