Deformations of glued G_2-manifolds
  We study how a gluing construction, which produces compact manifolds with holonomy G_2 from matching pairs of asymptotically cylindrical G_2-manifolds, behaves under deformations. We show that the gluing construction defines a smooth map from a moduli space of gluing data to the moduli space of torsion-free G_2-structures on the glued manifold, and that this is a local diffeomorphism. We use this to partially compactify the moduli space of torsion-free G_2-structures, including it as the interior of a topological manifold with boundary. The boundary points are equivalence classes of matching pairs of torsion-free asymptotically cylindrical G_2-structures. 
Johannes Nordstr\"om