arXiv:0809.4055 [math.DG]AbstractReferencesReviewsResources
Deformations of glued G_2-manifolds
Published 2008-09-24, updated 2009-10-13Version 2
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.
Comments: 13 pages; minor corrections, numbering changed to match print version
Journal: Comm. Anal. Geom. 17 (2009) 481-503
Categories: math.DG
Subjects: 53C29
Tags: journal article
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