Communications in Analysis and Geometry

Volume 17 (2009)

Number 3

Deformations of glued $G_{2}$-manifolds

Pages: 481 – 503



Johannes Nordström (Department of Mathematics, Imperial College London)


We study how a gluing construction, which produces compactmanifolds with holonomy $G_{2}$ from matching pairs ofasymptotically cylindrical \gtmfd s, behaves underdeformations. We show that the gluing construction definesa smooth map from a moduli space of gluing data to themoduli space $\defstr$ of torsion-free \gtstr s on theglued manifold, and that this is a local diffeomorphism. Weuse this to partially compactify $\defstr$, including it asthe interior of a topological manifold with boundary. Theboundary points are equivalence classes of matching pairsof torsion-free asymptotically cylindrical \gtstr s.

Published 1 January 2009