Deformations of asymptotically cylindrical G_2 manifolds

Details Deformations of asymptotically cylindrical G_2 manifolds Deformations of asymptotically cylindrical G_2 manifolds

2007-05-30

arxiv.org/abs/0705.4444v3

Math. Proc. Camb. Phil. Soc. 145 (2008) 311-348

Mathematics

Differential Geometry

31 pages, corrected proof of proposition 6.23

Scientific paper

10.1017/S0305004108001333

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.

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