2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222754We 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 6.23Differential Geometry53C25text