  We show that M-theory on spaces with irreducible holonomy represent Type IIA
backgrounds in which a collection of D6-branes wrap a supersymmetric cycle in a
manifold with a holonomy group different from the one appearing in the M-theory
description. For example, we show that D6-branes wrapping a supersymmetric
four-cycle on a manifold with G_2 holonomy is described in eleven dimensions by
M-theory on a space with Spin(7) holonomy. Examples of such Type IIA
backgrounds which lift to M-theory on spaces with SU(3), G_2, SU(4) and Spin(7)
holonomy are considered. The M-theory geometry can then be used to compute
exact quantities of the gauge theory on the corresponding D-brane
configuration.
