  We consider manifolds with special holonomy groups SU(3), G2 and Spin(7) as
suitable for compactification of superstrings, M-theory and F-theory (with only
one time) respectively. The relations of these groups with the octonions are
discussed, reinforcing their role in the physics of string theory and duality.
We also exhibit three triple exact sequences explaining the connections between
the mentioned special holonomy groups.
