I have been recently reading about "holonomy" groups (not to be confused with "homology"). It seems a rather esoteric subject that is not found in many introductions to topology.
Anyway, for a flat manifold, (e.g. a flat torus), is the holonomy group always either the simple group or a discrete group? (By flat I mean the Riemann tensor is zero everywhere not just the Ricci tensor).
My intuition says that in order to get a continuous holonomy group like $SO(n)$ your manifold would have to have some curvature. Would this be a correct assumption?
P.S. I would like to learn more about advanced topology, are there any good books to start?