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## trivial holonomy homomorphism [closed]

I have studied about the ' developing map " and ' holonomy homomorphism form the " foundations of hyperbolic geometry ; ratcliff " . I understand the concepts.but there is something I can't get. actually I am reading an article which uses the holonomy. I have a problem here. what are the applications of holonomy homomorphism. and specially and the most important , what can we understand if we know that the holonomy homomorphism of some manifold M is trivial at a base point?

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Euclidean space has trivial holonomy... – Ryan Budney Dec 6 at 8:43