Holonomy and Holonomy group

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 Holonomy.


Given a manifold, M, and a point p on M. We append a vector,v  at p, and subject it to parallel transport around a loop. The number of times we revolve around said loop to match the original orientation of v at p is the holonomy.


Take a loop over $I=[0,1]  i.e f(0) = f(1)$

We can write the group of parallel transport maps around a loop  $Hol_p(g)$.

Naturally $Hol_p(g) \rightarrow GL(T_p M)$

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