Talk:Connection (principal bundle)

Vertical space definition "Relation to Ehresmann connections"
The definition given is Vp=Tp(Pπ(p)) but I'm confused by this since π(p) is in the base space but this gives the impression that it is in the total space P. The definition given in C. Isham Modern Differential Geometry for Physicists is $$V_p = \{\tau\in T_p P | \pi_* \tau = 0\}$$ — Preceding unsigned comment added by Gannektakazoink (talk • contribs) 17:12, 5 January 2013 (UTC)
 * They coincide if Pπ(p) means the fiber π-1(π(p)) (which is a manifold) and Tp(Pπ(p)) means the tangent space to the fiber at the point p. In other words, vertical vectors are tangent vectors to the fibers, i.e., equivalence classes of curves in the fiber π-1(π(p)). Mgvongoeden (talk) 16:23, 29 May 2013 (UTC)

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