Talk:Connection (principal bundle)

Vertical space definition "Relation to Ehresmann connections"

The definition given is V_p=T_p(P_π(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 P_π(p) means the fiber π^-1(π(p)) (which is a manifold) and T_p(P_π(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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