Talk:Vertical bundle

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It seems to me that something isn't correct here:

The differential dπ:TE→π*TM identifies the quotient bundle TE/VE with the pullback bundle π*TM.

I think that if π:E→M , then dπ:TE→TM and not TE→π*TM.

π*TM is the pullback bundle, so that dπ : TE → π*TM is a morphism of vector bundles over E. Whereas, thinking of it as dπ : TE → TM, it is a mapping which covers π, so that the pair (dπ, π) is a vector bundle morphism. I have seen both in the literature, but the first way it is slightly more precise. silly rabbit (talk) 11:37, 13 March 2008 (UTC)