Pushforward (differential) - Factbites
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# Topic: Pushforward (differential)

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###### In the News (Thu 23 May 13)

 pushforward of Lie bracket - Information Technology Services one elementary result that you see when you first learn differential geometry is that the pushforward of the Lie bracket of two vector fields is the Lie bracket of the pushforward of the two vector fields, i.e. I assume that the proof of this statement is elementary, every textbook i have leaves this proof as an exercise (actually, some books do prove the corresponding more general statement in the case that \phi is not a bijection, in which case there is no well defined pushforward operation) when i try to move the \phi around using the identities of the pullback and the pushforward: www.physicsforums.com /archive/t-16057_Need_practice_in_Analog/t-42095_Astrophysics/t-10505_pushforward_of_Lie_bracket.html

 Maps and Curves Given a map phi:D to C between curves and a function, place or divisor on C, returns the pushforward of X along phi. Given a map phi:D to C between curves and a function, differential, place or divisor on C, returns the pullback of X along phi. We refer to the contravariant maps phi^ * as Pullback s and to the covariant maps phi_ *, corresponding to the Norm between the function fields, as Pushforward s. www.math.lsu.edu /magma/text1153.htm

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