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Math Help - does pushforward and the operator partial communicates with each other?

  1. #1
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    does pushforward and the operator partial communicates with each other?

    we know that pushforward and d is commutative.
    i'm confused that whether pushforward coomunicate with partial and conjugation?
    what's more,i wonder whether it's true that pushforward composited with pullback is identity.
    thx
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  2. #2
    Senior Member Tinyboss's Avatar
    Joined
    Jul 2008
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    Re: does pushforward and the operator partial communicates with each other?

    The pullback of the pushforward is not necessarily the identity--consider the case where the codomain has lower dimension than the domain, for example. If your map is a local embedding, however, the result will be true.
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