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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJun 14th 2010

    stub for Poincare lemma

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeFeb 4th 2011
    • (edited Feb 4th 2011)

    I have added a little bit of substance to Poincare lemma

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeFeb 4th 2011

    @Anyone - the flow of statements at Poincare lemma didn’t make sense to me, so I popped a note in. I made a small correction to a typo (manifolds had changed names mysteriously).

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeFeb 5th 2011
    • (edited Feb 5th 2011)

    Phew, I hadn’t been concentrating when typing. Thanks for catching this.

    Where it said “H dR (X)=H dR (Y)H_{dR}^\bullet(X) = H_{dR}^\bullet(Y)” is was supposed to say “H dR (f 1 *)=H dR (f 2 *)H_{dR}^\bullet(f_1^*) = H_{dR}^\bullet(f_2^*)”. Namely:

    if two cochain maps f 1 *f_1^* and f 2 *f_2^* are homotopic, then they induce the same maps in cohomology.

    Sorry. I have fixed it now. Any further typos? I need to call it quits now.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeFeb 6th 2011

    I have added more details. (Hopefully without weird typos this time!)

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJun 6th 2014
    • (edited Jun 6th 2014)

    I have expanded the Idea-section at Poincare lemma a bit, mentioning also the complex-analytic version and the incarnation of the statement as the local quasi-iso Ω dR \mathbb{R}\to \Omega^\bullet_{dR} (Ω hol \mathbb{C}\to \Omega^\bullet_{hol}). Wanted to do more, but am out of steam now.

  1. Fix definition of homotopy operator

    Tobias Diez

    diff, v18, current

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