most recent 30 from http://mathoverflow.net 2013-05-25T07:38:15Z http://mathoverflow.net/feeds/question/113970 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/113970/poincare-lemma-in-infinite-dimensions seub 2012-11-20T18:25:18Z 2012-11-20T18:41:47Z

<p>Hi everyone,</p> <p>Is the Poincaré lemma true in infinite dimensions?</p> <p>Here's a precise statement:</p> <p>Let $X$ be a Banach (or maybe Hilbert) vector space, $U$ a simply connected open set in $X$. Is it true that every closed (smooth) $1$-form on $U$ is exact?</p> <p>Thanks!</p>

http://mathoverflow.net/questions/113970/poincare-lemma-in-infinite-dimensions/113973#113973 Peter Michor 2012-11-20T18:41:47Z 2012-11-20T18:41:47Z

<p>Yes, it is, on convenient locally convex vector spaces. Convenient is a very weak completeness condition. See 33.20 in: </p> <p>Andreas Kriegl, Peter W. Michor: The Convenient Setting of Global Analysis. Mathematical Surveys and Monographs, Volume: 53, American Mathematical Society, Providence, 1997.<a href="http://www.mat.univie.ac.at/~michor/apbookh-ams.pdf" rel="nofollow">(pdf)</a></p>