User dan - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T13:56:08Z http://mathoverflow.net/feeds/user/12404 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/52828/is-every-contractible-loop-contained-in-a-darboux-chart Is every contractible loop contained in a Darboux chart? Dan 2011-01-22T14:21:50Z 2011-03-10T13:18:03Z <p>Let $(M,\omega)$ be a symplectic manifold and $\gamma:S^1 \rightarrow M$ be a contractible smooth loop. Is it possible to find an open set $U \subset M$ such that $\gamma(S^1) \subset U$ and such that there exists a Darboux chart $\phi : U \rightarrow \mathbb{R}^{2n}$?</p> <p>Clearly this isn't true if $\gamma$ is not assumed contractible (there might not be any chart on $M$ that contains $\gamma(S^1)$!). If $\gamma$ is contractible then there certainly do exists charts that contain $\gamma(S^1)$, but do there necessarily exist <em>Darboux</em> charts?</p>