Talk:Weinstein conjecture

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Is this still a stub? I can't ever tell... Orthografer 00:47, 3 November 2006 (UTC)

Higher dimensional open books[edit]

Dumb question: Is the third paragraph (which states that the existence of open books implies that any contact form is isotopic to one carrying a Reeb orbit) specific to dimension 3? Or do higher-dimensional contact manifolds also admit (analogues of) open books? 28 January 2008 —Preceding unsigned comment added by (talk) 16:07, 28 January 2008 (UTC)

There are open books in higher odd dimensions. There's a little info in the open book article. I would be interested to know whether the analogous notion of Giroux correspondence holds in higher dimensions. For example, I know not every smooth odd-dimensional manifold has a contact structure, and I don't think there's a general existence result for open books in odd dimensions either. Orthografer (talk) 03:25, 14 July 2008 (UTC)

Article omits any definition of the Weinstein conjecture[edit]

I cannot find any definition of the article's subject in the article.

If there is one thing the article ought to include, it is a statement of what the Weinstein conjecture is.

Can someone knowledgeable about the Weinstein conjecture please include one or more declarative sentences in the article which unequivocally define what it is? Thanks.

The article does include the following opening paragraph:

"In mathematics, the Weinstein conjecture refers to a general existence problem for periodic orbits of Hamiltonian or Reeb vector flows. More specifically, the current understanding is that a regular compact contact type level set of a Hamiltonian on a symplectic manifold should carry at least one periodic orbit of the Hamiltonian flow. The conjecture is stated for any Hamiltonian on any 2n-dimensional symplectic manifold."

But saying what the conjecture "refers to" or what "the current understanding is" -- is quite different from stating the conjecture.Daqu (talk) 19:01, 22 February 2010 (UTC)