User mustafa - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T21:05:34Z http://mathoverflow.net/feeds/user/26207 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/6675/periods-and-commas-in-mathematical-writing/106461#106461 Answer by Mustafa for Periods and commas in mathematical writing Mustafa 2012-09-05T22:06:34Z 2012-09-05T22:06:34Z <p>I disagree with the convention to punctuate formulas. What does it bring to the reader, besides confusion? (one time, I confused a comma and a prime, and I wasted a lot of time). </p> <p>The reader does not need punctuation after a formula anyway, because usually, he stops to understand it.</p> <p>Math formulas already harbor a lot of indexes and signs, so adding punctuation does not help.</p> http://mathoverflow.net/questions/106360/examples-of-manifolds-with-effective-circle-actions Examples of manifolds with effective circle actions? Mustafa 2012-09-04T16:00:33Z 2012-09-05T19:29:36Z <p>I would like to know examples of smooth compact connected manifolds, on which there exists an effective smooth circle action preserving a positive smooth volume, besides the simple example: $[0,1]^d \times \mathbb{S}^1$. Is there a classification of these manifolds?</p> http://mathoverflow.net/questions/106360/examples-of-manifolds-with-effective-circle-actions/106376#106376 Comment by Mustafa Mustafa 2012-09-05T13:22:34Z 2012-09-05T13:22:34Z I was primarily looking for elementary and &quot;concrete&quot; examples, that you provided in dimension 2. In dimension 3, Seifert manifolds can be examples, as mentioned by Liviu. The problem of classification may be too general indeed. http://mathoverflow.net/questions/106360/examples-of-manifolds-with-effective-circle-actions Comment by Mustafa Mustafa 2012-09-05T12:33:12Z 2012-09-05T12:33:12Z An effective action of a group $G$ on $M$ is an action such that there is a set of full measure $F \subset M$ such that for any $x \in F$, there is $g \in G$ such that $gx \not\eq x$. Yes, I allow boundary.