most recent 30 from http://mathoverflow.net 2013-05-22T20:03:42Z http://mathoverflow.net/feeds/question/116341 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/116341/pure-mapping-class-group-and-mapping-class-group yanqing 2012-12-14T02:52:31Z 2012-12-14T03:27:18Z

<p>Hi, everyone. </p> <p>I am not sure it is proper to ask the following question on here. </p> <p>Let $S$ be a genus $g\geq 1$ surface with 2-puncture, i.e. genus $g$ closed surface with 2 points removed. And there is a compact surface $S_{1}\subset S$ such that $S-S_{1}$ consists of 2 once-punctured disk. </p> <p>Now in Farb and Margalit' book "A primer on mapping class groups ", they defined the $Mod(S_{1})$ and $PMod(S)$. </p> <p>My first question is </p> <p>Is it true that we can treat $PMod(S)$ as a subgroup of $Mod(S_{1})$?</p>