Residual finiteness of fundamental groups of surfaces. - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T08:21:49Z http://mathoverflow.net/feeds/question/67355 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/67355/residual-finiteness-of-fundamental-groups-of-surfaces Residual finiteness of fundamental groups of surfaces. aglearner 2011-06-09T16:37:06Z 2011-06-09T17:28:48Z <p>What is a simple way to prove that for any compact two-dimensional surface $S$ and an element $g$ in $\mathbb \pi_1(S)$ there exists a finite index normal subgroup $\Gamma\subset \pi_1(S)$ such that $g\notin \Gamma$? </p> <p>In fact, who was first to prove this statement?</p> http://mathoverflow.net/questions/67355/residual-finiteness-of-fundamental-groups-of-surfaces/67357#67357 Answer by Mark Sapir for Residual finiteness of fundamental groups of surfaces. Mark Sapir 2011-06-09T16:58:35Z 2011-06-09T16:58:35Z <p>See <a href="http://www.math.umbc.edu/~campbell/CombGpThy/RF_Thesis/3_Knot_Manifold_Groups.html" rel="nofollow"> this text. </a> The proof is just a few lines. </p>