User weixu - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T03:20:36Z http://mathoverflow.net/feeds/user/6973 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/30195/to-differently-gluing-of-two-riemann-surfaces-with-boundary-we-get-different-surf/31512#31512 Answer by Weixu for To differently gluing of two Riemann surfaces with boundary we get different surfaces Weixu 2010-07-12T07:26:42Z 2010-07-12T07:26:42Z <p>When you glue $M$ and $N$, for example, along some boundary component $C$. Choose a closed geodesic $\gamma$ on $S$ intersect with $C$. It can be shown that the hyperbolic length of $\gamma$ is changed when you twist along $C$. This means that different twist makes different hyperbolic surface. </p>