most recent 30 from http://mathoverflow.net 2013-05-23T05:46:49Z http://mathoverflow.net/feeds/question/40200 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/40200/how-many-pants-decompositions-for-a-given-hyperbolic-surface-with-a-given-hyperbo Analysis Now 2010-09-27T19:45:39Z 2010-09-27T19:45:39Z

<p>Given a hyperbolic surface of genus g ( >= 2 )and given a fixed metric on it, how many pants decompositions exist for that surface? I tend to believe that it is finite ? For example, if we take a surface of genus 2, and fix a hyperbolic metric on it,then aren't there exactly two ways of cutting it into two pants ? I know one can give ( Dehn )twists along a geodesic along which we cut, but would that not change the metric ?</p> <p>Thanks !</p>