most recent 30 from http://mathoverflow.net 2013-05-20T03:24:36Z http://mathoverflow.net/feeds/question/78760 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/78760/are-there-replacements-for-the-curve-complex-that-make-up-for-its-weaknesses yanqing 2011-10-21T12:25:49Z 2011-10-24T12:30:25Z

<p>As far as I know, the most common structure of curves in surface is called the curve complex. John Hempel linked the curve complex and Heegaard Splitting and defined Heegaard Distance. There are lots of results about that, e.g., the work of Tseuyoshi Kobayashi, Ruifeng Qiu, Martin Scharlemann, Saul Schleimer, Maggy Tomova, Yair Minsky and so on.</p> <p>This structure has a weak point in that that you can not see any symmetry, and since it is not locally finite, we can not figure out the geodesic. My question is:</p> <blockquote> <p>Is there any other structure which can avoid the weak points?</p> </blockquote>