http://www.openproblemgarden.org/op/rank_vs_genus Comments for "Rank vs. Genus" en http://www.openproblemgarden.org/op/rank_vs_genus#comment-950 <p>Abert and Nikolov have found a connection between the `Rank vs Heegard Genus' problem and the `Fixed Price' problem in dynamics. Specifically, if every countable group has `fixed price' then the ratio of the Heegard genus and the rank of a hyperbolic 3-manifold can be arbitrarily large. For details, see http://arxiv.org/abs/math/0701361 .</p> Sun, 13 Jul 2008 18:46:05 +0200 Anonymous comment 950 at http://www.openproblemgarden.org http://www.openproblemgarden.org/op/rank_vs_genus <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/johnson_jesse">Johnson</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/topology">Topology</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Question</b>&nbsp;&nbsp; Is there a hyperbolic 3-manifold whose fundamental group rank is strictly less than its Heegaard genus? How much can the two differ by? </div> </tr></td> </table> </td> </tr> </table> Johnson, Jesse Topology http://www.openproblemgarden.org/op/rank_vs_genus#comment Mon, 07 Jul 2008 17:35:48 +0200 Jesse Johnson 1783 at http://www.openproblemgarden.org