Asymptotic dimension of graph manifold groups - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T22:33:19Z http://mathoverflow.net/feeds/question/82276 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/82276/asymptotic-dimension-of-graph-manifold-groups Asymptotic dimension of graph manifold groups Alessandro Sisto 2011-11-30T14:00:19Z 2012-03-06T14:25:12Z <blockquote> <p>Does every non-geometric graph manifold have fundamental group of asymptotic dimension 3?</p> </blockquote> <p>This is affirmed in <a href="http://arxiv.org/abs/0909.1098" rel="nofollow">http://arxiv.org/abs/0909.1098</a> for closed graph manifolds, but I am interested in non-closed graph manifolds as well. Notice that the asymptotic dimension of such groups is always at least 2 (obvious) and at most 3 (by a result of Bell and Dranishnikov).</p> http://mathoverflow.net/questions/82276/asymptotic-dimension-of-graph-manifold-groups/90365#90365 Answer by Alessandro Sisto for Asymptotic dimension of graph manifold groups Alessandro Sisto 2012-03-06T14:25:12Z 2012-03-06T14:25:12Z <p>I should have seen much earlier that it's 2. In fact, every non-closed graph manifold has a finite sheeted cover that fibers over the circle, see <a href="http://journals.cambridge.org/action/displayAbstract?fromPage=online&amp;aid=37203" rel="nofollow">here</a>. The fundamental group of such cover is an HNN extension of a free group, so that it has asymptotic dimension at most 2 by the main result of <a href="http://arxiv.org/abs/math/0111087" rel="nofollow">this paper</a>.</p>