The Hard Lefschetz property on Almost-Kahler manifolds - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-18T22:34:17Z http://mathoverflow.net/feeds/question/57983 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/57983/the-hard-lefschetz-property-on-almost-kahler-manifolds The Hard Lefschetz property on Almost-Kahler manifolds Hamed 2011-03-09T19:16:09Z 2011-03-11T08:10:16Z <p>In the realm of almost-Kahler geometry , to what extent , the hard Lefschetz property is still holds?</p> http://mathoverflow.net/questions/57983/the-hard-lefschetz-property-on-almost-kahler-manifolds/58003#58003 Answer by Dmitri for The Hard Lefschetz property on Almost-Kahler manifolds Dmitri 2011-03-09T22:27:43Z 2011-03-09T22:27:43Z <p>Since on any symplectic manifold you can easily find an almost-Kahler metric, this question can be reformulated as follows:</p> <p>"In the realm of symplectic geometry , to what extent , the hard Lefschetz property is still holds?"</p> <p>The answer is: It does not hold to a very large extent. There are a lot of examples of symplectic manifolds, where this property doesn't hold. In fact, checking that the hard Lefschetz property does not hold for a given symplectic manifold is one of the most favourite tools to establish that a given symplectic manifold is not Kahler. You can check, for example this page: <a href="http://en.wikipedia.org/wiki/Lefschetz_manifold" rel="nofollow">http://en.wikipedia.org/wiki/Lefschetz_manifold</a></p>