Minimal Diffeomorphisms and Cohomology - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-18T14:36:11Z http://mathoverflow.net/feeds/question/23793 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/23793/minimal-diffeomorphisms-and-cohomology Minimal Diffeomorphisms and Cohomology Paul Siegel 2010-05-06T22:30:56Z 2010-05-06T22:30:56Z <p>Let $M$ be a compact manifold and let $D$ be a minimal diffeomorphism from $M$ to itself (meaning there are no nontrivial invariant subspaces). I believe it was Connes who proved that if the first cohomology group of $M$ vanishes then the crossed product C* algebra $C(M) \times_D \mathbb{Z}$ has no nontrivial idempotents.</p> <p>I am wondering if this theorem has a (partial) converse. Ideally I would like a procedure which, under suitable assumptions on $M$ and $D$, associates a nontrivial projection to each cohomology class of $M$. I'm hoping this procedure would give an alternative way to construct the Powers-Rieffel projections associated to irrational rotation algebras, for example.</p> <p>Any ideas?</p>