Following up on my post a few days back about Dranishnikov’s talk… After the talk, Sasha asked me if I knew a reference where some “standard” facts about the real version of the coarse Baum-Connes conjecture were stated (as, for example, that the real coarse index of the Dirac operator vanishes for positive scalar curvature manifolds, or that the complex form of the coarse Baum-Connes conjecture implies the real form.
I was sure that these “well known to experts” results must be written down somewhere. Maybe they are, but I couldn’t find a clean reference. So I thought it might be helpful to put together a little note summarizing some of these standard facts. I’ve now posted this on the arXiv and it is available here. If you need the real version of CBC for something, this might be useful.
Originally, Nigel and I were going to cover the real version of everything in Analytic K-Homology. But at some point we got fed up with Clifford algebras and retreated to the complex world. I think that was the only way to get the book finished, but it has left a few loose ends!