Timeline for Baum-Connes conjecture
Current License: CC BY-SA 2.5
3 events
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| Feb 1, 2011 at 17:32 | comment | added | Paul Siegel | It's a good question, and I can only be of limited use in this regard. I have asked a few people (including Nigel, I think) outright if there are any known nontrivial geometric sufficient conditions on a group which would make it a counterexample, and the answer has consistently been a qualified no. It seems that for the conjecture to be false for a group there has to be some sort of mismatch between its large scale geometry and its harmonic analysis. To try to speculate any further would be straying too far from my (already limited) comfort zone. | |
| Feb 1, 2011 at 14:07 | comment | added | user6976 | @Paul: I know about the paper by Higson, Lafforgue and Skandalis. In particular, they are using Gromov's f.g. group containing expander to construct a counterexample to one of the versions of Baum-Connes conjecture. I wonder what kind of groups do they need to construct a counterexample to the main (original) Baum-Connes conjecture. As far as I know the conjecture is not proved even for uniform lattices in $SL_3(\mathbb{R})$. But perhaps those groups are just not wild enough for this. So what kind of wild groups are needed? | |
| Feb 1, 2011 at 11:28 | history | answered | Paul Siegel | CC BY-SA 2.5 |