Counterexamples to the Baum—Connes conjecture

By N. Higson, Vincent Lafforgue, G. Skandalis. 2002

328 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3152e1d1f2b9edb4bed55b795d65e2511003a030

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Rufus Willett
2. W. Lück
3. Arthur Bartels
4. Guoliang Yu
5. J. Tu
6. Ján Špakula
7. H. Reich
8. Martin Finn-Sell

In Applied Mathematics

1. J. Tu
2. Rufus Willett
3. Martin Finn-Sell
4. Ján Špakula
5. Guoliang Yu
6. Arthur Bartels
7. Dominik Gruber
8. H. Reich

In Mathematical Physics

1. W. Lück
2. Arthur Bartels
3. Rufus Willett
4. Guoliang Yu
5. H. Reich
6. J. Tu
7. Martin Finn-Sell
8. Ján Špakula

Citations in the corpus

• Fibred coarse embeddings, a-T-menability and the coarse analogue of the Novikov conjecture (2013, background): “Certain types of expander graph are known to be counterexamples to the BaumConnes conjecture [13, 12, 30, 31, 19] and within this class, it is possible to prove some positive results under hypotheses on the structure of the expander; it is known that certain families do satisfy the coarse analogue o”
• The coarse Baum–Connes conjecture and groupoids (2002, background): “This conjecture is known to be true in many cases [10], but not in general [3].”
• The Borel Conjecture for hyperbolic and CAT(0)-groups (2009, methodology): “Counterexamples to the Baum-Connes Conjecture with coefficients are groups with expanders [33].”
• Property (T) and rigidity for actions on Banach spaces (2005, methodology): “le [N1] (and [PS],[Rz]). It has also been an important tool in providing interesting (counter) examples: to Day’s “von Neumann conjecture” [Gr1, 5.6] and in the context of the Baum– Connes conjecture [HLS] (related to [Gr2]). Initially defined in terms of unitary representations, property (T) turned ”
• Coefficients for the Farrell¿Jones Conjecture (2005, background): “Of course the development of a Farrell-Jones Conjecture with Coeffi- cients was motivated by this analogy. The reader should be warned that the BaumConnes Conjecture with Coefficients is know to be wrong [HLS02]. At present it is not clear whether the Farrell-Jones Conjecture with Coefficients 3.2 fails f”
• Infinitely presented graphical small cancellation groups are acylindrically hyperbolic (2014, methodology): “Groups containing expander graphs in a suitable way have provided the only known counterexamples to the Baum-Connes conjecture with coefficients [HLS02].”
• On a small cancellation theorem of Gromov (2003, background): “It is the basic construction involved in the announcement of a counter-example to the Baum-Connes conjecture with coefficients (see [HLS02] which elaborates on [Gro03], or [Ghy03] for a survey).”