The maximal coarse Baum-Connes conjecture for spaces which admit a fibred coarse embedding into Hilbert space
By Xiaoman Chen, Qin Wang, Guoliang Yu. 2012
85 citations recorded by the source corpus.
We introduce a notion of fibred coarse embedding into Hilbert space for metric spaces, which is a generalization of Gromov's notion of coarse embedding into Hilbert space. It turns out that a large class of expander graphs admit such an embedding. We show that the maximal coarse Baum-Connes conjecture holds for metric spaces with bounded geometry which admit a fibred coarse embedding into Hilbert space.
Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/17266a1cba484f9df12488821108af1071f73c17
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In Applied Mathematics
- Rufus Willett
- Martin Finn-Sell
- E. Guentner
- Guoliang Yu
- P. Baum
- Nathanial P. Brown Narutaka Ozawa
- Assaf Naor
- Ján Špakula
In Mathematical Physics
- Rufus Willett
- Martin Finn-Sell
- Guoliang Yu
- E. Guentner
- P. Baum
- Ján Špakula
- Nathanial P. Brown Narutaka Ozawa
- Qin Wang
In Statistics and Probability
Citations in the corpus
- Geometric property (T) (2013, background): “(5) A sequence of finite graphs (Xn) with geometric property (T) cannot also admit a fibered coarse embedding into Hilbert space [5], or have the boundary Haagerup property [7], unless supn |Xn| is finite (Theorem 8.”
- Fibred coarse embeddings, a-T-menability and the coarse analogue of the Novikov conjecture (2013, methodology): “We explain the relationship between this conjecture and the work of [6] and give a new method to prove the maximal coarse Baum-Connes conjecture in this instance that has additional consequences.”
- Expanders, exact crossed products, and the Baum–Connes conjecture (2013, background): “Moreover, some of the known expander-based counterexamples to the original Baum-Connes conjecture become confirming examples for our reformulated conjecture.”