K-theory for the maximal Roe algebra of certain expanders

By Oyono-Oyono Herv'e, Guoliang Yu. 2009

73 citations recorded by the source corpus.

We study in this paper the maximal version of the coarse Baum-Connes assembly map for families of expanding graphs arising from residually finite groups. Unlike for the usual Roe algebra, we show that this assembly map is closely related to the (maximal) Baum-Connes assembly map for the group and is an isomorphism for a class of expanders. We also introduce a quantitative Baum-Connes assembly map and discuss its connections to K-theory of (maximal) Roe algebras.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/77fbb2c599d96d16f437149f970412dec61dfc97

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. Guoliang Yu
3. Ján Špakula
4. E. Guentner
5. Martin Finn-Sell
6. Nathanial P. Brown Narutaka Ozawa
7. Zhizhang Xie

In Mathematical Physics

1. Rufus Willett
2. Martin Finn-Sell
3. Guoliang Yu
4. Ján Špakula
5. E. Guentner
6. P. Baum
7. Nathanial P. Brown Narutaka Ozawa
8. Qin Wang

In Statistical and Nonlinear Physics

1. Rufus Willett
2. Guoliang Yu
3. Martin Finn-Sell
4. Ján Špakula
5. E. Guentner

Citations in the corpus

• Maximal and reduced Roe algebras of coarsely embeddable spaces (2011, background): “The authors would further like to thank Guoliang Yu for encouragement to pursue this research and Erik Guentner for helpful discussions about E-theory.”
• Fibred coarse embeddings, a-T-menability and the coarse analogue of the Novikov conjecture (2013, background): “In particular many expanders are known to satisfy this property, such as those coming from a-T-menable discrete groups or those of large girth [6, 19].”
• 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.”
• Geometric property (T) (2013, result): “The treatment in [18] was quite brief; moreover, we expect that geometric property (T) will see some applications outside of K-theory and higher index theory.”
• Higher index theory for certain expanders and Gromov monster groups I (2010, background): “the coarse Novikov conjecture), or of its maximal version, is known to be true for certain classes of expanders by work of Gong–Wang–Yu [15], Chen– Tessera–Wang–Yu [10], Guentner–Tessera–Yu [17] and Oyono-Oyono–Yu [32].”