K-Exactness

The discrete groups which are fundamental groups of manifolds are at the heart of some of the most challenging problems in geometry and topology. These problems have motivated mathematicians to use both geometry and functional analysis (including C -algebras) to study groups. This geometry and functional analysis approach is culminated in the statement of the Baum-Connes conjecture. K- theory is the language of the Baum-Connes conjecture, as well as the setting for most approaches to its proof. The study of K-nuclearity of C -algebras and K-amenability of groups have contributed significantly to our understanding of the Baum-Connes conjecture. Similarly, K-exactness of C -algebras and groups is the K-theoretic version of exactness. Indeed, a group G is called K-exact if the minimal tensor product by Cr G preserves the K-theoretic cyclic six-term exact sequence, regardless of whether it preserves short exact sequences of C -algebras. It is known that every coarsely embeddable group satisfies the coarse Baum-Connes. In this work we investigate the relationship between K-exactness and coarse embeddability of groups into a Hilbert space H.

Autorentext

I graduated from Bilkent University, Ankara Turkey. I got my Ph.D. in mathematics at Purdue University in 2005. I worked as a visiting assistant professor at the University of Mississippi; Northwestern University; Indiana University, Bloomington. Right now I am working as an assistant professor at Antalya International University.