Abstract: The notion of asymptotic dimension was introduced by Gromov as a tool for studying the large scale geometry of finitely generated groups. In 1998 Yu stimulated widespread interest in this concept when he proved the Novikov conjecture for groups that have finite asymptotic dimension and a classifying space with the homotopy type of a finite CW-complex. More recently, Guentner, Tessera and Yu developed a new coarse geometric concept called decomposition complexity, generalizing the notion of asymptotic dimension. In this talk I will present the basics about asymptotic dimension and decomposition complexity, providing many examples along the way. If time permits I will discuss joint work in progress with Andrew Nicas about decomposition complexity.
An Introduction to Asymptotic Dimension and Decomposition Complexity