Abstract: In the first part of the talk, I will review the concepts of finite asymptotic dimension and finite decomposition complexity. Then I will introduce the notion of regular decomposition complexity. In the second part, I will explain how these notion lead to injectivity results for assembly maps, for example in algebraic K-theory. Parts of this talk are joined work with A. Nicas and D. Rosenthal and with U. Bunke, A. Engel and C. Winges.
Finite Decomposition Complexity and Assembly Maps