GROUPOIDS WITH TORSION-FREE ISOTROPY AND THEIR INVARIANTS

I will introduce groupoids with torsion-free isotropy and several (topological) dynamical systems of interest which give rise to groupoids in this class. We will apply methods from homotopy theory to study the K-theory of the associated groupoid C*-algebras, and we will borrow sheaf-manipulating techniques from algebraic geometry to study the homology of these groupoids. The case of basic sets of Axiom A systems will be a recurring example throughout the talk.