Topology Seminar: Man Chuen Cheng

It was a result of Greenlees and Sadofsky that classifying spaces of finite groups satisfy a Morava K-theory version of Poincare duality, which was proved by showing the contractibility of the corresponding Tate spectrum. In this series of two talks, I will explain the proof, discuss its generalization to quotient orbifolds and consequences with examples. Some background in equivariant stable homotopy theory will be given. If time permits, I will also explain why the duality map can be viewed as coming from a Spanier-Whitehead type construction for differentiable stacks.