Poincare duality in Morava K-theory for classifying spaces of orbifolds

TL;DR

This paper extends Morava K-theory duality from finite group classifying spaces to orbifolds, using stack theory to establish a Poincare duality framework with concrete examples.

Contribution

It generalizes the Morava K-theory duality map to orbifolds by employing differentiable stacks, creating a stack-based Poincare duality for classifying spaces.

Findings

Established a K(n)-version of Poincare duality for orbifold classifying spaces

Constructed a stack version of the duality map using differentiable stacks

Provided examples and calculations illustrating the duality

Abstract

Greenlees and Sadofsky showed that the classifying spaces of finite groups are self-dual with respect to Morava K-theory K(n). Their duality map was constructed using a transfer map. We generalize their duality map and prove a K(n)-version of Poincare duality for classifying spaces of orbifolds. By regarding these classifying spaces as the homotopy types of certain differentiable stacks, our construction can be viewed as a stack version of Spanier-Whitehead type construction. Some examples and calculations will be given at the end.