Crepant resolutions of Calabi-Yau orbifolds

A Calabi-Yau orbifold is locally modeled on C^n/G where G is a finite subgroup of SL(n, C). One way to handle this type of orbifolds is to resolve them using a crepant resolution of singularities. We use analytical techniques to understand the topology of the crepant resolution in terms of the finite group G. This gives a generalization of the geometrical McKay Correspondence.