A Necessary and Sufficient Condition on Diffeomorphisms

Abstract:

      We introduce anti-sheaves for C^r-manifolds and a category of anti-sheaves. The adjoint equivalence between the category of anti-sheaves and the category of C^r-manifolds is established. Using such an equivalence, we obtain a characterization for deciding whether two given manifolds arc C^r-diffeomorphic in terms of inherent W.(G)- sheaves. This provides the first known criterion for determining whether two given man- ifolds are diffeomorphic.