Elliptic theory on manifolds with corners: I. Dual manifolds and pseudodifferential operators

Abstract

In this first part of the paper, we define a natural dual object for manifolds with corners and show how pseudodifferential calculus on such manifolds can be constructed in terms of the localization principle in C ∗-algebras. In the second part, these results will be applied to the solution of Gelfand's problem on the homotopy classification of elliptic operators for the case of manifolds with corners.