ABSTRACT
In this chapter, we consider the index problem for elliptic operators on a compact singular manifold M. We deal only with manifolds with cone or edge singularities, the former being formally a special case of the latter if the edge X is zerodimensional. To avoid unnecessary wordiness and parallel statements, we adopt the convention that for dimX = 0 the term “edge symbol,” as well as the corresponding notation σ∧, refers to the conormal symbol σc whenever our argument pertains to both edge and conical cases. If some results are valid (or make sense) only for one of the two cases, we always indicate this explicitly. The operators are always assumed to act in the weighted Sobolev spaces Hs,γ(M) or Ws,γ(M). Unless specified otherwise, γ is fixed (and can safely be assumed to be zero).
