NONCOMMUTATIVE RESIDUES AND MANIFOLDS WITH CONICAL SINGULARITIES

For even singular point on a manifold with conical singularities a tra ce can be constructed on the ''Cone Algebra with Asymptotics'' introdu ced by B.-W. Schulze. Each of them vanishes on operators supported in the interior and is therefore different from the noncommutative residu e established by Wodzicki. On the ideal of operators with zero conorma l symbol, however, we find another tract which coincides with the nonc ommutative residue in the interior. All these traces are shown to be e ssentially unique on a slightly extended version of the cone algebra. (C) 1997 Academic Press.