Noncommutative Residues and Manifolds with Conical Singularities

For every singular point on a manifold with conical singularities a trace can be constructed on the “Cone Algebra with Asymptotics” introduced by B.-W. Schulze. Each of them vanishes on operators supported in the interior and is therefore different from the noncommutative residue established by Wodzicki. On the ideal of operators with zero conormal symbol, however, we find another trace which coincides with the noncommutative residue in the interior. All these traces are shown to be essentially unique on a slightly extended version of the cone algebra.