Homology of Pseudodifferential Operators I. Manifolds with Boundary
نویسنده
چکیده
The Hochschild and cyclic homology groups are computed for the algebra of ‘cusp’ pseudodifferential operators on any compact manifold with boundary. The index functional for this algebra is interpreted as a Hochschild 1-cocycle and evaluated in terms of extensions of the trace functionals on the two natural ideals, corresponding to the two filtrations by interior order and vanishing degree at the boundary, together with the exterior derivations of the algebra. This leads to an index formula which is a pseudodifferential extension of that of Atiyah, Patodi and Singer for Dirac operators; together with a symbolic term it involves the ‘eta’ invariant on the suspended algebra over the boundary previously introduced by the first author.
منابع مشابه
Index and Homology of Pseudodifferential Operators on Manifolds with Boundary
We prove a local index formula for cusp-pseudodifferential operators on a manifold with boundary. This is known to be equivalent to an index formula for manifolds with cylindrical ends, and hence we obtain a new proof of the classical Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary, as well as an extension of Melrose’s b-index theorem. Our approach is based on ...
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