The index of \(b\)-pseudodifferential operators on manifolds with corners. (English) Zbl 1089.58016
The author characterizes the multi-cylindrical (or \(b\)-type) pseudodifferential operators that are Fredholm on weighted Sobolev spaces and he generalizes the Atiyah-Patodi-Singer index formula to the operators on compact manifolds with corners of arbitrary codimension. The index formula contains the usual interior term manufactured from the analytic Atiyah-Singer density coming from the local symbols of the operator and also contains boundary correction terms corresponding to the sum over each hypersurface of regulized \(b\)-eta-type invariants of the induced operators on the boundary faces and the sum over all the ranks of the poles of the inverses of the normal operators of the operator at the hypersurfaces with signs, and contains the term coming from the principal symbol restricted to the hypersurfaces and the poles of the inverses of the normal operators at the hypersurfaces, and the sum of all the \(b\)-eta invariants at all the codimension \(k \geq 2\) faces.
Reviewer: Yong Seung Cho (Seoul)
MSC:
| 58J20 | Index theory and related fixed-point theorems on manifolds |
| 47A53 | (Semi-) Fredholm operators; index theories |
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