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On the index of elliptic operators on manifolds with edges. (English) Zbl 1138.58310

Sb. Math. 196, No. 9, 1271-1305 (2005); translation from Mat. Sb. 196, No. 9, 23-58 (2005).
Summary: Necessary and sufficient conditions for the representation of the index of elliptic operators on manifolds with edges in the form of the sum of homotopy invariants of symbols on the smooth stratum and on the edge are found. An index formula is obtained for elliptic operators on manifolds with edges under symmetry conditions with respect to the edge covariables.

MSC:

58J20 Index theory and related fixed-point theorems on manifolds
47G30 Pseudodifferential operators
47L80 Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)
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