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On invariant index formulas for spectral boundary value problems. (English. Russian original) Zbl 1034.58020
Differ. Equations 35, No. 5, 709-718 (1999); translation from Differ. Uravn. 35, No. 5, 705-714 (1999).
The Atiyah-Patodi-Singer index formula consists of two terms: the “inner” term and the “$$\eta$$-invariant”. Generally, the inner term is not invariant with respect to homotopy of the principal symbol. In this paper, the authors describe a class of operators for which one can single out the homotopy invariant part of the inner term, and they relate all the rest to the second term.

##### MSC:
 58J20 Index theory and related fixed-point theorems on manifolds 58J28 Eta-invariants, Chern-Simons invariants 58J32 Boundary value problems on manifolds