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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.

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