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Local invariants of spectral asymmetry. (English) Zbl 0538.58038
The eta invariant of Atiyah-Patodi-Singer is a spectral invariant measuring the spectral asymmetry of a Riemannian manifold. A priori the value of eta at \(s=0\) is not regular and one must prove that the local pole integrates to zero. The residue is an example of a spectral invariant given by a local formula which vanishes on definite operators and which is additive with respect to direct sums. In the present paper, the author considers slightly more general such invariants and manages to prove that they all vanish in even dimensions and on certain odd dimensional manifolds. He also corrects some errors in an earlier paper discussing the regularity of the global eta function at \(s=0\).
Reviewer: P.Gilkey

MSC:
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
35P20 Asymptotic distributions of eigenvalues in context of PDEs
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References:
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