Local invariants of spectral asymmetry
type: Item
instance of: scholarly article
title: Local invariants of spectral asymmetry
zbMATH Open document ID: 0538.58038
DOI: 10.1007/BF01403095
published in: Inventiones Mathematicae
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143093
review text: 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 \(s=0\).
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 35P20
zbMATH DE Number: 3856073
zbMATH Keywords: elliptic pseudo-differential operator
zbMATH Keywords: meromorphic function
zbMATH Keywords: trivial spectral asymmetry
zbMATH Keywords: eta invariant
zbMATH Keywords: global eta function
Wikidata QID: Q56689641
author: Mariusz Wodzicki
reviewed by: Peter B. Gilkey
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3856073