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SPECTRAL ASYMMETRY, ZETA FUNCTIONS, AND THE NONCOMMUTATIVE RESIDUE

RAPHAËL PONGE

Department of Mathematics, Ohio State University, Columbus, USA

Max Planck Institute for Mathematics, Bonn, Germany.

https://doi.org/10.1142/S0129167X06003825Cited by:10 (Source: Crossref)

Abstract

In this paper we study the spectral asymmetry of (possibly nonselfadjoint) elliptic ΨDO's in terms of the difference of zeta functions coming from different cuttings. Refining previous formulas of Wodzicki in the case of odd class elliptic ΨDO's, our main results have several consequence concerning the local independence with respect to the cutting, the regularity at integer points of eta functions and a geometric expression for the spectral asymmetry of Dirac operators which, in particular, yields a new spectral interpretation of the Einstein–Hilbert action in gravity.

Keywords:

AMSC: Primary 58J50, Primary 58J42, Secondary 58J40

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