Spectral Asymmetry, Zeta Functions and the Noncommutative Residue

Details Spectral Asymmetry, Zeta Functions and the Noncommutative Residue Spectral Asymmetry, Zeta Functions and the Noncommutative Residue

2003-10-08

arxiv.org/abs/math/0310102v8

Int. J. Math. 17 (2006) 1065-1090

Mathematics

Differential Geometry

v8: final version. To appear in Int. Math. J., 22 pages

Scientific paper

In this paper we study the spectral asymmetry of (possibly nonselfadjoint) elliptic PsiDO'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 PsiDO'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.

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