English

Spectral Asymmetry, Zeta Functions and the Noncommutative Residue

Differential Geometry 2007-06-13 v8 Operator Algebras Spectral Theory

Abstract

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.

Keywords

Cite

@article{arxiv.math/0310102,
  title  = {Spectral Asymmetry, Zeta Functions and the Noncommutative Residue},
  author = {Raphael Ponge},
  journal= {arXiv preprint arXiv:math/0310102},
  year   = {2007}
}

Comments

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