Spectral asymmetry and Riemannian geometry. III

1 January 1976

journal article
research article
Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society

Vol. 79 (1) , 71-99
https://doi.org/10.1017/s0305004100052105

Abstract

In Parts I and II of this paper ((4), (5)) we studied the ‘spectral asymmetry’ of certain elliptic self-adjoint operators arising in Riemannian geometry. More precisely, for any elliptic self-adjoint operator A on a compact manifold we definedwhere λ runs over the eigenvalues of A. For the particular operators of interest in Riemannian geometry we showed that ηA(s) had an analytic continuation to the whole complex s-plane, with simple poles, and that s = 0 was not a pole. The real number ηA(0), which is a measure of ‘spectral asymmetry’, was studied in detail particularly in relation to representations of the fundamental group.

Keywords

RIEMANNIAN GEOMETRY

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