Spectral asymmetry and Riemannian geometry. III

Atiyah, M. F. ; Patodi, V. K. ; Singer, I. M. (1976) Spectral asymmetry and Riemannian geometry. III Mathematical Proceedings of the Cambridge Philosophical Society, 79 (1). pp. 71-99. ISSN 0305-0041

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Related URL: http://dx.doi.org/10.1017/S0305004100052105


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 defined ηA(s)=Σλ+0signλ|λ|-8, where 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.

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Deposited On:25 Apr 2011 09:41
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