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Spectral asymmetry and Riemannian geometry. III
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 defined 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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Cited by
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Self-Adjoint Fredholm Operators And Spectral Flow
Phillips, J. (1996) · Canadian Mathematical Bulletin · doi:10.4153/cmb-1996-054-4 · Cited by 120
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Kummer, W., & Vassilevich, D. V. (1999) · Physical Review D · doi:10.1103/physrevd.60.084021 · Cited by 39
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Hofmann, D., & Kummer, W. (2005) · The European Physical Journal C · doi:10.1140/epjc/s2005-02129-9 · Cited by 9
Metadata
- Authors
- Atiyah, M. F., Patodi, V. K., & Singer, I. M.
- Venue
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publisher
- Cambridge University Press (CUP)
- Published
- 1976-01
- Volume
- 79
- Issue
- 1
- Pages
- 71-99
- ISSN
- 0305-0041 (ISSN-L)
- 1469-8064
- OpenAlex
- W4248945936
- Cited by
- 683
- References
- 0
- FWCI
- 2.69
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Spectral asymmetry and Riemannian geometry. III. https://app.cochat.ai/papers/10.1017/s0305004100052105
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- Atiyah, M. F., Patodi, V. K., & Singer, I. M. (1976). Spectral asymmetry and Riemannian geometry. III. Mathematical Proceedings of the Cambridge Philosophical Society. https://doi.org/10.1017/s0305004100052105
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