Celebratio Mathematica — Singer

I. M. Singer: a brief biography

Works connected to Vijay Kumar Patodi

Filter the Bibliography List

year	title	people

			clear

M. F. Atiyah, V. K. Patodi, and I. M. Singer: “Spectral asymmetry and Riemannian geometry,” Bull. London Math. Soc. 5 (July 1973), pp. 229–234. MR 331443 Zbl 0268.58010 article

M. F. Atiyah	Related	Volume
Vijay Kumar Patodi	Related

M. F. Atiyah, V. K. Patodi, and I. M. Singer: “Spectral asymmetry and Riemannian geometry, I,” Math. Proc. Cambridge Philos. Soc. 77 (1975), pp. 43–69. MR 397797 Zbl 0297.58008 article

M. F. Atiyah	Related	Volume
Vijay Kumar Patodi	Related

M. F. Atiyah, V. K. Patodi, and I. M. Singer: “Spectral asymmetry and Riemannian geometry, II,” Math. Proc. Cambridge Philos. Soc. 78 : 3 (November 1975), pp. 405–432. MR 397798 Zbl 0314.58016 article

M. F. Atiyah	Related	Volume
Vijay Kumar Patodi	Related

M. F. Atiyah, V. K. Patodi, and I. M. Singer: “Spectral asymmetry and Riemannian geometry, III,” Math. Proc. Cambridge Philos. Soc. 79 : 1 (1976), pp. 71–99. MR 397799 Zbl 0325.58015 article

In Parts I and II of this paper [1975a; 1975b] 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 \[ \eta_A(s) = \sum_{\lambda\neq 0}\operatorname{sign} \lambda \,|\lambda|^{-s}, \] where \( \lambda \) runs over the eigenvalues of \( A \). For the particular operators of interest in Riemannian geometry we showed that \( \eta_A(s) \) had an analytic continuation to the whole complex \( s \)-plane, with simple poles, and that \( s = 0 \) was not a pole. The real number \( \eta_A(0) \), which is a measure of ‘spectral asymmetry’, was studied in detail particularly in relation to representations of the fundamental group.

M. F. Atiyah	Related	Volume
Vijay Kumar Patodi	Related