Hostname: page-component-6bf8c574d5-685pp Total loading time: 0 Render date: 2025-03-07T03:27:25.558Z Has data issue: false hasContentIssue false
  • English
  • Français

Spectral asymmetry and Riemannian geometry. II

Published online by Cambridge University Press:  24 October 2008

M. F. Atiyah ,
V. K. Patodi  and
I. M. Singer
M. F. Atiyah
Affiliation:
Oxford University Tata Institute for Fundamental Research, Bombay Massachusetts Institute of Technology, Cambridge, Massachusetts
V. K. Patodi
Affiliation:
Oxford University Tata Institute for Fundamental Research, Bombay Massachusetts Institute of Technology, Cambridge, Massachusetts
I. M. Singer
Affiliation:
Oxford University Tata Institute for Fundamental Research, Bombay Massachusetts Institute of Technology, Cambridge, Massachusetts
Get access Rights & Permissions [Opens in a new window]

Extract

In Part I of this paper (6) we proved various index theorems for manifolds with boundary including an extension of the Hirzebruch signature theorem. We now propose to investigate the geometric and topological implications of these theorems in a variety of contexts.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 78 , Issue 3 , November 1975 , pp. 405 - 432
Copyright
Copyright © Cambridge Philosophical Society 1975

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Atiyah, M. F., Bott, R. and Patodi, V. K.On the heat equation and the index theorem. Inventions math. 19 (1973), 279–330.CrossRefGoogle Scholar
(2)Atiyah, M. F., Bott, R. and Patodi, V. K. The heat equation and the Lefschetz formula. (To appear.)Google Scholar
(3)Atiyah, M. F. and Hirzebruch, F.Vector bundles and homogeneous spaces. Proc. Symposia Pure Maths. vol. III (Amer. Math. Soc.), 1961;.CrossRefGoogle Scholar
(4)Atiyah, M. F. and Singer, I. M.The index of elliptic operators: III. Ann. of Math. 87 (1968), 546–604.CrossRefGoogle Scholar
(5)Atiyah, M. F., Singer, I. M. and Patodi, V. K.Spectral asymmetry and Riemannian geometry. Bull. Lond. Math. Soc. 5 (1973), 229–234.CrossRefGoogle Scholar
(6)Atiyah, M. F., Patodi, V. K. and Singer, I. M.Spectral asymmetry and Riemannian geometry: I. Math. Proc. Camb. Phil. Soc. 77 (1975), 43.CrossRefGoogle Scholar
(7)Atiyah, M. F. and Smith, L.Compact Lie groups and the stable homotopy of spheres. Topology 13 (1974), 135–142.CrossRefGoogle Scholar
(8)Chern, S. S. and Simons, J.Characteristic forms and geometric invariants. Ann. of Math. 99 (1974), 48–69.CrossRefGoogle Scholar
(9)Lichnerowicz, A.Spineurs harmoniques. C. R. Acad. Sci., Paria, 257 (1963), 7–9.Google Scholar
(10)Stong, R. E.Notes on cobordiem theory (Princeton University Press, 1968).Google Scholar
(11)Wilson, G.K-theory invariants for unitary G-bordism. Quart. J. Math. 24 (1973), 499–526.CrossRefGoogle Scholar