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Spectral asymmetry and Riemannian geometry. II

  • M. F. Atiyah (a1), V. K. Patodi (a1) and I. M. Singer (a1)


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.



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(1)Atiyah, M. F., Bott, R. and Patodi, V. K.On the heat equation and the index theorem. Inventions math. 19 (1973), 279330.
(2)Atiyah, M. F., Bott, R. and Patodi, V. K. The heat equation and the Lefschetz formula. (To appear.)
(3)Atiyah, M. F. and Hirzebruch, F.Vector bundles and homogeneous spaces. Proc. Symposia Pure Maths. vol. III (Amer. Math. Soc.), 1961;.
(4)Atiyah, M. F. and Singer, I. M.The index of elliptic operators: III. Ann. of Math. 87 (1968), 546604.
(5)Atiyah, M. F., Singer, I. M. and Patodi, V. K.Spectral asymmetry and Riemannian geometry. Bull. Lond. Math. Soc. 5 (1973), 229234.
(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.
(7)Atiyah, M. F. and Smith, L.Compact Lie groups and the stable homotopy of spheres. Topology 13 (1974), 135142.
(8)Chern, S. S. and Simons, J.Characteristic forms and geometric invariants. Ann. of Math. 99 (1974), 4869.
(9)Lichnerowicz, A.Spineurs harmoniques. C. R. Acad. Sci., Paria, 257 (1963), 79.
(10)Stong, R. E.Notes on cobordiem theory (Princeton University Press, 1968).
(11)Wilson, G.K-theory invariants for unitary G-bordism. Quart. J. Math. 24 (1973), 499526.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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