Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A comment on the Novikov conjecture

Authors: Jerome Kaminker and John G. Miller
Journal: Proc. Amer. Math. Soc. 83 (1981), 656-658
MSC: Primary 57R67; Secondary 55R40
MathSciNet review: 627714
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the Novikov conjecture on the homotopy invariance of characteristic numbers of nonsimply connected manifolds is equivalent to the injectivity of Wall's map from homology of groups to the surgery obstruction groups. These statements are then shown to be equivalent to their analogs for rational equivalences of rational homology manifolds.

References [Enhancements On Off] (What's this?)

  • [1] Gerald A. Anderson, Surgery on Λ-homology manifolds, Illinois J. Math. 24 (1980), no. 4, 653–675. MR 586804
  • [2] Ronald G. Douglas, 𝐶*-algebra extensions and 𝐾-homology, Annals of Mathematics Studies, vol. 95, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1980. MR 571362
  • [3] P. E. Conner and E. E. Floyd, Differentiable periodic maps, Ergebnisse der Mathematik und ihrer Grenzgebiete, N. F., Band 33, Academic Press Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1964. MR 0176478
  • [4] John W. Morgan and Dennis P. Sullivan, The transversality characteristic class and linking cycles in surgery theory, Ann. of Math. (2) 99 (1974), 463–544. MR 0350748,
  • [5] Andrew Ranicki, Localization in quadratic 𝐿-theory, Algebraic topology, Waterloo, 1978 (Proc. Conf., Univ. Waterloo, Waterloo, Ont., 1978) Lecture Notes in Math., vol. 741, Springer, Berlin, 1979, pp. 102–157. MR 557165
  • [6] C. T. C. Wall, Surgery on compact manifolds, Academic Press, London-New York, 1970. London Mathematical Society Monographs, No. 1. MR 0431216

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57R67, 55R40

Retrieve articles in all journals with MSC: 57R67, 55R40

Additional Information

Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society