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The index of manifolds with toral actions and geometric interpretations of the σ(∞, (S1, Mn)) invariant of atiyah and singer

  • Katsuo Kawakubo
  • Frank Raymond
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 298)

Keywords

Geometric Interpretation Orbit Space Toral Action Mapping Cylinder Generalize Manifold 
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References

  1. [1]
    Atiyah, M. F. and Singer, I. M., The index of elliptic operators: III, Ann. of Math. 87 (1968), 546–604.MathSciNetzbMATHCrossRefGoogle Scholar
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    Bredon, G. E., Cohomology fiber spaces, the Smith-Gysin sequence, and orientation in generalized manifolds, Mich. Math. J. 10 (1963), 321–333.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    Conner, P. E. and Raymond, F., Injective operations of the toral groups, to appear in Topology.Google Scholar
  4. [4]
    Kawakubo, K. and Raymond, F., The index of manifolds with toral actions and geometric interpretations of σ(∞, (S1, Mn)) invariant of Atiyah and Singer, to appear in Inventiones Math.Google Scholar
  5. [5]
    Kawakubo, K. and Uchida, F., On the index of a semi-free S1-action, Proc. Japan Acad. 46 (1970), 620–622 and J. Math. Soc. Japan 23 (1971), 351–355.MathSciNetzbMATHCrossRefGoogle Scholar
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    Kwun, K. W. and Raymond, F., Mapping cylinder neighborhoods, Mich. Math. J. 10 (1963), 353–357.MathSciNetzbMATHCrossRefGoogle Scholar
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    Ossa, E., Fix punktfreie S1-Aktionen, Math. Ann. 186 (1970), 45–52.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    Raymond, F., The orbit spaces of totally disconnected groups of transformations on manifolds, Proc. A. M. S. 12 (1961), 1–7.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1972

Authors and Affiliations

  • Katsuo Kawakubo
    • 1
  • Frank Raymond
    • 2
  1. 1.Osaka University and Institute for Advanced StudyJapan
  2. 2.University of Michigan and Institute for Advanced StudyUSA

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