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On the nonexistence of free differentiable $ S\sp{3}$-actions on homotopy spheres


Authors: Hsu-tung Ku and Mei-chin Ku
Journal: Proc. Amer. Math. Soc. 21 (1969), 101-103
MSC: Primary 57.47
MathSciNet review: 0236949
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  • [1] Glen E. Bredon, Exotic actions on spheres, Proc. Conf. on Transformation Groups (New Orleans, La., 1967) Springer, New York, 1968, pp. 47–76. MR 0266239
  • [2] James Eells Jr. and Nicolaas Kuiper H., An invariant for certain smooth manifolds, Ann. Mat. Pura Appl. (4) 60 (1962), 93–110. MR 0156356
  • [3] F. Hirzebruch, Topological methods in algebraic geometry, Third enlarged edition. New appendix and translation from the second German edition by R. L. E. Schwarzenberger, with an additional section by A. Borel. Die Grundlehren der Mathematischen Wissenschaften, Band 131, Springer-Verlag New York, Inc., New York, 1966. MR 0202713
  • [4] W. C. Hsiang and W. Y. Hsiang, Some free differentiable actions of $ S^1$ and $ S^3$ on 11-spheres, Quart. J. Math. Oxford Ser. (2) (1964), 371-374.
  • [5] Michel A. Kervaire and John W. Milnor, Groups of homotopy spheres. I, Ann. of Math. (2) 77 (1963), 504–537. MR 0148075
  • [6] Deane Montgomery and C. T. Yang, Differentiable actions on homotopy seven spheres. II, Proc. Conf. on Transformation Groups (New Orleans, La., 1967) Springer, New York, 1968, pp. 125–134. MR 0245041

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DOI: https://doi.org/10.1090/S0002-9939-1969-0236949-5
Article copyright: © Copyright 1969 American Mathematical Society