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Characteristic spheres of free differentiable actions of $ S\sp{1}$ and $ S\sp{3}$ on homotopy spheres


Authors: Hsu-tung Ku and Mei-chin Ku
Journal: Trans. Amer. Math. Soc. 156 (1971), 493-504
MSC: Primary 57.31
DOI: https://doi.org/10.1090/S0002-9947-1971-0276992-7
MathSciNet review: 0276992
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  • [1] A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces. I, Amer. J. Math. 80 (1958), 458-538. MR 21 #1586. MR 0102800 (21:1586)
  • [2] W. Browder, Surgery and the theory of differentiable transformation groups, Proc. Conference on Transformation Groups (New Orleans, La., 1967), Springer, New York, 1968, pp. 1-46. MR 0261629 (41:6242)
  • [3] W. Browder and G. R. Livesay, Fixed point free involutions on homotopy spheres, Bull. Amer. Math. Soc. 73 (1967), 242-245. MR 34 #6781. MR 0206965 (34:6781)
  • [4] J. Eells, Jr. and N. H. Kuiper, An invariant for certain smooth manifolds, Ann. Mat. Pura Appl. (4) 60 (1962), 93-110. MR 27 #6280. MR 0156356 (27:6280)
  • [5] F. Hirzebruch, Topological methods in algebraic geometry, 3rd ed., Die Grundlehren der math. Wissenschaften, Band 131, Springer-Verlag, New York, 1966. MR 34 #2573. MR 0202713 (34:2573)
  • [6] W. C. Hsiang, A note on free differentiable actions of $ {S^1}$ and $ {S^3}$ on homotopy spheres, Ann. of Math. (2) 83 (1966), 266-272. MR 33 #731. MR 0192506 (33:731)
  • [7] 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) 15 (1964), 371-374. MR 30 #3479. MR 0173266 (30:3479)
  • [8] H. T. Ku and M. C. Ku, Free differentiable actions of $ {S^1}$ and $ {S^3}$ on homotopy 11-spheres, Trans. Amer. Math. Soc. 138 (1969), 223-228. MR 38 #6630. MR 0238354 (38:6630)
  • [9] M. A. Kervaire and J. W. Milnor, Groups of homotopy spheres. I, Ann. of Math. (2) 77 (1963), 504-537. MR 26 #5584. MR 0148075 (26:5584)
  • [10] D. Montgomery and C. T. Yang, Differentiable actions on homotopy seven spheres. II, Proc. Conference on Transformation Groups (New Orleans, La., 1967), Springer, New York, 1968, pp. 125-134. MR 39 #6353. MR 0245041 (39:6353)
  • [11] -, Free differentiable actions on homotopy spheres, Proc. Conference on Transformation Groups (New Orleans, La., 1967), Springer, New York, 1968, pp. 175-192. MR 39 #6354. MR 0245042 (39:6354)
  • [12] P. Orlik and C. P. Rourke, Free involutions on homotopy $ (4k + 3)$-spheres, Bull. Amer. Math. Soc. 74 (1968), 949-953. MR 37 #4819. MR 0229245 (37:4819)
  • [13] S. Lòpez de Medrano, Involutions of homotopy spheres and homology 3-spheres, Bull. Amer. Math. Soc. 73 (1967), 727-731. MR 35 #6153. MR 0215312 (35:6153)
  • [14] -, Some results on involutions of homotopy spheres, Proc. Conference on Transformation Groups (New Orleans, La., 1967), Springer, New York, 1968, pp. 167-174. MR 0253349 (40:6564)

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DOI: https://doi.org/10.1090/S0002-9947-1971-0276992-7
Article copyright: © Copyright 1971 American Mathematical Society

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