Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Ambient surgery and tangential homotopy quaternionic projective spaces.


Author: Douglas N. Hertz
Journal: Trans. Amer. Math. Soc. 145 (1969), 517-545
MSC: Primary 57.10
DOI: https://doi.org/10.1090/S0002-9947-1969-0250320-6
MathSciNet review: 0250320
Full-text PDF Free Access

References | Similar Articles | Additional Information

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

  • [1] A. Haefliger, Plongements différentiables de variétés dans variétés, Comment. Math. Helv. 36 (1961), 820-823. MR 0145538 (26:3069)
  • [2] -, Knotted $ (4k - 1)$-spheres in 6k-space, Ann. of Math. (2) 75 (1962), 452-466. MR 0145539 (26:3070)
  • [3] F. Hirzebruch, Über die quaternionalen projectiven Räume, S.-B. Math.-Nat. Kl. Bayer. Akad. Wiss. 1953, 301-312. MR 0065155 (16:389a)
  • [4] Wu-Chung, Hsiang, A note on free differentiable actions of $ {S^1}$ and $ {S^3}$ on homotopy spheres, Ann. of Math. 83 (1966), 266-272. MR 0192506 (33:731)
  • [5] Wu-Chung Hsiang, J. Levine and R. Szczarba, On the normal bundle of a homotopy sphere embedded in Euclidean space, Topology 3 (1965), 173-181. MR 0175138 (30:5323)
  • [6] M. Kervaire and J. Milnor, Groups of homotopy spheres, Ann. of Math. 77 (1963), 504-537. MR 0148075 (26:5584)
  • [7] R. Lashof, Some theorems of Browder and Novikov on homotopy equivalent manifolds with an application, University of Chicago, Notes.
  • [8] J. Milnor, A procedure for killing the homotopy groups of differentiable manifolds, Proc. Sympos. Pure Math., Vol. III, Amer. Math. Soc., Providence, R. I., 1961, pp. 39-55. MR 0130696 (24:A556)
  • [9] -, On manifolds homeomorphic to the 7-sphere, Ann. of Math. 64 (1956), 399-405. MR 0082103 (18:498d)
  • [10] J. Munkres, Elementary differential topology, Princeton Univ. Press, Princeton, N. J., 1963. MR 0163320 (29:623)
  • [11] -, Obstructions to the smoothing of piecewise differentiable homeomorphisms, Ann. of Math. 72 (1960), 521-554. MR 0121804 (22:12534)
  • [12] S. Novikov, Homotopically equivalent smooth manifolds. I, Izv. Akad. Nauk SSSR Ser. Mat 28 (1964), 365-474; English transl., Amer. Math. Soc. Transl. (2) 48 (1965), 271-396. MR 0162246 (28:5445)
  • [13] S. Smale, Differentiable and combinatorial structures on manifolds, Ann. of Math. 74 (1961), 498-502. MR 0133133 (24:A2967)
  • [14] N. Steenrod, The topology of fibre bundles, Princeton Univ. Press, Princeton, N. J., 1951. MR 0039258 (12:522b)
  • [15] D. Sullivan, On the Hauptvermutung for manifolds, Bull. Amer. Math. Soc. 73 (1967), 598-600. MR 0212811 (35:3676)
  • [16] R. Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17-87. MR 0061823 (15:890a)
  • [17] J. Wagoner, Surgery on a map and an approach to the Hauptvermutung, Thesis, Princeton University, Princeton, N. J., 1966.
  • [18] C. T. C. Wall, An extension of results of Novikov and Browder, Amer. J. Math. 88 (1966), 20-32. MR 0212826 (35:3691)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57.10

Retrieve articles in all journals with MSC: 57.10


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1969-0250320-6
Article copyright: © Copyright 1969 American Mathematical Society

American Mathematical Society