4-connected differentiable 11-manifolds with certain homotopy types

Rieko MATSUKAWA

doi:10.2969/jmsj/01620143

Rieko MATSUKAWA

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1964 Volume 16 Issue 2 Pages 143-158

DOI https://doi.org/10.2969/jmsj/01620143

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Published: 1964 Received: December 17, 1963 Available on J-STAGE: September 26, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 26, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. F. Adams, Applications of the Grothendieck-Atiyah-Hirzebruch functor K(X), Colloquium on Algebraic Topology, Mat. Inst. Aarhus Univ., 1962, 104-113.
2) A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces III, Amer. J. Math. 82 (1960), 491-504.
3) M. Eichler, Quadratische Formen und orthogonale Gruppen, Berlin, 1952.
4) M. Eichler, Die Ähnlichkeitsklassen indefiniter Gitter, Math. Z., 55 (1952), 216-252.
5) F. Hirzebruch, Neue topologische Methoden in der algebraischen Geometrie, Berlin, 1956.
6) B. W. Jones, The arithmetic theory of quadratic forms, New York, 1950.
7) J. Milnor, On simply connected 4-manifolds, Symp. Intern. de Topologia Algebraica, Mexico, 1958, 122-128.
8) J. Milnor, Differentiable manifolds which are homotopy spheres, (mimeographed), Princeton Univ., 1959.
9) J. Milnor, A procedure for Killing homotopy groups of differentiable manifolds, Proc. of Symp. Differential Geometry, 1961, 39-55.
10) J. Milnor and M. Kervaire, Bernoulli numbers, homotopy groups and a theoremof Rohlin, Proc. of Intern. Congr. of Math., Edinburgh, 1958, 454-458.
11) S. Smale, Generalized Poincaré's conjecture in dimensions greater than four, Ann. of Math., 74 (1961), 391-406.
12) S. Smale, On the structure of 5-manifolds, Ann. of Math., 75 (1962), 38-46.
13) S. Smale, On the structure of manifolds, Amer. J. Math., 84 (1962), 387-399.
14) N. E. Steenrod, The topology of fibre bundles, Princeton, 1951.
15) I. Tamura, On Pontrjagin classes and homotopy types of manifolds, J. Math. Soc. Japan, 9 (1957), 250-262.
16) I. Tamura, Homeomorphy classification of total spaces of sphere bundles over spheres, J. Math. Soc. Japan, 10 (1958), 29-43.
17) I. Tamura, Differentiable 7-manifolds with a certain homotopy type, J. Math. Soc. Japan, 14 (1962), 292-299.
18) H. Toda, Composition methods in homotopy groups of spheres, Ann. of Math. Studies, 49, Princeton, 1962.
19) C. T. C. Wall, Classification of (n-1)-connected 2n-manifolds, Ann. of Math., 75 (1962), 163-189.

Right : [1] J. F. Adams, Applications of the Grothendieck-Atiyah-Hirzebruch functor K(X), Colloquium on Algebraic Topology, Mat. Inst. Aarhus Univ., 1962, 104-113.
[2] A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces III, Amer. J. Math. 82 (1960), 491-504.
[3] M. Eichler, Quadratische Formen und orthogonale Gruppen, Berlin, 1952.
[4] M. Eichler, Die Ähnlichkeitsklassen indefiniter Gitter, Math. Z., 55 (1952), 216-252.
[5] F. Hirzebruch, Neue topologische Methoden in der algebraischen Geometrie, Berlin, 1956.
[6] B. W. Jones, The arithmetic theory of quadratic forms, New York, 1950.
[7] J. Milnor, On simply connected 4-manifolds, Symp. Intern. de Topologia Algebraica, Mexico, 1958, 122-128.
[8] J. Milnor, Differentiable manifolds which are homotopy spheres, (mimeographed), Princeton Univ., 1959.
[9] J. Milnor, A procedure for Killing homotopy groups of differentiable manifolds, Proc. of Symp. Differential Geometry, 1961, 39-55.
[10] J. Milnor and M. Kervaire, Bernoulli numbers, homotopy groups and a theorem of Rohlin, Proc. of Intern. Congr. of Math., Edinburgh, 1958, 454-458.
[11] S. Smale, Generalized Poincaré's conjecture in dimensions greater than four, Ann. of Math., 74 (1961), 391-406.
[12] S. Smale, On the structure of 5-manifolds, Ann. of Math., 75 (1962), 38-46.
[13] S. Smale, On the structure of manifolds, Amer. J. Math., 84 (1962), 387-399.
[14] N. E. Steenrod, The topology of fibre bundles, Princeton, 1951.
[15] I. Tamura, On Pontrjagin classes and homotopy types of manifolds, J. Math. Soc. Japan, 9 (1957), 250-262.
[16] I. Tamura, Homeomorphy classification of total spaces of sphere bundles over spheres, J. Math. Soc. Japan, 10 (1958), 29-43.
[17] I. Tamura, Differentiable 7-manifolds with a certain homotopy type, J. Math. Soc. Japan, 14 (1962), 292-299.
[18] H. Toda, Composition methods in homotopy groups of spheres, Ann. of Math. Studies, 49, Princeton, 1962.
[19] C. T. C. Wall, Classification of (n-1)-connected 2n-manifolds, Ann. of Math., 75 (1962), 163-189.

Date of correction: September 26, 2006 Reason for correction: - Correction: PDF FILE Details: -

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