Nagoya Mathematical Journal

Homotopy classification of mappings of a $4$-dimensional complex into a $2$-dimensional sphere

Nobuo Shimada

Full-text: Open access

Article information

Source
Nagoya Math. J., Volume 5 (1953), 127-144.

Dates
First available in Project Euclid: 14 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1118799399

Mathematical Reviews number (MathSciNet)
MR0052774

Zentralblatt MATH identifier
0050.17403

Subjects
Primary: 56.0X

Citation

Shimada, Nobuo. Homotopy classification of mappings of a $4$-dimensional complex into a $2$-dimensional sphere. Nagoya Math. J. 5 (1953), 127--144. https://projecteuclid.org/euclid.nmj/1118799399


Export citation

References

  • [1] N.E.Steenrod, Products ofcocycles andextension of mappings, Ann.of Math., 48 (1947), 290-320.
  • [2] N. E.Steenrod, Cohomology invariants of mappings, Ann. of Math., 50(1949), 954-988.
  • [3] H. Cartan, Une therie axiomatique descarres de Steenrod, Comp. Rend. Paris, 230 (1950), 425-427.
  • [4] L. Pontrjagin, A classification of mappings of the3dimensional complex into the 2-di- mensional sphere, Rec. Math. (Mat,Sbornik), N.S.9 (51) (1941), 331-363.
  • [5] L. Pontrjagin, Mappings of the 3dimensional sphere into an -dimensional complex, Doklady Akad. Nauk SSSR, 34(1942), 35-37
  • [6] L. Pontrjagin, Homotopy classification of thethe mapping of an ( 2)-dimensional sphere onn dimensional one, Doklady Akad. Nauk SSSR, 70 (1950), 957-959.
  • [7] H.Whitney, Onproducts in a complex, Ann. of Math., 39 (1938), 397-432.
  • [8] H.Whitney, Classification of the mappings of a 3-complex into a simply connected space, Ann. of Math., 50 (1949), 270-284.
  • [9] H. Whitney, An extension theorem for mappings into simply connected spaces, ibid., 285-296.
  • [10] M.M.Postnikov, The classification of continuous mappings of a 3 dimensional poly- hedron into a simply connected polyhedron of arbitray dimension, Doklady Akad. Nauk SSSR (N.S.) 64 (1949), 461-462.
  • [11] M.M. Postnikov, Classification of continuous mappings of an (l)-dimensional com- plex into a connected topological space which is aspherical in dimensions less than Doklady Akad. Nauk SSSR, (N.S.) 71 (1950), 1027-1028.
  • [12] G. W.Whitehead, A generalization of the Hopf invariant, Ann. of Math., 51 (1950), 192-237.
  • [13] Ga W. Whitehead. The (w2)-nd homotopy group of thew-sphere, Ann, of Math., 52
  • [14] A. L. Blakers and W. S. Massay, Homotopy groups of a triad I, Ann. of Math., 53 (1951), 161-205.
  • [15] S. Eilenberg, Cohomology and continuous mappings, Ann. of Math., 41 (1940), 231-251.
  • [16] J. H. C. Whitehead, On simply connected, 4-dimensional polyhedra, Comm. Math. Helv., 22 (1949), 48-90.
  • [17] J. H. C. Whitehead, A certain exact sequence, Ann. of Math., 52 (1950), 51-110.
  • [18] J. H. C. Whitehead, On the theory of obstructions, Ann. of Math., 54 (1951), 68-84.
  • [19] M. Nakaoka, On Whitney's extension theorem, Jour, of Inst. Polytechnics Osaka City Univ., vol. 2, No. 1. (Series A) (1951), 31-37.
  • [20] N. Shimada and H. Uehara, On a homotopy classfication of mappings of an (l di- mensional complex into an arcwise connected topological space which is aspherical in dimensions less than n(n2),Nagoya Math. Jour., 3 (1951), 67-72.
  • [21] N. Shimada and H. Uehara, Classification of mappings of an ( 2)-complex into an (n –1)-connected space with vanishing (i l)-st homotopy group, Nagoya Math. Jour., 4 (1952), 43-50. Mathematical Institute, Nagoya University