On certain cohomological operations

Tsuneyo YAMANOSHITA

doi:10.2969/jmsj/00840300

Tsuneyo YAMANOSHITA

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JOURNAL FREE ACCESS

1956 Volume 8 Issue 4 Pages 300-344

DOI https://doi.org/10.2969/jmsj/00840300

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Published: 1956 Received: June 12, 1956 Available on J-STAGE: August 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: August 29, 2006 Reason for correction: - Correction: DTRECEIVED Details: Right : 19560612

Date of correction: August 29, 2006 Reason for correction: - Correction: AFFILIATION Details: Wrong :
1) Musashi Institute of Technology and University of okyo

Right :
1) Musashi Institute of Technology and University of Tokyo

Date of correction: August 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. Adem, The iteration of the Steenrod squares in algebraic topology. Proc. Nat. Acad. Sci. U.S.A. 38 (1952). pp. 720-726.
2) J. Adem, Relations on iterated reduced powers. Proc. Nat. Acad. Sci. U.S.A. 39 (1953) pp. 636-638.
3) A. Borel, Sur l'homologie et la cohomologie des groupes de Lie compacts connexes. Amer. Journ. of Math. 76 (1954), pp. 273-342.
4) H. Cartan and J. P. Serre, Espaces fibrès et groupes d'homotopie I, Compt. Rend. 234 (1952) pp. 288-290.
5) H. Cartan, Sur les groupes d'Eilenberg-MacLane, I et II. Proc. Nat. Acad. Sci. U.S.A. 40 (1954), pp. 467-471, pp. 704-707.
6) J. P. Serre, Homologie singulière des espaces fibrès. Applications. Ann. of Math. 54 (1951), pp. 425-505.
7) J. P. Serre, Cohomologie modulo 2 des complexes d'Eilenberg-MacLane, Comment. Math. Helv. 27 (1953) pp. 198-232.
8) W. S. Massey, Some problem in algebraic topology and the theory of fibre bundles. Ann. of Math. 62 (1955) pp. 327-359.
9) N. E. Steenrod, Products of cocycles and extensions of mappings. Ann. of Math. 48 (1947) pp. 290-320.
10) N. E. Steenrod, Reduced powers of cohomology classes, Ann. of Math. 56 (1952) pp. 37-67.
11) R. Thom, Quelques propriétés globales des variétés différentiables. Comment. Math. Helv. 48 (1954), pp. 17-86.
12) H. Toda, Sur les groupes d'homotopie des sphères. Calcul de groupes d'homotopie des sphères, C. R. Acad. Sci. Paris, 240 (1955), pp. 42-44, 147-149.
13) T. Yamanoshita, On the unstable homotopy groups of spheres, Proc. Jap. Nat. Acad. 31 (1955), pp. 610-611.
14) N. Yoneda, On the homology theory of modules, Fac. Sci. Univ. Tokyo. Sec. I, Vol., 7 Part 2 (1954) pp. 193-227.
15) J. H. C. Whitehead, On simply connected, 4-dimensional polyhedra, Comm. Math. Helv. 22 (1949), pp. 48-92.
16) T. Kudo, A transgression theorem, Mem. Fac. Sci. Kyusyu Univ. 9 (1956)
17) E. Thomas, A generalization of the Pontrjagin square. Proc. Nat. Acad. of Sci. U.S.A. 42 (1956) pp. 266-269. The author has seen this paper after presenting his paper to the Society.

Right : [1] J. Adem, The iteration of the Steenrod squares in algebraic topology. Proc. Nat. Acad. Sci. U. S. A. 38 (1952). pp. 720-726.
[2] J. Adem, Relations on iterated reduced powers. Proc. Nat. Acad. Sci. U. S. A. 39 (1953) pp. 636-638.
[3] A. Borel, Sur l'homologie et la cohomologie des groupes de Lie compacts connexes. Amer. Journ. of Math. 76 (1954), pp. 273-342.
[4] H. Cartan and J. P. Serre, Espaces fibrès et groupes d'homotopie I, Compt. Rend. 234 (1952) pp. 288-290.
[5] H. Cartan, Sur les groupes d'Eilenberg-MacLane, I et II. Proc. Nat. Acad. Sci. U. S. A. 40 (1954), pp. 467-471, pp. 704-707.
[6] J. P. Serre, Homologie singulière des espaces fibrès. Applications. Ann. of Math. 54 (1951), pp. 425-505.
[7] J. P. Serre, Cohomologie modulo 2 des complexes d'Eilenberg-MacLane, Comment. Math. Helv. 27 (1953) pp. 198-232.
[8] W. S. Massey, Some problem in algebraic topology and the theory of fibre bundles. Ann. of Math. 62 (1955) pp. 327-359.
[9] N. E. Steenrod, Products of cocycles and extensions of mappings. Ann. of Math. 48 (1947) pp. 290-320.
[10] N. E. Steenrod, Reduced powers of cohomology classes, Ann. of Math. 56 (1952) pp. 37-67.
[11] R. Thom, Quelques propriétés globales des variétés différentiables. Comment. Math. Helv. 48 (1954), pp. 17-86.
[12] H. Toda, Sur les groupes d'homotopie des sphères. Calcul de groupes d'homotopie des sphères, C. R. Acad. Sci. Paris, 240 (1955), pp. 42-44, 147-149.
[13] T. Yamanoshita, On the unstable homotopy groups of spheres, Proc. Jap. Nat. Acad. 31 (1955), pp. 610-611.
[14] N. Yoneda, On the homology theory of modules, Fac. Sci. Univ. Tokyo. Sec. I, Vol., 7 Part 2 (1954) pp. 193-227.
[15] J. H. C. Whitehead, On simply connected, 4-dimensional polyhedra, Comm. Math. Helv. 22 (1949), pp. 48-92.
[16] T. Kudo, A transgression theorem, Mem. Fac. Sci. Kyusyu Univ. 9 (1956)
[17] E. Thomas, A generalization of the Pontrjagin square. Proc. Nat. Acad. of Sci. U. S. A. 42 (1956) pp. 266-269. The author has seen this paper after presenting his paper to the Society.

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