Mathematische Zeitschrift

, Volume 103, Issue 2, pp 85–93 | Cite as

Vector fields on low dimensional manifolds

  • Emery Thomas
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Adem, J.: The iteration of the Steenrod squares in algebraic topology. Proc. Nat. Acad. Sci., U.S.A.38, 720–726 (1952).Google Scholar
  2. 2.
    Bredon, G., andA. Kosinski: Vector fields on π-manifolds. Annals of Math.84, 85–90 (1960).Google Scholar
  3. 3.
    Dold, A., andH. Whitney: Classification of oriented sphere bundles over a 4-complex. Annals of Math.69, 667–677 (1959).Google Scholar
  4. 4.
    Eckmann, B.: Systeme von Richtungsfeldern auf Sphären. Comment. Math. Helv.15, 1–26 (1943).Google Scholar
  5. 5.
    —, andP. Hilton: Operators and Cooperators in homotopy theory. Math. Ann.141, 1–21 (1960).Google Scholar
  6. 6.
    Hermann, R.: Secondary obstructions for fiber spaces. Bull. Amer. Math. Soc.65, 5–8 (1959).Google Scholar
  7. 7.
    Hirzebruch, H., andH. Hopf: Felder von Flächenelementen in 4-dimensionalen Mannigfaltigkeiten. Math. Annalen136, 156–172 (1958).Google Scholar
  8. 8.
    James, I. M., andE. Thomas: An approach to the enumeration problem..., Journ. Math. and Mech.14, 485–506 (1965).Google Scholar
  9. 9.
    Kervaire, M.: Courbure intégrale generalisée et homotopie. Math. Annalen131, 229–252 (1956).Google Scholar
  10. 10.
    Massey, W.: On the cohomology ring of a sphere bundle. Journ. Math. and Mech.7, 265–289 (1958).Google Scholar
  11. 11.
    Steenrod, N.: Products of cocyles and extensions of mappings Annals of Math.48, 290–320 (1947).Google Scholar
  12. 12.
    Stiefel, E.: Richtungsfelder und Fernparallelismus inn-dimensionalen Mannigfaltigkeiten. Comment. Math. Helv.8, 305–353 (1936).Google Scholar
  13. 13.
    Thomas, E.: On the cohomology of the real Grassmann complexes. Trans. Amer. Math. Soc.96, 67–89 (1960).Google Scholar
  14. 14.
    —: Homotopy classification of maps by cohomology homomorphisms. Trans. Amer. Math. Soc.111, 138–151 (1964).Google Scholar
  15. 15.
    —: Cross-sections of stably equivalent vector bundles. Quart. J. Math. (2)17, 53–57 (1966).Google Scholar
  16. 16.
    Thomas, E.: Seminar on fiber spaces. Lecture Notes in Mathematics No. 13, Berlin-Heidelberg-New York: Springer 1966.Google Scholar
  17. 17.
    —: Postnikov invariants and higher order cohomology operations. Annals of Math.85, 184–217 (1967).Google Scholar
  18. 18.
    —: The index of a tangent 2-field. Comment. Math. Helv.86, 110 (1967).Google Scholar
  19. 19.
    —: Real and Complex vector fields on manifolds. Journ. Math. and Mech.16, 1183–1206 (1967).Google Scholar
  20. 20.
    Thomas, E.: Fields of tangentk-planes on manifolds. (To appear.)Google Scholar
  21. 21.
    Thomas, E.: The span of a manifold. (To appear.)Google Scholar
  22. 22.
    Whitehead, G.: Homotopy properties of the real, orthogonal groups. Ann. of Math.43, 132–146 (1943).Google Scholar
  23. 23.
    Wu, W.: Classes caracteristique eti-carrés d'une variété. C. R. Acad. Sci. Paris230, 508–511 (1950).Google Scholar

Copyright information

© Springer-Verlag 1968

Authors and Affiliations

  • Emery Thomas
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

Personalised recommendations