manuscripta mathematica

, Volume 57, Issue 3, pp 263–280

Two-plane sub-bundles of nonorientable real vector-bundles

  • Maria Hermínia de Paula Leite Mello

DOI: 10.1007/BF01437484

Cite this article as:
de Paula Leite Mello, M.H. Manuscripta Math (1987) 57: 263. doi:10.1007/BF01437484


Let ζ be a nonorientable m-plane bundle over a CW complex X of dimension m or less. Given a 2-plane bundle η over X, we wish to know whether η can be embedded as a sub-bundle of ζ. The bundle η need not be orientable. When ζ is even-dimensional there is the added complication of twisted coefficients. In that case, we use Postnikov decomposition of certain nonsimple fibrations in order to describe the obstructions for the embedding problem. Emery Thomas [11] and [12] treated this problem for ζ and η both orientable. The results found here are applied to the tangent bundle of a closed, connected, nonorientable smooth manifold, as a special case.

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Maria Hermínia de Paula Leite Mello
    • 1
  1. 1.Instituto de Matemática Departamento de Matemática Aplicada (GMA)Universidade Federal FluminenseNiterói, RJBrazil