Tangent $2$-fields on even-dimensional nonorientable manifolds

Benedict J. Pollina
1982 Transactions of the American Mathematical Society  
This paper uses the Postnikov decomposition of a nonsimple fibration to describe the obstructions to a tangent 2-field on an even-dimensional nonorientable manifold. Our purpose in this article is to prove the following theorem. Main Theorem. Let M be a closed, nonorientable manifold of dimension m, where m is even and m > 2. Let %(M) in Hm(M; ZW¡<M)) and sl£m_x(M) in
doi:10.1090/s0002-9947-1982-0648087-9 fatcat:cv2bjpyev5h5dmbmlug4kwwwpi