International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 4, Pages 701-711

Smooth structures on sphere bundles over spheres

Samuel Omoloye Ajala1,2

1Institute for Advanced Study, School of Mathematics, Princeton 08543, New Jersey, USA
2Department of Mathematics, University of Lagos, Akoka - Yaba, Lagos, Nigeria

Received 30 May 1986

Copyright © 1988 Samuel Omoloye Ajala. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In [1] R. De Sapio gave a classification of smooth structures of a p-sphere bundle over a q-sphere with one cross-section and p<q. In [2] J. Munkres also gave a classification up to concordance of differential structures in the case where the bundle has at least two cross-sections. In [3] R. Schultz gave a classification in the case pq. Here we will give a classification of the p-sphere bundle over a q-sphere without any cross-section and p<q.