International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 4, Pages 701-712
doi:10.1155/S0161171288000857

Smooth structures on sphere bundles over spheres

Abstract

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 p≥q. Here we will give a classification of the p-sphere bundle over a q-sphere without any cross-section and p<q.