Cobordism classes of fiber bundles

Daniel Francis Xavier O’Reilly

Vol. 69 (1977), No. 2, 467–475

DOI: 10.2140/pjm.1977.69.467

Abstract

This paper treats the problem of determining which unoriented cobordism classes have a representative which is the total space of a fiber bundle over a sphere. We are looking for a necessary and sufficient condition for a closed, compact, differentiable manifold to be cobordant to the total space of a fiber bundle over S^k.

Our results on bundles over S⁴ and S⁸ extend the results of P. E. Conner [3,4], E. E. Floyd [4], R. O. Burdick [2], W. D. Neumann [6], R. L. W. Brown [1] and R. E. Stong [7].

Mathematical Subject Classification

Primary: 57D75, 57D75

Milestones

Received: 19 July 1976

Published: 1 April 1977