Quelques classes de cobordisme non orienté refusant de se fibrer sur des sphères (Q1102584)

Conner and Floyd raised the problem of finding which unoriented cobordism classes can be represented by the total space of a fibring over the sphere S k. The main result of this paper is that if \(M^{k+p}\) fibers over S k with \(p<(k-2)/2\) or p odd and \(p=(k-2)/2\) then M must bound. The main idea of the author's approach is that for M fibered over S k with M nonbounding one can sometimes argue that the homology of the fiber cannot be finite dimensional.