Abstract:
 Given a closed ndimensional manifold whose fundamental group is $\mathbb Z$, when is M a fiber bundle over the circle $S^1$? This is a problem of theoretical importance in the study of high dimensional manifolds. A classical result of BrowderLevine gives a necessary and sufficient condition when the dimension $n \ge 6$. In this talk I will discuss a solution of this problem for $n=5$ from the point of view of classification. In the topological category, we will see that the BrowderLevine condition is still true and in the smooth category there will be further obstructions related to the topology of smooth 4manifolds. This is a joint work with M.Kreck.
