In this paper, we study various topological properties of generic smooth maps between manifolds whose regular fibers are disjoint unions of homotopy spheres. In particular, we show that if a closed 4-manifold admits such a generic map into a surface, then it bounds a 5-manifold with nice properties. As a corollary, we show that each regular fiber of such a generic map of the 4-sphere into the plane is a homotopy ribbon 2-link and that any spun 2-knot of a classical knot can be realized as a component of a regular fiber of such a map.
|Number of pages||22|
|Journal||Journal of the Mathematical Society of Japan|
|Publication status||Published - Jan 1 2005|
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