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 -manifold admits such a generic map into a surface,then it bounds a -manifold with nice properties. As a corollary, we show that each regular fiber of such a generic map of the -sphere into the plane is a homotopy ribbon -link and that any spun -knot of a classical knot can be realized as a component of a regular fiber of such a map.
"Generic smooth maps with sphere fibers." J. Math. Soc. Japan 57 (3) 881 - 902, July, 2005. https://doi.org/10.2969/jmsj/1158241939