## Journal of the Mathematical Society of Japan

### Generic smooth maps with sphere fibers

#### Abstract

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.

#### Article information

Source
J. Math. Soc. Japan, Volume 57, Number 3 (2005), 881-902.

Dates
First available in Project Euclid: 14 September 2006

https://projecteuclid.org/euclid.jmsj/1158241939

Digital Object Identifier
doi:10.2969/jmsj/1158241939

Mathematical Reviews number (MathSciNet)
MR2139738

Zentralblatt MATH identifier
1091.57021

#### Citation

SAEKI, Osamu; SUZUOKA, Keiichi. Generic smooth maps with sphere fibers. J. Math. Soc. Japan 57 (2005), no. 3, 881--902. doi:10.2969/jmsj/1158241939. https://projecteuclid.org/euclid.jmsj/1158241939

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