Journal of the Mathematical Society of Japan

Generic smooth maps with sphere fibers

Osamu SAEKI and Keiichi SUZUOKA

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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

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

First available in Project Euclid: 14 September 2006

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Zentralblatt MATH identifier

Primary: 57R45: Singularities of differentiable mappings
Secondary: 57N13: Topology of $E^4$ , $4$-manifolds [See also 14Jxx, 32Jxx] 57Q45: Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}

generic map stable map Stein factorization regular fiber special generic map homotopy ribbon 2-link 4-manifold nonsingular stable map


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.

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