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July, 2005 Generic smooth maps with sphere fibers
Osamu SAEKI, Keiichi SUZUOKA
J. Math. Soc. Japan 57(3): 881-902 (July, 2005). DOI: 10.2969/jmsj/1158241939

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.

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Osamu SAEKI. Keiichi SUZUOKA. "Generic smooth maps with sphere fibers." J. Math. Soc. Japan 57 (3) 881 - 902, July, 2005. https://doi.org/10.2969/jmsj/1158241939

Information

Published: July, 2005
First available in Project Euclid: 14 September 2006

zbMATH: 1091.57021
MathSciNet: MR2139738
Digital Object Identifier: 10.2969/jmsj/1158241939

Subjects:
Primary: 57R45
Secondary: 57N13, 57Q45

Rights: Copyright © 2005 Mathematical Society of Japan

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Vol.57 • No. 3 • July, 2005
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