Open Access
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


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.


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

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

Primary: 57R45
Secondary: 57N13 , 57Q45

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

Rights: Copyright © 2005 Mathematical Society of Japan

Vol.57 • No. 3 • July, 2005
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