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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Necessary and sufficient conditions for s-Hopfian manifolds to be codimension-2 fibrators


Authors: Young Ho Im and Yongkuk Kim
Journal: Proc. Amer. Math. Soc. 129 (2001), 2135-2140
MSC (2000): Primary 57N15, 55M25; Secondary 57M10, 54B15
Published electronically: December 13, 2000
MathSciNet review: 1825927
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Abstract: Fibrators help detect approximate fibrations. A closed, connected $n$-manifold $N$ is called a codimension-2 fibrator if each map $p: M \to B$ defined on an $(n+2)$-manifold $M$ such that all fibre $p^{-1}(b), b\in B$, are shape equivalent to $N$ is an approximate fibration. The most natural objects $N$ to study are s-Hopfian manifolds. In this note we give some necessary and sufficient conditions for s-Hopfian manifolds to be codimension-2 fibrators.


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Additional Information

Young Ho Im
Affiliation: Department of Mathematics, Pusan National University, Pusan, 609-735, Korea
Email: yhim@hyowon.pusan.ac.kr

Yongkuk Kim
Affiliation: Department of Mathematics, Kyungpook National University, Taegu, 702-701, Korea
Email: yongkuk@knu.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05998-0
PII: S 0002-9939(00)05998-0
Keywords: Codimension-2 fibrator, s-Hopfian manifold, Hopfian group, approximate fibration
Received by editor(s): October 19, 1999
Published electronically: December 13, 2000
Additional Notes: The first author’s research was supported by Korea Research Foundation Grant (KRF-2000-041-D00023)
The second author’s research was supported by Korea Research Foundation Grant (KRF-2000-015-DP0034)
Communicated by: Ralph Cohen
Article copyright: © Copyright 2000 American Mathematical Society