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Connected sums of manifolds which induce approximate fibrations

Author: Yongkuk Kim
Journal: Proc. Amer. Math. Soc. 128 (2000), 1497-1506
MSC (1991): Primary 57N15, 55M25; Secondary 57M10, 54B15
Published electronically: February 3, 2000
MathSciNet review: 1670391
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Abstract: Codimension-2 fibrators are $n$-manifolds which automatically induce approximate fibration, in the following sense: given any proper mapping $p$ from an $(n+2)$-manifold onto a $2$-manifold such that each point-preimage is a copy of the codimension-2 fibrator, $p$ is necessarily an approximate fibration. In this paper, we give some answers to the following question: given an $n$-manifold $N$ which is a nontrivial connected sum, when is $N$ a codimension-2 fibrator?

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Additional Information

Yongkuk Kim
Affiliation: Department of Mathematics, The University of Tennessee at Knoxville, Knoxville, Tennessee 37996-1300
Address at time of publication: Department of Mathematics, Kyungpook National University, Taegu, 702-701, Korea

Keywords: Connected sum, approximate fibration, codimension-2 fibrator, hopfian manifold, hyperhopfian group, residually finite group
Received by editor(s): February 12, 1998
Published electronically: February 3, 2000
Communicated by: Ralph Cohen
Article copyright: © Copyright 2000 American Mathematical Society