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

 

Codimension 2 nonfibrators with finite fundamental groups


Author: R. J. Daverman
Journal: Proc. Amer. Math. Soc. 127 (1999), 881-888
MSC (1991): Primary 55R65, 57N15, 57N10; Secondary 57S37, 57N55
MathSciNet review: 1646311
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Abstract: Fibrators are $n$-manifolds which automatically induce approximate fibrations, in the following sense: given any proper mapping $p$ from an $(n+k)$-manifold onto a finite-dimensional metric space such that, up to shape, each point-preimage is a copy of the fibrator, $p$ is necessarily an approximate fibration. This paper sets forth new examples, for the case $k=2$, of nonfibrators whose fundamental groups are finite.


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Additional Information

R. J. Daverman
Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1300
Email: daverman@novell.math.utk.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05192-8
PII: S 0002-9939(99)05192-8
Keywords: Approximate fibration, fibrator, homotopy equivalence, degree, local winding function, Lens space, hopfian manifold, locally flat
Received by editor(s): May 24, 1997
Additional Notes: This research was supported in part by NSF Grant DMS-9401086.
Communicated by: Ralph Cohen
Article copyright: © Copyright 1999 American Mathematical Society