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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Embeddings in generalized manifolds


Authors: J. L. Bryant and W. Mio
Journal: Trans. Amer. Math. Soc. 352 (2000), 1131-1147
MSC (2000): Primary 57N35; Secondary 57P99
Published electronically: September 17, 1999
MathSciNet review: 1694282
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Abstract: We prove that a ($2m-n+1$)-connected map $f\colon M^m\to X^n$ from a compact PL $m$-manifold $M$ to a generalized $n$-manifold $X$ with the disjoint disks property, $3m\le 2n-2$, is homotopic to a tame embedding. There is also a controlled version of this result, as well as a version for noncompact $M$ and proper maps $f$ that are properly ($2m-n+1$)-connected. The techniques developed lead to a general position result for arbitrary maps $f\colon M\to X$, $3m\le 2n-2$, and a Whitney trick for separating $P\hspace*{-1pt}L$submanifolds of $X$ that have intersection number 0, analogous to the well-known results when $X$ is a manifold.


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Additional Information

J. L. Bryant
Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306
Email: bryant@math.fsu.edu

W. Mio
Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306
Email: mio@math.fsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02531-3
PII: S 0002-9947(99)02531-3
Keywords: Generalized manifolds, embeddings
Received by editor(s): December 4, 1997
Published electronically: September 17, 1999
Additional Notes: Partially supported by NSF grant DMS-9626624.
Article copyright: © Copyright 1999 American Mathematical Society