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

A collaring theorem for codimension one manifolds


Authors: Robert J. Daverman and Fred C. Tinsley
Journal: Proc. Amer. Math. Soc. 120 (1994), 969-972
MSC: Primary 57N45; Secondary 57N35, 57N40, 57N70
MathSciNet review: 1205486
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Abstract: The chief result implies that an $ n$-manifold $ S$ embedded in the interior of an $ (n + 1)$-manifold $ M$ as a closed, separating subset is locally flatly embedded if the embedding is well behaved in a locally peripheral sense and if $ S$ has arbitrarily close neighborhoods $ Q$ such that the fundamental groups of appropriate components of $ Q\backslash S$ admit a uniform finite upper bound on the number of generators.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1205486-8
PII: S 0002-9939(1994)1205486-8
Keywords: Codimension one manifold, locally flat embedding, locally peripherally collared, wild Cantor set, open collar neighborhood
Article copyright: © Copyright 1994 American Mathematical Society