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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A collaring theorem for codimension one manifolds
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by Robert J. Daverman and Fred C. Tinsley
Proc. Amer. Math. Soc. 120 (1994), 969-972
DOI: https://doi.org/10.1090/S0002-9939-1994-1205486-8

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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Bibliographic Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 120 (1994), 969-972
  • MSC: Primary 57N45; Secondary 57N35, 57N40, 57N70
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1205486-8
  • MathSciNet review: 1205486