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

 

Extending monotone decompositions of manifolds


Author: John J. Walsh
Journal: Proc. Amer. Math. Soc. 74 (1979), 197-201
MSC: Primary 57N15; Secondary 54B15
MathSciNet review: 521898
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Abstract: Let $ {M^m}\;(m \geqslant 3)$ be a compact, connected PL manifold and let $ X \subseteq M$ be a proper, closed subset of the interior of M such that for each open, connected subset $ U \subseteq M$ either $ U - (X \cap U)$ is connected or $ X \cap {\text{bd}}(U) \ne \emptyset $. Let P be a connected and simply connected polyhedron with $ \dim P \geqslant 3$. There exists a monotone mapping f from M onto P with each component of X being a point-inverse of f. In the case with M oriented and P the m-sphere, there exists such a monotone mapping of each degree.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0521898-1
PII: S 0002-9939(1979)0521898-1
Article copyright: © Copyright 1979 American Mathematical Society