Extending monotone decompositions of manifolds
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- by John J. Walsh PDF
- Proc. Amer. Math. Soc. 74 (1979), 197-201 Request permission
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.References
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Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 74 (1979), 197-201
- MSC: Primary 57N15; Secondary 54B15
- DOI: https://doi.org/10.1090/S0002-9939-1979-0521898-1
- MathSciNet review: 521898