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

 

Generalized $ 3$-manifolds whose nonmanifold set has neighborhoods bounded by tori


Author: Matthew G. Brin
Journal: Trans. Amer. Math. Soc. 264 (1981), 539-555
MSC: Primary 57P99; Secondary 57N10
MathSciNet review: 603780
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Abstract: We show that all compact, ANR, generalized $ 3$-manifolds whose nonmanifold set is 0-dimensional and has a neighborhood system bounded by tori are cell-like images of compact $ 3$-manifolds if and only if the Poincaré conjecture is true. We also discuss to what extent the assumption of the Poincaré conjecture can be replaced by other hypotheses.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0603780-8
PII: S 0002-9947(1981)0603780-8
Article copyright: © Copyright 1981 American Mathematical Society