Generalized $3$-manifolds whose nonmanifold set has neighborhoods bounded by tori
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- by Matthew G. Brin
- Trans. Amer. Math. Soc. 264 (1981), 539-555
- DOI: https://doi.org/10.1090/S0002-9947-1981-0603780-8
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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.References
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Bibliographic Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 264 (1981), 539-555
- MSC: Primary 57P99; Secondary 57N10
- DOI: https://doi.org/10.1090/S0002-9947-1981-0603780-8
- MathSciNet review: 603780