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

Brin, Matthew G.

doi:10.1090/S0002-9947-1981-0603780-8

Generalized $3$-manifolds whose nonmanifold set has neighborhoods bounded by tori
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Trans. Amer. Math. Soc. 264 (1981), 539-555 Request permission

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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A contractible open

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