Generalized -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 -manifolds whose nonmanifold set is 0-dimensional and has a neighborhood system bounded by tori are cell-like images of compact -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:
https://doi.org/10.1090/S0002-9947-1981-0603780-8

Article copyright:
© Copyright 1981
American Mathematical Society