Mappings from -manifolds onto -manifolds

Author:
Alden Wright

Journal:
Trans. Amer. Math. Soc. **167** (1972), 479-495

MSC:
Primary 57A10

DOI:
https://doi.org/10.1090/S0002-9947-1972-0339186-3

MathSciNet review:
0339186

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Abstract: Let *f* be a compact, boundary preserving mapping from the 3-manifold onto the 3-manifold . Let denote the integers mod a prime *p*, or, if , the integers. (1) If each point inverse of *f* is connected and strongly 1-acyclic over , and if is orientable for , then all but a locally finite collection of point inverses of *f* are cellular. (2) If the image of the singular set of *f* is contained in a compact set each component of which is strongly acyclic over , and if is orientable for , then can be obtained from by cutting out of a compact 3-manifold with 2-sphere boundary, and replacing it by a -homology 3-cell. (3) If the singular set of *f* is contained in a 0-dimensional set, then all but a locally finite collection of point inverses of *f* are cellular.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1972-0339186-3

Keywords:
Monotone mapping,
3-manifold,
acyclic mapping,
decomposition space,
strongly acyclic

Article copyright:
© Copyright 1972
American Mathematical Society