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Resolving acyclic images of three-manifolds

Published online by Cambridge University Press:  24 October 2008

J. L. Bryant  and
R. C. Lacher
J. L. Bryant
Affiliation:
Florida State University, Tallahassee
R. C. Lacher
Affiliation:
Florida State University, Tallahassee
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Our main result is that a locally contractible Z2-acyclic image of a 3-manifold without boundary is the cell-like image of a 3-manifold without boundary (all mappings being proper). Consequently, such images are generalized 3-manifolds (that is, finite-dimensional and Z-homology 3-manifolds). A refinement of the proof allows the omission of the Z2-acyclicity hypothesis over a zero-dimensional set; an application is the result of D. R. McMillan, Jr., to the effect that a generalized 3-manifold with compact zero-dimensional singular set admits a resolution if and only if a deleted neighbourhood of the singular set embeds in a compact, orientable 3-manifold.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 88 , Issue 2 , September 1980 , pp. 311 - 319
Copyright
Copyright © Cambridge Philosophical Society 1980

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