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Resolving acyclic images of three-manifolds

  • J. L. Bryant (a1) and R. C. Lacher (a1)
Abstract

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.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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