Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The finite dimensionality of integral homology $ 3$-manifolds

Author: John J. Walsh
Journal: Proc. Amer. Math. Soc. 88 (1983), 154-156
MSC: Primary 57N10; Secondary 54F45, 55M10
MathSciNet review: 691298
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This note establishes that an integral homology $ 3$-manifold has covering dimension equal to three.

References [Enhancements On Off] (What's this?)

  • [Bo] A. Borel, Seminar On transformation groups, Ann. of Math. Studies, No. 46, Princeton Univ. Press, Princeton, N. J., 1960. MR 0116341 (22:7129)
  • [Br$ _{1}$] G. E. Bredon, Sheaf theory, McGraw-Hill, New York, 1967. MR 0221500 (36:4552)
  • [Br$ _{2}$] -, Wilder manifolds are locally orientable, Proc. Nat. Acad. Sci. U.S.A. 63 (1969), 1079-1081. MR 0286109 (44:3325)
  • [HW] W. Hurewicz and H. Wallman, Dimension theory, Princeton Univ. Press, Princeton, N. J., 1941. MR 0006493 (3:312b)
  • [KW] G. Kozlowski and J. Walsh, Cell-like mappings on $ 3$-manifolds, Topology (to appear). MR 683754 (85c:57012)
  • [La] R. C. Lacher, Cell-like mappings and their generalizations, Bull Amer. Math. Soc. 83 (1977), 495-552. MR 0645403 (58:31095)
  • [Mc] D. R. McMillan, Acyclicity in three-manifolds, Bull. Amer. Math. Soc. 76 (1970), 942-964. MR 0270380 (42:5269)
  • [Na] J. Nagata, Modern dimension theory, Interscience, New York, 1965.
  • [Wa] J. J. Walsh, Dimension, cohomological dimension, and cell-like mappings, Shape Theory and Geometric Topology (S. Mardešić and J. Segal, eds.), Springer-Verlag, New York, 1981. MR 643526 (83a:57021)
  • [Wi] R. L. Wilder, Monotone mappings on manifolds. II, Michigan Math. J. 5 (1958), 19-23. MR 0097798 (20:4265)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57N10, 54F45, 55M10

Retrieve articles in all journals with MSC: 57N10, 54F45, 55M10

Additional Information

Keywords: Cohomology $ 3$-manifolds, cohomological dimension, covering dimension, acyclic mapping, cell-like mapping
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society