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)

 
 

 

General position theorems for generalized manifolds


Author: J. L. Bryant
Journal: Proc. Amer. Math. Soc. 98 (1986), 667-670
MSC: Primary 57P05; Secondary 57N75, 57Q65
DOI: https://doi.org/10.1090/S0002-9939-1986-0861772-8
MathSciNet review: 861772
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is an open question as to whether a generalized $ n$-manifold, $ n \geqslant 5$, that satisfies the disjoint disks property is a topological manifold. In this paper it is shown that any such space $ X$ satisfies general position properties for maps of polyhedra into $ X$.


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

  • [1] G. E. Bredon, Sheaf theory, McGraw-Hill, New York, 1967. MR 0221500 (36:4552)
  • [2] J. Bryant, On embeddings of compacta in euclidean space, Proc. Amer. Math. Soc. 23 (1969), 46-51. MR 0244973 (39:6286)
  • [3] J. W. Cannon, Shrinking cell-like decompositions of manifolds. Codimension three, Ann. of Math. (2) 110 (1979), 83-112. MR 541330 (80j:57013)
  • [4] R. J. Daverman and J. Walsh, A ghastly generalized $ n$-manifold, Illinois J. Math. 25 (1981), 555-576. MR 630833 (83h:57026)
  • [5] W. Hurewicz and H. Wallman, Dimension theory, Princeton Univ. Press, Princeton, N. J., 1948. MR 0006493 (3:312b)
  • [6] F. Quinn, Resolutions of homology manifolds and the topological characterization of manifolds, Invent. Math. 72 (1983), 267-284. MR 700771 (85b:57023)
  • [7] -, An obstruction to the resolutions of homology manifolds, preprint.
  • [8] M. A. Stan'ko, The embedding of compacta in euclidean space, Mat. Sb. 83 (125) (1970), 234-255 (=Math. USSR-Sb. 12 (1970), 234-255). MR 0271923 (42:6804)
  • [9] J. Walsh, General position properties of generalized manifolds: a primer, Proc. Idaho State Topology Conf., 1985.
  • [10] R. L. Wilder, Topology of manifolds, Amer. Math. Soc. Colloq. Publ., vol. 32, Amer. Math. Soc., Providence, R.I., 1949. MR 0029491 (10:614c)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57P05, 57N75, 57Q65

Retrieve articles in all journals with MSC: 57P05, 57N75, 57Q65


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0861772-8
Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society